General Interstellar Issue

Journal of the British Interplanetary Society

VOLUME 71 NO.10 OCTOBER 2018 General Interstellar Issue

DIRECT MULTIPIXEL IMAGING OF AN EXO-EARTH with a Solar Gravitational Lens Telescope Slava G. Turyshev A TELESCOPE AT THE SOLAR GRAVITATIONAL LENS: Problems and Solutions Geoffrey A. Landis ET PROBES, NODES, AND LANDBASES: a Proposed Galactic Communications Architecture and Implied Search Strategies John Gertz NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS from total energy expenditure on board, annual food production and spacefarming techniques Frédéric Marin, Camille Beluffi, Rhys Taylor & Loïc Grau EFFECTS OF ENHANCED GRAPHENE REFLECTION on the Performance of Sun-launched Interstellar Arks Gregory L. Matloff

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Published by the British Interplanetary Society. Registered Company No: 402498. Registered Charity No: 250556. Printed by Latimer Trend & Company Ltd, Estover Road, Plymouth, PL6 7PY, England. © 2019 British Interplanetary Society. No part of this magazine may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or recording by any information storage or retrieval system without prior permission from the Publishers. contents VOLUME 71 NO.10 OCTOBER 2018

358 Correspondence 361 DIRECT MULTIPIXEL IMAGING OF AN EXO-EARTH with a Solar Gravitational Lens Telescope Slava G. Turyshev

369 A TELESCOPE AT THE SOLAR GRAVITATIONAL LENS: Problems and Solutions Geoffrey A. Landis

375 ET PROBES, NODES, AND LANDBASES: a Proposed Galactic Communications Architecture and Implied Search Strategies John Gertz

382 NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS from total energy expenditure on board, annual food production and spacefarming techniques Frédéric Marin, Camille Beluffi, Rhys aylorT & Loïc Grau

394 EFFECTS OF ENHANCED GRAPHENE REFLECTION on the Performance of Sun-launched Interstellar Arks Gregory L. Matloff

OUR MISSION STATEMENT The British Interplanetary Society promotes the exploration and use of space for the benefit of humanity, connecting people to create, educate and inspire, and advance knowledge in all aspects of astronautics.

JBIS Vol 71 No.10 October 2018 357 CORRESPONDENCE

Correspondence

STEPHEN ASHWORTH and JAMES SCHWARTZ correspond on the subject of Dr Schwartz's recent paper “Worldship Ethics: Obligations to the Crew”, JBIS, 71, pp.53-64, 2018.

To: the Editor of JBIS the generations pass and as political fashions come and go. 19 July 2018 Those questions are therefore likely to be addressed in an Dear Sir, evolutionary setting, in which solutions most conducive to the growth and multiplication of space colonies inevitably James Schwartz’s new paper on worldship ethics makes some out-compete solutions which cater more for specific interesting points [1]. I believe he is perfectly correct to ideological stances, such as one which would prioritise “the conclude that the ethical and political problems he raises will best possible life” (p.56) for the individuals inhabiting those apply also to permanent space settlements within the Solar colonies. In the longer term one can perhaps foresee colony System, and that therefore by the time technology and the conditions converging on a range of solutions in which economy have advanced to the point where worldship travel the needs of the colony as a whole are balanced against the on an interstellar scale is possible, the planners of such voyages needs of the individual. The success of democratic societies will be able to call on extensive relevant practical experience. in the latter half of the 20th century has shown that free and happy citizens are more productive than heavily restricted This, however, raises new questions for ethicists to ponder. and unhappy ones. Yet there will presumably remain broad For, given that the problems characteristic of worldship cultural differences, causing cultures more tolerant of living will begin to be addressed well before interstellar flight crowding and employing stricter levels of social discipline to becomes possible, two new factors come into play. tend to numerically dominate the Solar System in accordance with evolutionary logic, regardless of any accusations of Firstly, unlike the worldship case, there would exist a exploitation of their own citizens which may be flung at them plausible scenario in which a sense of urgency is attached by their more ethically circumspect neighbours. to a space colonisation programme. This would be the case if it is undertaken in pursuit, not of species survival, but of At the same time, the learning curve will surely be eased the more deeply felt cause of national survival. Suppose that by the gradient of difficulty inherent in the Solar System. a great power struggle is underway on Earth similar to the Space colonies may be established first in Earth orbit, later 20th-century Cold War, and that extraterrestrial colonisation in the Main Asteroid Belt, then among the Jupiter Trojans is seen either as a safety-valve release for aggressive energies and satellites, then among the satellite families of the more and a demonstration of superiority (as was the Apollo distant outer giant planets, and finally in the Kuiper Belt. The programme), or as an insurance policy in case of disaster degree of remoteness and hence the level of self-sufficiency (such as global nuclear war), or both. Under such conditions, demanded of the colonies furthest from Earth would thus Schwartz’s statement that worldship travel is only plausibly gradually increase over a millennium or two of growth, until likely to occur in contexts where it is an optional activity only a small step remained for the transition to worldship would no longer be relevant: the same problems of living in a conditions. confined space habitat would have to be tackled in the course of an activity perceived by all its participants as urgent. It is therefore possible to state that the problems described in Schwartz’s paper will be tackled incrementally over many Secondly, even under the most peaceful of international generations, and that different solutions may well be found by relations, the prospect of early space colonies being different groups of actors. established by terrestrial great powers raises the question of how different cultural attitudes will bear upon the ethics One further factor should not be forgotten: the rise of and political organisation developed for those colonies. artificial intelligence. While at present the technologies for American, European, Russian, Asian and Oriental powers this are rapidly improving, they will presumably top out at might give significantly different answers to questions of some future point, though what the balance will then be reproductive, educational, vocational and other freedoms, between the human and machine organisation of society and the answers in any one culture might also vary in time as remains for now unpredictable.

358 Vol 71 No.10 October 2018 JBIS CORRESPONDENCE

Genuinely intelligent machines will certainly demand a To: the Editor of JBIS, say in political and industrial decision-making, both on Earth 26 July 2018 and off it. If the transition is well managed, the machines will end up running the societies of the future better than Dear Sir, humans could have done, maximising people’s opportunities and choices both in space and on planetary surfaces. On In a thoughtful letter, Stephen Ashworth raises some the other hand, in the most pessimistic scenarios the interesting issues along the margins of my paper, “Worldship machines may limit human freedoms or even destroy them Ethics: Obligations to the Crew’ (JBIS 71: 53-64). What altogether. All that can be said for certain is that the model of I have to say in response is not so much a rebuttal of any democratic liberal capitalism which governs the developed of the specific concerns he raises. Instead I would like to world at present will change profoundly before worldship explain why the kinds of concerns Ashworth raises should travel becomes possible, and perhaps even before space not be interpreted as justifying or permitting any abrogation colonisation has begun. of the duties that I have argued we have regarding future space settlers and worldship crew. All quotations are from Schwartz’s expectation that human worldship voyagers will Ashworth’s letter. need to continue to educate themselves in the knowledge and skills for maintaining their ship seems likely to be superseded Ashworth worries that my assumption that worldship by the artificial intelligence revolution. Worldships will travel will not be undertaken with urgency or haste might have a technological heritage going back to interstellar misfire in the case of solar system settlement, for instance if robotic probes as well as to interplanetary passenger ships a national power under duress decided that space settlement operating within the Solar System. The former will require was necessary “as a safety-value release for aggressive energies full autonomy from human decision-making. The resulting and a demonstration of superiority. . . or as an insurance vehicles could be more like living organisms than the possibility in case of disaster. . . ’ I find it doubtful that a state traditional idea of a machine, maintaining themselves with would settle on this means of preservation—after all, if a state the help of inbuilt self-testing and repair systems and with a had the resources and technologies required for establishing crew of specialised robots far better than humans could. self-sufficient space settlements, then it probably could defend its terrestrial interests with relative ease. It could well be that worldship voyages are initiated by the worldships themselves after consulting with a Solar System- Nevertheless, suppose the point here is granted. What wide network of centres of intelligence, most of which may be follows? Not much, I would insist. machine while some are still human. The ships may choose to take human passengers for companionship, or because First, early space settlers and their children are likely organic life still has something to offer in symbiosis with to experience similar hardships to worldship crew and technology that machine life alone cannot. shipborn, and thus, are at a similar risk of being exploited wrongfully. Exploitation is a prima facie wrong, i.e., it is Schwartz’s intent is that ethical issues ought ideally to be ethically impermissible unless it is necessary for realizing a definitively resolved before worldship travel is begun (p.53). sufficiently great overall good. Thus, a state’s mere feeling of It seems that the process of trial and error by which this will being threatened, or its mere desire to show off its capabilities, happen will stretch over a period of many centuries, and do not rate highly here—they are not the kinds of reasons will involve many lifetimes of thought and experience from that would ethically justify exploitation. We correctly censure both human and digital minds. But, given the opportunities states for these kinds of activities already, and there is no open for a civilisation based primarily on artificial structures reason to assess similar cases any differently in space. Just in orbital space rather than planetary surfaces, it will be a because states might perceive settlement as urgent does not critically important process for the long-term future of the mean that settlement is in fact needed urgently. resulting human-machine civilisation. Second, obligations to preserve the existence of states, Yours sincerely, if ethics even admits of such things (after all, one’s moral worth is never a function of one’s citizenship status), are Stephen Ashworth secondary to the obligation to preserve humanity as a whole.

JBIS Vol 71 No.10 October 2018 359 CORRESPONDENCE

Therefore exploitation is even less tolerable in the case of ‘state the creation of oppressive societies. preservation settlement’ than it is in the case of settlement for the purpose of preserving the entire species. Morality This is something we should only do if we have literally no places higher—not lower—demands on unilateral, nationalist other option for our survival (and this being our only option settlements, which would accomplish comparative less as far over the next few centuries seems highly doubtful). On the as humanity is concerned. other hand, if oppressive regimes are not inevitable, then we have an obligation to work as hard as we can to avoid creating Regarding the possibility of disagreement among states them. It helps no one to abrogate our responsibilities simply over reproductive autonomy and other personal liberties, because we cannot predict with great certainty exactly how we should be wary of slipping into relativism. It is true that human societies will adapt to the novel environments of “answers in any one culture… vary’ and that there is variation space. While we should permit these societies some degree of “as the generations pass and as political fashions come and autonomy (after all, perhaps some of these cultures will adapt go’, nevertheless the overall trend has been one of increasing in ways beneficial to all human societies), we ought also to personal liberties, even among societies we do not usually step in if things take a turn for the worst. Just as we ought to associate with liberal principles. I suspect that individuals do here on Earth. who have experienced both oppressive and free cultures usually prefer the latter over the former. We should take When dealing with such long-range issues, one has to make this as evidence that open societies are laudable and worth certain simplifying assumptions in order to say anything striving for. of any substance, lest discussion becomes speculation built on speculation built on speculation, etc. For largely this This brings us to Ashworth’s worry that oppressive systems reason I did not consider the various complications artificial may be adaptive in space settlements (a point argued for intelligences might raise. And as Ashworth points out, we nicely by Kelly Smith in Cultural Evolution and the Colonial may see issues related to space settlement and worldship Imperative’, in Dissent, Revolution and Liberty Beyond Earth, travel very differently if advanced artificial intelligences are edited by Charles Cockell, pp. 169-187, Springer International involved, can provide for the needs of settlers and crew, etc. 2016). While I agree that we cannot predict with much While such intelligences may mitigate many of the biggest confidence the future shape of any settlements we establish, worries about, e.g., education and vocational freedom, there that does not absolve us from any possible wrongdoing still remain concerns about reproductive autonomy. While associated with the conditions of life in these settlements. If an artificial intelligence might free settlers (or a worldship we initiate settlement in full knowledge that the settlement crew) of the need to toil endlessly just to survive, it would not will likely devolve into a totalitarian, oppressive nightmare, provide small populations with adequate opportunities for, we are then responsible for the creation of this totalitarian, e.g., romantic fulfillment. Regardless of the state of artificial oppressive nightmare. intelligence, we have an obligation to provide future settlers and worldship crews with opportunities for living fulfilling It must be remembered that what we are talking about lives, even if many of these individuals are not cisgendered, is creating a society. We have an obligation to refrain from heterosexual, or willing to reproduce on demand. The creating societies we know are likely to manifest oppressive promise of beneficent machine stewards does not diminish forms of social organization. I am not permitted to create our obligation to attempt to make settlers’ lives better than the conditions which led to the rise of fascism in early and our own. Without imputing this perspective to Ashworth, it mid-20th century Germany, walk away, and then pretend is appalling that so many space settlement advocates seem to my hands are clean of the great atrocities committed shortly accept the contrary as the cost of doing business. It is precisely thereafter. Similarly, I don’t get to set up a space society (or this kind of myopia that leads others to complain that space worldship mission), walk away, and then pretend that I am not settlement is not the kind of enterprise we are ready for. responsible for the deplorable conditions I find a generation We cannot consistently care about the fate of humanity and or so later. Though I am not accusing Ashworth of disputing individual humans while at the same time insisting that no this point, I suspect many would be tempted to disagree, at human cost is too great a price to pay for space settlement. It least based on the tone of the rhetoric surrounding space does not help matters if some of these unfortunate humans settlement, which so often appears inured to the significance never experience or know of a better life, and thus, do not of these issues, and sees space settlement as an overriding perceive themselves to be victims of exploitation. value to be pursued at any cost. Yours sincerely, So it is worth driving the point home again: If oppressive regimes are inevitable in space, then we must face up to the Dr James Schwartz fact that if we create space settlements, we will be culpable for Department of Philosophy, Wichita State University

360 Vol 71 No.10 October 2018 JBIS JBIS VOLUME 71 2018 PAGES 361-368

DIRECT MULTIPIXEL IMAGING OF AN EXO-EARTH with a Solar Gravitational Lens Telescope SLAVA G. TURYSHEV1, MICHAEL SHAO1, LEON ALKALAI1, LOUIS FREIDMAN2, NITIN ARORA1, STACY WEINSTEIN-WEISS1, and VIKTOR T. TOTH3 1Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-0899, USA; 2Executive Director Emeritus, The Planetary Society; 3Ottawa, Ontario K1N 9H5, Canada email [email protected]

Nature offers a powerful instrument that has yet to be explored. It is the Solar Gravitational Lens (SGL): the gravitational field of the Sun, which has the ability to bend and focus light similar to a lens. In the foreseeable future, a small telescope (1-2 m) could operate on the focal line of the SGL at distances between 600–800 astronomical units (AU) from the Sun, to provide high-resolution images of a distant exoplanet. This instrument could deliver thousand-by-thousand-pixel images of “Earth 2.0” at distances of up to 100 light years (ly) and with a spatial resolution of ~10 km on its surface--sufficient to discern surface features such as continents. Although theoretically feasible, the engineering aspects of building an astronomical telescope that is designed to operate at such a large distance from Earth have not been addressed before. - The question of getting there and the issues of operating a spacecraft at such enormous distances with the required precision will be addressed. Aspects of concept design and spacecraft requirements for a mission to the distant regions of the outer solar system will be discussed. This step is a necessary precursor to any future robotic missions to another star.

Keywords: Solar gravitational lens, Direct imaging of exoplanets

1 INTRODUCTION

According to Einstein’s general relativity, gravity imparts refrac- tive properties on spacetime, causing a massive object to act as a lens by bending photon trajectories. As a result, gravitation-ally deflected rays of light passing by all sides of the lensing mass converge at a focus, as shown in Fig. 1. Gravitational lensing has been observed over cosmological distances where relatively nearby galaxies or clusters of galaxies, act as gravitational Fig.1 An exo-Earth imaged with a solar gravitational lens. The exo- lenses for background galaxies. This also occurs in The Milky Earth occupies a 1km × 1km area at the image plane. Using a 1m Way Galaxy, where microlensing of stars in the Galactic bulge telescope as a single-pixel detector gives a 1000×1000-pixel image. or in the Magellanic Clouds are caused by intervening (sub-) stellar bodies. In Earth’s Solar System, this effect was originally While all currently envisioned NASA exoplanetary concepts observed by Eddington in 1919 (thus, formally confirming Ein- aim at getting just a single pixel to study an exoplanet, a mission stein’s theo-ry) and is now routinely accounted for in astronom- to the SGL opens up a breathtaking possibility for direct 1000 ical observations as well as deep space navigation [1]. × 1000-pixel imaging and spectroscopy of an Earth-like planet located up to 30 pc from the Earth with a resolution of ~10 km Of the solar system bodies, only the Sun is massive enough on its surface. Such a possibility is truly unique and was never for the focus of its gravitational de-flection to be within the stud-ied before in the context of a realistic mission. Application range of a realistic mission. The focus of the SGL is a semi-in- of this effect, using Earth’s Sun, and developing a mission to use finite line that begins at ~547 AU. The “focal line” (FL) of the this capability to image Earth-like planets is novel and timely, SGL is broadly defined as the area beyond 547 AU from the Sun given the yield of exoplanet candidates from transit detection on the line that connects the center of a distant source and the missions. center of the Sun. By naturally focusing light from the distant source [2, 3], the SGL provides tremendous brightness amplifi- In the pencil-sharp region along the focal line, the amplification (~1011 at λ=1 µm) and extreme angular resolution (~10−9 cation and angular resolution of the SGL stay nearly constant arcsec) in a narrow field of view [4, 5, 6, 7]. The entire image of – well beyond 2,500AU [7]. To appreciate the enormity of the an Earth-sized exoplanet is projected by the lens into a small magnifying power and resolution of such a system, it is noted region with diameter of ~1.5 km in the immediate vicinity of that with a 1 m telescope placed on the FL of the SGL at 750 the focal line. AU from the Sun, the SGL has a light collecting area that is equivalent to a telescope with a diameter of ~80 km and an angular resolution of an optical interferometer with a baseline of This paper was presented at the Tennessee Valley Interstellar 16 Earth radii. Such a telescope would provide high-resolution Workshop 2017 Symposium, Huntsville, USA. images and spectros-copy of a habitable exoplanet.

JBIS Vol 71 No.10 October 2018 361 SLAVA G. TURYSHEV et al

As seen from a telescope at the FL, light from an exoplanet forms an annulus, surrounding the edge of the Sun (Fig. 1). This light, while magnified greatly, is still much dimmer than the Sun. A modest coronagraph (~106 suppression) would be used to block the solar corona, so that the exoplanet's light could be detected at the telescope.

At 550AU, the Sun subtends ~3.5". For λ=1 µm, the diffraction-limited resolution of a 1 m tele-scope is ~0.25". Thus, there is no need to go beyond ~630 AU to distinguish the annulus from the solar disk. The majority of light in this narrow annulus comes from a ~10 km × 10 km region on the exoplanet’s surface. However, there would be additional light outside the annulus from adjacent areas on the exoplanet.

The image of the exo-Earth at 30 parsecs (pc) or about 100 ly, would span ~1 km at the location of the spacecraft on the optical axis of the SGL. The spacecraft would have to scan this 1 km × 1 km area one pixel at a time (or consist of a constellation of several apertures), to develop a multi-pixel image of an exo- Earth with a resolution of 1000 × 1000 pixels (Fig. 2). Effects of the radial/azimuthal plasma density of the solar corona [3,6,7] on the structure of lensing caustic must be taken into account, including analysis of second-order effects and the chromatic Fig.2 An image of the Earth with a resolution of 1000 × 1000 pixels. structure of the caustic. aperture, which is currently under construction in Chile. A tel- The main question for this study is not “how to get to the escope with an 80-km aperture in space is beyond technological focal region?”, rather, “what does it take to operate a spacecraft reach. Although intriguing, a robotic mission to the SGL still at such enormous distances with the needed precision?” Spe- needs a lot of planning, design and technology development. cifically, this study will concern i) how a mission to the focal The following will discuss preliminary considera-tions for such region of the SGL may be used to obtain high-resolution direct a concept. imaging and spectroscopy of an exoplanet by detecting, tracking and studying the Einstein ring (Fig. 1) around the Sun [7] 2.1 The a priori properties of the target and ii) how such information could be used to unambiguously detect and study life on another planet. The location of the SGL telescope is determined by its target. As such, it is a single-target in-strument, so the target must be A mission to the distant regions of the solar system seems well justified. Evaluating what may already be known about the theoretically feasible; however, the engineering aspects of exoplanet (e.g., rotation period, prevalence of clouds) will be building such an astronomical telescope on the large scales important for establishing mission requirements, optimizing involved were not addressed before. To date, no one has per- the reconstruction of a spatially resolved image and motivating formed a design study for such a mission. The on-going NASA precur-sor projects. Innovative Advanced Concepts (NIAC) study [8] will provide a first examination and will document feasibility and expected The occurrence rate of Earth-sized terrestrial planets in the outcomes. habitable zones of Sun-like (spectral type FGK) stars remains a much-debated quantity. Only a handful of such planets have Prior studies have looked at the SGL as an amplifier. The been dis-covered [14]. Current estimates range from 2% [15] SGL was viewed as an addition to one-pixel detectors at the to 22% [16,17]. The SIMBAD database lists 8589 F stars, 5309 focus of a parabolic receiver dish [2, 9, 10, 11, 12, 13]. For the G stars and 1688 K stars within 30 pc. It is likely that, in the amplifier appli-cation, gain of the dish receiver was essential. near future we will detect at least one terrestrial planet in the However, the imaging properties of the SGL, where the image habitable zone of a star within 30 pc. Such a dis-covery may be occupies many pixels in the region near the optical axis, were excepted from HabEx and LOIVOIR missions that could pave never explored, especially in the context of a deep space mis- the way to an SGL mission. sion. It is considered that a mission to the focal region of the SGL could provide this mission with the first direct multi-pixel Imaging Earth 2.0 around a G star that is not transiting is high-resolution images and spectroscopy of a potentially habit- preferred. A mission to the SGL’s focus could follow a “big Ter- able Earth-like exoplanet. restrial Planet Finder” that observes an exo-Earth around a G star and measures its spectra. The selected target must be poten- 2 TOW ARDS A MISSION TO THE SOLAR GRAVITY LENS tially habitable. If the planetary atmos-phere contains oxygen FOCUS and signs of habitability, the next step would be to launch the mission to the SGL to image this planet at 1000 linear pixels. Ever since Galileo invented a telescope, the making of astro- The planet’s orbit would have to be measured using astrometry nomical telescopes has been an evolving discipline. The task or radial velocity measurements, combined with direct imaging. of designing a modern telescope is complex, involving consid- If the planetary orbit is inclined, it will transit, providing a radi- eration of materials, detectors, precision manufacturing, tools us. These measurements would allow the mission to obtain the for optical and thermal analysis, etc. The largest telescope so required information and point the spacecraft accurately. far is the European Extremely Large Telescope with its 39.3 m

362 Vol 71 No.10 October 2018 JBIS DIRECT MULTIPIXEL IMAGING OF AN EXO-EARTH with a Solar Gravitational Lens Telescope

Once a terrestrial habitable zone planet near Earth is detected, significant resources will be de-voted to characterizing the planet and its system. The knowledge gained from this will include i) orbital ephemeris, to at least milliarcsecond accuracy and precision, ii) knowledge of the atmos-phere, including temperature, structure, chemical composition and albedo, which are all inferred from non-spatially resolved spectroscopy, iii) estimates of rotation rate, gained from temporal monitoring of the spectroscopy and iv) some understanding of cloud and surface properties from Doppler imaging [18].

The SGL mission would begin after the discovery of an exo- Earth, indicating at least ~20 years of “cruise” before the spacecraft would reach 550 AU. During those 20 years, the parent star’s location would have been observed with 1 μas precision at least 100 times, so that its position would be known at the 0.1 μas level or to ~450 km at a distance of 30 pc. The orbital period of the planet would be known to within 1%, meaning that the semi-major axis will be known to ~0.7% or ~1 million km. If the planet is in a face-on orbit, the radial distance to ~1 million km will be known; however, the error bar in the tangential direction will be a factor of ~6 larger. The diameter of the Earth is ~13,000 km, so the area in the sky that will be searched is an 80 × 500 μas grid. Once the telescope on the focal line of the SGL Fig.3 Simulated coronagraph performance showing solar light detects the planet, it would scan a much smaller area to define suppression at the level of 2 × 10−7, sufficient for imaging with the the “edges” of the planet. Astrometry of the star when the planet SGL. was dis-covered would have measured its mass; knowing its size provides the planet’s average density. differ-ential motions (e.g., exo-Earth rotation). Within 100 ly, a 1 AU habitable zone will project to ~0.033" (with dependence Exoplanet imaging requires several challenging key tech- on spectral type), so that such a planet may be detectable with nologies, such as the determination of an exoplanet astromet- an ul-tra-high contrast (10−10) using a 3λ / d coronagraph with ric orbit at better than the nanoarcsecond (nas) level as well as a 9-m regular telescope in space. Given the rapid development the motion and stabilization of the spacecraft over millions of of coronagraph capabilities, it can be assumed that direct im- pointing maneuvers with limited power. However, these chal- aging will provide spectrophotometric characterization of the lenges are not impossible and could be addressed with the next exo-Earth. generation of already available technologies. The telescope has to have a coronagraph to block the light 2.2 Heliocentric ranges for the SGL mission from the Sun. At 1 µm, the magnifi-cation of the SGL is ~2 × 1011 (27.5 mag), so an exoplanet, which is a 32.4 mag object, will By using light rays with larger impact parameters b, noise would be-come a ~4.9 mag object. When averaged over a 1 m telescope be limited from the bright solar corona, simplifying corona- (the magnification is ~2 × 109), it would be 9.2 mag, which is graph design. At 550 AU, the Sun subtends ~3.5''. At λ = 0.6 µm, sufficiently bright (even on the solar corona background). An the diffraction-limited size of a 1 m telescope is 1.22 λ/d ~ 0.25''. image obtained with the SGL includes contributions from the A 3λ/d = 0.3" coronagraph is ~1/5 of the solar diameter. Thus, Sun and zodiacal light. A conventional coronagraph would there is no need to go to large distances to compensate for solar block just the light from the Sun; however, the coronagraph co-rona brightness. In fact, it will begin with b = 1.1Rʘ (1 Rʘ ~ needs to transmit light only from the Einstein ring where the 695,700 km is the solar radius), cor-responding to a heliocentric planet light would be. distance of ~660 AU. From that distance, the Sun subtends an angle of 2.9", while the apparent angular diameter of the circle To validate the design assumptions, a preliminary corona- with a radius of b = 1.1Rʘ is 3.2". If the mission stopped at 660 graph design and related simulations were performed. The need AU, it would move in the image plane to build an image of the to suppress the Sun's light by a factor of 10−6 when imaging with exo-planet. However, reaching these distances in ~20 years im- the SGL is significantly less demanding than modern-day ex- plies moving at radial velocities >30 AU / year, which makes oplanet coronagraphs that suppress the parent star's light by a stopping impractical. Thus, proceeding outward along the focal factor of 10−10 to detect an exo-Earth. However, the design is line while continuing the imaging campaign. An impact param- not quite trivial. The main difference is that the Sun is an -ex eter of b = 1.25Rʘ corresponds to the distance of 854 AU. From tended object. The coronagraph bears a greater resemblance to that distance, the Sun subtends an angle of 2.24", while the circle the original “coronagraph” used in solar astronomy than to the with a radius of b = 1.25Rʘ subtends 2.81". As a result, the heli- exoplanet coronagraphs being studied for exoplanet imaging. A ocentric region of interest for this mis-sion would be the range traditional solar coronagraph uses sharp edge masks in both the 660–850 AU. focal plane and pupil plane. A more complex mask is used to achieve better rejection than is possible with just binary masks. 2.3 Instrument design The performance of the coronagraph is evaluated using The instrument should implement a miniature diffraction-lim- computer codes used by the WFIRST coronagraph team. The ited, high-resolution spectrograph, enabling Doppler imaging initial results suggest that the mission may be conducted 800– techniques, taking full advantage of the SGL amplification and 900 AU from the Sun, using a 2-m telescope to suppress the

JBIS Vol 71 No.10 October 2018 363 SLAVA G. TURYSHEV et al

Sun's light to a level below the solar corona. Fig. 3 shows the intensity at the image plane after the coronagraph of the dif- fracted light from the Sun and the flux from the solar corona after going through the coronagraph. Thus, we have demonstrated the feasibility of designing a coronagraph needed for an imaging mission to the SGL. There are options to reduce the diameter of the telescope down to ~0.5-1.0 m. We continue to investigate these options and their implications for the mission design and operations.

2.4 Imaging with the SGL

The key mission and instrument requirements are guided by the process of image formation in the context of a realistic space mission capable of operating at large heliocentric distances. Recently, a wave optics treatment was developed [7] for the SGL and was able to describe the process of image formation by the lens. It is understood the structure and properties of the caustic formed by the lens and can study its spatial, temporal and spectral characteristics. This new knowledge is guiding this mission design.

Starting at 547 AU, the SGL forms a folded caustic. For λ = Fig.4 Rotational deconvolutions: The top is the input map, which 1 µm, the magnification on the SGL optical axis is 1 × 1011 with is the albedo map of the Earth used to generate light curves. The a resolution of ~1 nas. Because of the high magnification and bottom is the albedo map calculated by “inverting” the light curves tre-mendous resolving power of the SGL, the entire image of back to a 2D image. an exo-Earth occupies an area of ~1 km × 1 km in the image plane around the optical axis. Initial acquisition of an orbiting one to use a 1-exo-day light curve and perform longitudinal and rotating exoplanet may be done (as it moves across the field deconvolution. of view) using the recently developed technique of synthetic tracking [19, 20], capable of finding fast-moving, dim targets. To investigate this approach we used the images of Earth that were taken with the NASA EPIC spacecraft at the L1 La- Imaging with the SGL is done on a pixel-by-pixel basis. A grange point as raw data. For now, we ignored the fact that raster scan would have to be conduct-ed, moving the spacecraft clouds move and come and go. The input data is used to pro- in the image plane. Each pointing corresponds to the forma- duce an albedo map parameterized by longitudes and latitudes. tion of an Einstein ring from light from adjacent surface areas The half of the planet that is visible at any given time is integrat- on the planet. To build a 1000 × 1000-pixel image, a sample ed to produce a light curve that represents the variation of the of the image pixel-by-pixel will be needed, while moving in total flux, as seen by the SGL. the image plane with steps of 2 km/1000 = 2 m. This can be achieved by relying on a combination of inertial navigation and This light curve can be inverted with a straightforward a constellation of three laser beacon spacecraft placed in 1 AU pseudo-inverse to produce a longitudinal map of the planet. If solar orbit, whose orbital plane is coplanar to the image plane. it is assumed that the planet’s spin axis is not exactly aligned Other celestial navigation techniques have also been suggested with its orbital axis, then over the course of a year the illumi- and need study. nation over latitude also changes. Fig. 4 shows the input albedo map and the output of the 2D rotational deconvolution. Contamination from the parent star is a major problem for all modern planet-hunting concepts. Because of the high an- This type of deconvolution requires a very high photometric gular resolution of the SGL, the parent star will be completely signal-to-noise ratio (SNR). The SNR loss in doing this type of resolved from the planet. Its light will be amplified thousands deconvolution is roughly proportional to the number of pixels. of kilometers from the optical axis that cor-responds to the di- Also, this produces not an image of the planet's surface but an rection to the planet; therefore, making the parent star contam- albedo map. If 100 pixels in lati-tude and 300 in longitude are ination issue neg-ligible in this scenario. had, the 30,000-pixel albedo map will have roughly 30,000 hits on the photometric SNR. Fortunately, the huge effective col- To verify the approach, rotational image reconstruction lecting area of the SGL has this SNR. Although, a significant- simulations were performed. There is more than one approach ly smaller telescope, such as a 1 km filled aperture telescope, to creating a multipixel image of the exo-Earth. In this phase of would not be enough. the study, a technique often called rotational tomography was examined. The basic idea is that with the highly aberrated im- Much more work is needed in this area; however, it has been age of the exo-Earth at the SGL focus light is detected from the shown that some of the biggest po-tential problems are not whole planet. If light can be blocked from a part of the planet, showstoppers. Given the enormous amplification of the SGL, say a 50×50 km region, it will result in a very slight dimming of perform-ing spectroscopic research of the exoplanet, even the total flux. The difference between these two numbers is the spectropolarimetry, will be considered. It will not just be an flux from the 50 × 50 km region that was blocked. Unfortunate- image, rather, a spectrally resolved image over a broad range ly, light cannot be blocked from just one patch of the planet. of wavelengths, providing a powerful diagnostic for the atmos- However, since the planet rotates, different parts of the planet phere, surface material characterization and biolog-ical pro- will rotate into view over one revolution. This approach allows cesses on an exo-Earth.

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2.5 Concept design V Escape leg

By 2017, Voyager 1 has traveled to a distance of ~141 AU from the Sun in 40 years since its launch in 1977. It is currently travelling at ~17.26 km/s (or 3.64 AU / year) relative to the Sun. It KBO Powered flybyΔ V recently entered the Interstellar Medium (ISM) as humanity’s first (functioning) interstellar spacecraft. To reach the SGL focal region, the spacecraft needs to travel a distance greater than Jupiter 550 AU. A spacecraft traveling at the speed of Voyager 1 would take >150 years to reach this region. Flybys of Venus, Earth, Given the long travel times, a new kind of mission concept DSMs is needed to make an SGL mission possible. The main enabling Mars aspect of such a mission would be the need to travel fast and survive longer. While current technology lacks transit to another star anytime soon, this mission is com-pelled to target the SGL as an explicit destination for robotic exploration and science investiga-tions as a first step in a long road ahead to- Earth wards a potential Earth-like exoplanet. launch

One of the key challenges for this mission is the mission design and techniques needed enable an SGL probe. There have been many articles investigating the merits of different ways Fig.5 Notional type 1 trajectory. for propel-ling robotic spacecraft to large heliocentric distances outside the solar system. The possibilities include laser elec- its center. Characteristics of the two class of trajectories are tric propulsion, nuclear fission, nuclear fusion, solar sail, laser discussed below: sail, electric sail, microwave sail, magnetic sail, antimatter, and others. Although the merits of maturing these ef-forts over the Type 1: Trajectories with a powered Jupiter flyby. Fig. 5 shows coming years and decades are acknowledged, most of them a notional type 1 trajectory. The trajectory can be broken are not readily applica-ble to a near-term mission launching down into three phases: in mid-2020s. A summary of mission designs was recently presented [21]. 1. Energy buildup phase: In this phase, the spacecraft increases its orbital energy and achieves required phasing As a potential design, a 200×200 m sail might achieve a solar (for targeting a direction opposite to the sun-exoplanet system exit velocity of 25 AU/year with a notional mass state- line). The energy build phase may involve a combina- ment for this example of 30 kg for the spacecraft bus; 13 kg tion of multiple inner solar system gravity assists and for a radioisotope power system providing 100 watts of electric deep space maneuvers (for targeting, leveraging or plane power and possibly a small maneuver-ing capability; and a 1.6 change). This technique has been successfully used on kg sail with a density of ~0.04 g / m2 (equivalent to 0.25-mi- many missions, including Cassini, Jupiter and Juno. cron polyi-mide or a possible sail from carbon nanotubes). It remains to be determined if the radioisotope system can be 2. Powered flyby phase: In this phase, the spacecraft ap- smaller or potentially contribute to the exit velocity with a pro- proaches Jupiter on a hyperbolic trajec-tory (relative to pulsive boost. the planet), performs a Δv at or near perijove, and escapes the Jupiter plane-tary system at significantly higher rela- The KISS 2014 study [22] considered pure chemical Ob- tive velocity. In the frame centered at the Sun, this re-sults erth maneuvers near the Sun using Solar Probe Plus derived in a powered gravity assist at Jupiter, resulting in a large thermal shielding technology at ranges as small as 3Rʘ. Al- increase in spacecraft velocity with respect to the Sun. ternatively, it was found that solar sails could allow for high The Jupiter flyby is used for targeting a particular escape escape velocities with perihelia of 20Rʘ (0.1 AU) but would direction for imaging a selected exoplanet at the focus of require sail area-to-mass ratios larger than those achieved cur- the SGL rently [23]. While, chemical propulsion is limited to an escape velocity of 15–16 AU / year, solar sail trajectories may reach 3. Escape phase: In this phase, the spacecraft escapes the velocities ~25 to 30 AU / year. To go faster would require very solar system, performing scientific observations as it ven- advanced technologies like a large nuclear reactor or space- tures deep into the local ISM towards the focal area of the based high-power laser propulsion. SGL. Further increases in speed using radioisotope-powered electric propulsion may also be useful. Chemical propulsion with two classes of mission trajectories are considered: Type 1 trajectories, which rely on a pow- Type 2: Trajectories with a perihelion maneuver. Fig. 6 shows a ered Jupiter flyby to get the required change in velocity; Type 2 notional type 2 trajectory. The trajectory can be broken down trajectories, which rely on an impulsive maneuver very close to into four phases: the Sun. Maneuvers at the perihelion (closest point to the Sun) and at the perijove (closest point during Jupiter flyby) take 1. Energy buildup phase: This phase is similar to a type 1 advantage of the well-known Oberth effect [24], which states trajectory, where the spacecraft in-creases its energy and that the efficiency of a propulsive maneuver is proportional to achieves required phasing (for targeting a “hair-pin” Jupi- the speed of the spacecraft. This effect is directly proportional ter flyby). The energy buildup phase may involve a com- to the mass of the gravitational body and the distance from bination of multiple inner solar system gravity assists and

JBIS Vol 71 No.10 October 2018 365 SLAVA G. TURYSHEV et al

deep space maneuvers (for targeting, leveraging, or plane V Escape leg change). In the past, this approach was used for Ulysses Sun-dive leg mission and is planned for Solar Probe Plus.

2. Sun-dive phase: In this phase, the spacecraft performs a dramatic Jupiter “hairpin” gravity assist, putting it on a Sun-dive trajectory. For a given perihelion distance from

the Sun, the required relative velocity at Jupiter can be an- Earth alytically calculated by assuming post-flyby ap-helion at launch Perilhelion Jupiter. As an example, for a limiting perihelion distance of 2.8 solar radii requires a relative velocity at Jupiter of

~12 km/sec. Jupiter 3. Perihelion maneuver phase: As the spacecraft approaches the perihelion, it performs a Δv (Oberth maneuver) which results in a large change in spacecraft energy and Flybys of Venus, hence its velocity with respect to the Sun. For an optimal Earth, Mars DSMs type 2 trajectory, the Jupiter flyby does the required plane change for targeting the particular escape direction while the Δv at perihelion maximizes spacecraft escape speed. Fig.6 Notional type 2 trajectory.

To help understand the effect of the perihelion maneuver a solar sail, electric sail or electric propulsion may be further, Fig. 7 shows escape velocity contours (in AU / year) for deployed during this phase once the spacecraft reach- parametrically varying values of perihelion distance (x-axis) es to a safe distance from the Sun. All of these trade- and Δv executed at perihelion (y-axis). For this plot, the solar offs between various propulsion options will be part approach trajectory is assumed to be parabolic (a very good of the proposed study. approximation for type 2 trajectories). As expected, the solar system escape speed increases substantially as the perihelion To enable a raster scan in the image plane, a pair of connect- distance goes down and as the magnitude of the perihelion ed spacecraft with a boom (or tether) of variable length could maneuver goes up. As an example, a 5 km/s Δv at 4 solar radii be used. Alternatively, one could fly a swarm (or constellation) would result in an escape velocity of 11 AU / year, a little over of small and maneuverable spacecraft with a mother craft on 3 times that of Voyager-1. Going as close as 2 solar radii would the principal optical axis. This approach al-lows probing the result in an escape speed of 14 AU / year. Regarding such close spatial structure of the caustic as a function of time and has the flybys of the Sun, it should be noted that while the planned potential to al-low sampling, modeling and removal of imaging Solar Probe Plus mission is currently designed for an 8.5 solar systematic errors due to possible radial, azi-muthal and tempo- radii perihelion, the earlier design (called the Solar Probe mis- ral departures from the idealized caustic structure. The role of sion) was designed to achieve a final perihelion of 4 solar radii, swarms will be explored, reducing navigation and maneuver i.e., 3 solar radii from the surface, which is difficult and needs requirements for individual spacecraft due to the proper mo- further study. tion of the exoplanet and its orbital motion around its parent star. 4. Escape phase: In this phase, the spacecraft escapes the solar system, performing scientific observations, Therefore, even without a solar sail or an electric sail, a type as it ventures deep into the local ISM towards the SGL 2 trajectory leaving the solar system at 11 AU / year would take focal region. To further increase the escape velocity, ~50 years to get to the focus of the SGL, a great improvement over Voyager 1. For this trajectory design some technology advances are needed that would build up-on the current state-of- the-art integrated into the upcoming Solar Probe mission. One of these advances would be the heat shield technology that is needed to survive close proximity to the Sun during a fast-solar flyby. Other obvious areas would include the on-board propulsion capabilities to allow for the motion of the spacecraft in the image plane while at the SGL, significant spacecraft autonomy to enable autonomous navigation and signal tracking, on- board data pro-cessing, high data-rate optical communication and navigation. All these options are currently be-ing investigated.

3 DISCUSSION

The capability of high-resolution imaging of alien worlds is the most exciting benefit of a mission to the focus of the SGL. This is a breakthrough concept that could produce direct multi-pixel images and perform high-resolution spectroscopy of a habitable exoplanet. Such a mission concept could lead to finding seasonal changes, oceans, continents, features of sur- Fig.7 Solar system escape speed contours in AU/yr. face topogra-phy and signatures of life on an exo-Earth, which

366 Vol 71 No.10 October 2018 JBIS DIRECT MULTIPIXEL IMAGING OF AN EXO-EARTH with a Solar Gravitational Lens Telescope would be an amazing and exciting scientific result. Earth-sized planets in the habitable zone to use in developing a design reference mission for the SGL mission. The Kepler spacecraft detected a plethora of exoplanets, putting the possibility that another Earth-like world exists into Natural questions to ask are: What are the next steps? societal perspective. Without the SGL, follow-ups on Kepler When can robotic probes be sent towards Earth-like destina- candi-dates with other current exoplanet characterization tech- tions? Sending robotic missions to explore exoplanets in-situ nologies yields unresolved images at low spectral resolution is a greater chal-lenge (completely unsolved), since even the (typically R < 100). The next steps in the remote exploration of closest potential candidate lies >250,000 AU from Earth; thus, exoplanets include TESS [25] which will extend Kepler’s work achieving resolved images of the planet candidates is critical to by performing an all-sky survey to identify additional exoplanet understand and plan the first steps in a long-term approach. A candidates; JWST [26] which will be used for targeted follow-up mission to the SGL offers the potential to further char-acterize on candi-date planets; and missions in formulation, such as the an Earthlike or potentially habitable exoplanet. It could be used Exo-C [27], Exo-S [28] and LUVOIR [29, 30] concepts. to image an exo-Earth around a star that is 30 pc away from the Sun with a pixel resolution of ~10 km × 10 km on its surface. JWST will likely spend months of observing time to try to This is not feasible with any other known approach. This mis- evaluate atmospheric properties (pos-sibly biomarkers) on sion could be used to de-termine seasonal changes, monitor a limited number of targets (possibly only one). Even with oceans, continents, surface topography, and perhaps signs of JWST, there is a possibility for only a marginal detection [31]; life on an exo-Earth. It is time to explore this potential mission the same may be true with the 30-m ground-based telescopes. in further detail. Without including the large number of Kepler detections, to date ~62% of known ex-oplanets are within 100 pc; besides, Acknowledgments ~80% of Earth-like (i.e., super-Earth) planets are within 100 pc. This offers a great starting point for a candidate list for the SGL The work described here was carried out at the Jet Propulsion concept. Given that detec-tions of small planets are expected to Laboratory, California Institute of Technology, under a con- be ubiquitous [32] in the coming decade, learning about Earth- tract with the National Aeronautics and Space Administration. like exoplanets with atmospheres, free oxygen, water, etc. is an- We also acknowledge the initial consideration of this work by ticipated. It is expected to have a reasonable number of truly the Keck Institute for Space Studies. © 2018. All rights reserved.

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Received 31 July 2018 Approved 19 October 2018

368 Vol 71 No.10 October 2018 JBIS JBIS VOLUME 71 2018 PAGES 369-374

A TELESCOPE AT THE SOLAR GRAVITATIONAL LENS: Problems and Solutions GEOFFREY A. LANDIS NASA John Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135 USA email [email protected]

Gravity bends light; therefore, the gravity of the sun forms a lens. In principle, a spacecraft sent to the distance of the solar gravitational focus could be used as a gravitational lens telescope. Several possible objectives for such a mission have been proposed. The mission would utilize the gravitational lens as a telescope to image and map an extrasolar planet, with the assumption that, before launch, a nearby target planet has been discovered. Moreover, various potential applications-- ranging from astronomy to SETI to communications--have been proposed as well. Previous discussions regarding the use of a gravitational lens as a telescope have been notably lacking in key design details. Thus, it is important to consider the issues with this concept as well as some approaches to mitigate such difficulties in order to make this mission a reality.

Keywords: Gravitational lens, Interstellar precursor

1 INTRODUCTION

According to Einstein’s general theory of relativity, the gravity of a massive body deflects light. Therefore, the gravitational field of the Sun acts as a lens [1]. The minimal distance to the focus of the Sun’s gravitational lens is approximately 550 astronomical units (AU), about 82 billion kilometers, the distance at which the focussed rays skim the edge of the solar limb. The Sun continues to act as a lens beyond this minimum; at longer distances, the focused light passes increasingly far from the solar limb. Although this distance is large, it has been proposed by Eshleman [2] and others [3-6] that a mission to the gravitational focus of the Sun could use this effect as a lens (e.g. to form a long focal-length telescope) that could be much larger than the lens of any physical telescope. Since the lens is effectively extremely large, the aperture for gathering light (or, Fig.1 Artist’s concept of a solar sail making a close pass to the sun. in the more general case, gathering electromagnetic radiation) is large, and the resolution is, in principle, very high. Several possible objectives for such a mission have been proposed. In this paper, I will use as the example case a mis- A mission to the gravitational focus of the Sun, beyond the sion to use the gravitational lens as a telescope to image and edge of the solar system, but far closer than the nearest stars, is map an extrasolar planet, with a baseline assumption that a attractive because it could be a target for an interstellar precur- target planet for observation has been discovered in an orbit sor. For example, it was listed as a precursor goal in the 1998 Jet about a nearby star before the launch of the mission. Propulsion Laboratory (JPL) workshop “Robotic Interstellar Exploration in the Next Century” [7], because it is one of the Although the system is described as a “lens,” and the design few possible targets of any interest that lie beyond Kuiper belt, is in a sense a “telescope,” it is considerably different in na- but still closer than the nearest stars. Reaching such a large dis- ture from a conventional lens, or a conventional telescope. A tance in a reasonable time requires advanced propulsion tech- spacecraft does not simply reach the focal point and then look nologies, similar to the technologies proposed for interstellar back “through” the gravitational lens to see a magnified image, flight. Proposed methods of reaching the focal distance include in the way that looking through a conventional telescope will electric propulsion, laser or solar sails. For example, if a solar yield an image. sail makes a close pass to the Sun (Fig. 1), a high solar-escape velocity can be achieved [8,9]; thus, allowing a mission to the The light from the target planet is magnified, but is also dis- solar gravitational focus sooner rather than later. torted into the form of an annular ring of light surrounding the Sun, known as an “Einstein ring” (Fig. 2 overleaf). As noted in a previous paper [6], the geometrical distortion of this This paper was presented at the Tennessee Valley Interstellar Einstein ring sets limits on the amplification, magnification, Workshop 2017 Symposium, Huntsville, USA. and geometrical focal blur of the telescope.

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W (width of Einstein ring)

(radius of Einstein ring)

Apparent radius of Sun Light from planet being imaged is smeared out across this annulus

Fig.2 The view from a point along the gravitational focus. The light from the planet being imaged is smeared into an annulus surrounding the solar disk, the “Einstein Ring”; it is this ring which is the light input to the gravitational lens telescope. The radius of the Einstein ring equals the apparent radius of the sun at the minimum focus distance and increases as the distance increases beyond this. This image is not to scale (if the image were to scale, the width W of the Einstein ring would be too narrow to distinguish).

2 RESOLUTION, FOCUS AND INTENSITY the variations in density of the corona are large. These variations produce a randomness in the phase of the focused light An important aspect of the gravitational lens telescope is the that is considerably larger than the ~500 nm wavelength of resolution, which, in principle, can be immensely high. The the light. Koechlin et al. [13] calculate the uniform deflection amount by which the focus deviates from an ideal point, the due to the index of refraction of the corona as 10 meters from loss of resolution (or “blur”) in the image, is characterized by the center of the ideal focal point. Although it is not explicit- the point spread function (PSF). The PSF of the optical sys- ly calculated in their paper, the variation in this index causes tem can be found from analysis of the individual effects that an approximately similar amount of focal blur. Other smaller degrade the focus; thus, the total point spread is the convolu- effects, such as the perturbation due to the gravity of other tion of the individual effects. A good approximation is that the bodies in the solar system, are also discussed by Koechlin et errors in focus are independent and thus the width of the PSF al.. The gravity of Jupiter dominates these effects, and adds an squared can be approximated as the sum of the squares of the astigmatism to the focal point. individual components. One expressed advantage of the gravitational lens is the The diffraction-limited resolution of the gravitational lens high gain, which is the amplification of the power received at has been the subject of several previous analyses [10-14]. It is the telescope or the number of photons received from the tar- useful to calculate the diffraction-limited performance, since get per unit time1. From the focal point, the target is seen as diffraction sets a lower limit to the possible resolution of any the Einstein ring surrounds the Sun. The amplification occurs optical system; however, the main result of such analysis is to because the projected solid angle of the Einstein ring is larg- show that, for optical wavelengths, the resolution of the gravita- er than the solid angle subtended by the unmagnified planet. tional lens telescope is limited by factors other than diffraction. Since the surface brightness is unchanged by gravitational deflection, the total flux at the focal point is increased propor- Spherical aberration is inherent in the lens action of a gravitational field and thus cannot be easily corrected. The loss of focus due to spherical aberration of the lens is larger than the diffraction limitations for optical imaging applications. The focal blur due to spherical abberation can be calculated from the geometry of the Einstein ring, resulting in a blur with a characteristic width of exactly half the diameter of the planet imaged, regardless of the distance or the size of the focal plane [6].

Another cause of defocus is due to the variations in the index of refraction of the solar corona. The focused light passes through the plasma of the Sun’s corona. Although the index of refraction of the coronal plasma is close to unity, it is not exactly unity. Fig. 3 shows the corona; as can be seen, PHOTO COURTESY BERND THALLER 1 Gain is conventionally expressed in logarithmic units, while amplification is in linear units;. If desired, gain in magnitudes can be Fig.3 The non-uniformity of solar corona can be seen in this image calculated as 2.5 times the log10 of the amplification factor.. of the sun taken during the August 2017 solar eclipse.

370 Vol 71 No.10 October 2018 JBIS A TELESCOPE AT THE SOLAR GRAVITATIONAL LENS: Problems and Solutions tional to the solid angle viewed. hundreds, possibly thousands, of such small probes out and use each one as a lightbucket to collect light from a single spot For a focal plane exactly at the minimum focal distance, on the focal plane. this amplification, X, is: The planet’s orbital motion would carry it across the size of X = 2(rSun/rplanet)(d/F), (1) this focal plane in a period of about 40 seconds. This means that an image would have to be acquired quickly. This motion, where d is the distance to the object and F is the focal length of however, brings up another possible solution to the problem the telescope. The amplification of the signal from an Earth-di- of the image size: an image could be put together by raster- ameter planet at 10 LY distance is by a factor of 6,400: the grav- ing a detector across the focal plane. Since the planet naturally itational lens multiplies the number of photons received by a moves across the focal plane, a line of detectors could assemble telescope at the focal point by a factor of 6,400. Essentially, the a picture of the planet as the image moves across the detector telescope receives a number of photons from the whole planet line. If the probe carrying the focal plane had sufficient lateral equivalent to that of a telescope of 80 times larger in diameter. motion capability, a single detector could raster scan the entire image of the planet. However, the pointing and occultation re- 3 DIFFICULTIES IN IMPLEMENTATION quirements (discussed below) would make this difficult.

As shown in the previous paper [6], the difficulties in use of the Image brightness is also a problem. The amplification of -im solar gravitational lens as a telescope can be summarized: age brightness can be calculated from the geometry. The amount of light collected from a potential planet at 10 LY is increased by 1. The size of the image on the focal plane and speed of tran- the gravitational lens by a factor of 6,400 times. This implies that sit of the image a telescope 1 m in diameter collects the same amount of light as 2. The requirement for an occulter and the noise due to the a telescope 80 m in diameter without the lens. corona of the Sun 3. The inherent focal blur However, the speed at which the planet moves past the focal plane reduces the total amount of photons collected. As- 4. POSSIBLE APPROACHES TO USING THE tronomical telescopes focus on one spot for long periods of GRAVITATIONAL LENS time. Therefore, since the planet will move past focal plane in 40 seconds, the imager at the focal plane cannot perform It is clear that using the gravitational lens of the Sun as a tel- such long integrations, which are needed for reducing signal escope is considerably more difficult than simply placing a to noise ratio. spacecraft at the focal line and looking at the image. The mission is required to receive and interpret the light from the 4.2 Occulter planet distorted into the “Einstein ring” (Fig. 3), while rejecting or subtracting other sources of light. The minimal gravitational focus distance is defined by the distance from the Sun at which the Einstein ring apparent- 4.1 Image Size ly touches the disk of the Sun; at distances farther along the line of focus, the apparent size of the disk will be smaller and As Genta and Vulpetti pointed out [15], the size of the image thus the ring will be more visibly separated from the Sun. Us- produced by the gravitational lens is a problem. The size of the ing the lens as a telescope involves collecting light from the image of the planet on the focal plane is proportional to the ring. This requires pointing the imaging plane of the telescope focal length of the telescope. From geometrical optics, the size nearly directly at the Sun. The light from the Sun will greatly of the object being viewed on the image plane, Xi, is related to overwhelm any signal from a planet. The first caution stressed the size of the object being imaged, Xo, as: to anyone upon receiving a telescope warns them not to point it directly at the Sun; however, that is exactly what must be Xi = Xo (F/d), (2) done in this case. To image the planet, the direct light of the Sun must be blocked using either a coronagraph [16] or an where the focal length of the gravitational lens telescope, F, occulter. A conventional coronagraph is difficult because of must be greater than the minimal focal distance of 82 billion the high magnification of the image; however, design studies kilometers. For a mission to an imaging point at 0.01 light of a coronagraph for this purpose have yet to be done, and years (630 AU, slightly farther than the minimal focal distance approaches to solving the problem are likely. of 550 AU) targeting a planet at a distance of 10 LY, approximately the distance of Epsilon Eridani, the image of an Earth- An alternate solution would be to use an occulting disk: a sized planet at the focal plane will be 12.5 km in diameter. second spacecraft in the shape of a circle that is placed between the imaging spacecraft and the Sun, functioning as an The gravitational lens telescope is quite different, then, artificial eclipse. Use of such occulting spacecraft have been from a classic telescope; with the image larger than the tele- proposed for imaging extrasolar planets (“starshades”) and the scope itself, the imaging plane images only a single pixel of the main engineering difficulties, such as suppressing the diffrac- image. A typical telescope would image the planet by placing tion around the edge of the disk, have been addressed [17, 18]. an imaging array at the focal plane; if this approach were used, However, the fact that a second occulting spacecraft is needed the imager would require a focal plane consisting of an array will considerably complicate the design of any spacecraft that of elements spanning a distance of 12.5 km by 12.5 km. This does not sit in a specific place. The approach of sending hun- may not be an insurmountable difficulty, however. The “Break- dreds of individual sails, each one to collect the light at a single through Starshot” project, for example, envisions high-veloci- spot on the focal plane, would require an equal number of oc- ty laser-pushed sails, each of which is about 4 meters in diam- culting spacecraft, each one positioned extremely precisely to eter, and extremely low in cost. It would be possible to send exactly block the Sun.

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An occulter does not completely solve the problem, since it Disk of planet imaged will block the light from the disk of the Sun and not the corona. As visible in Fig. 3, the corona extends well outward from the Sun, and has a considerable background brightness. Also, the noise due to the corona implies limits to the effective use- fulness of the lens. Discussions of gravity lens telescopes tend Central 50% to emphasize the high magnification of the telescope; however, it is important to point out that the signal source is still only 3.5 arc seconds across, so even with the high magnification, Central 10% the absolute intensity of the signal is still small. The coronal light, combined with the required short exposures due to the planet’s orbital motion, will make achieving a high signal to noise ratio problematic.

A possible approach to this problem is to move farther along the focal line, whereby the Einstein ring being imaged is farther from the Sun and thus moved to a position farther Rp (radius of planet) from the brightest part of the inner corona. However, to move to a position where the Einstein ring is, for instance, one solar radius from the Sun, makes the mission much more difficult. Fig.4 Focal blur of the image of a candidate planet. This would require a mission four times as far--about 2200 AU instead of the 550 AU originally calculated for the mission. width of the Einstein ring could image the planet directly, In addition to the light from the Sun, light from the prima- without need for the gravitational lens. ry star of the target planet may also add noise to the signal. Except for the transient cases of occasional exact alignment, With a sophisticated deconvolution technique, it may be the star’s light will not be magnified by the gravitational lens, possible to sharpen the image by scanning across the planet. but the star is enough brighter than the planet that the prima- By using the portion of the image closer to the axis, it would ry light will also need to be blocked. contribute proportionally more to the total image, possibly taking the rotation of the planet into account. However, it is 4.3 Focal Blur clear that the magnification of the planetary image at kilometer scales cannot be achieved. From geometrical optics, discussed in the previous paper [6], it is possible to calculate the geometrical component of the 4.4. Imaging the Einstein Ring focal blur. Technically, the focal blur is caused by the large, negative spherical aberration of the lens--the part of the lens The surface of the planet is smeared out into the Einstein ring. focusing at a given distance is only a narrow annulus. Regions More precisely, the gravitational lens maps the surface of the of the lens farther from the axis (rays travelling away from the planet onto the Einstein ring. It is interesting to look in more Sun) focus to a distance farther away, while regions closer to detail at this mapping; the point exactly on the optical axis is the axis (rays closer to the Sun) focus to a closer distance. Al- mapped to the central circle of the Einstein ring. Every other though the central spot on the target planet is intensified rel- point on the planet is mapped onto the Einstein ring twice, ative to the rest of the planet, most of the light received at the in mirror images, once inside and once outside of the central focal plane is not from the central spot; it is the progressively circle. This is shown in schematic in Fig. 5. farther out of focus from the various parts of the planet being imaged. Focal blur is inherent in the gravitational lens; it does The width of the Einstein ring, of course, is far too narrow not change with position or magnification. to be resolved by a telescope at the focal plane. However, it only takes a relatively modest telescope to resolve the circum- Fig. 4 depicts a candidate planet being imaged, with the ference of the ring, 10 arc seconds at the closest focal distance. amount of light coming from each portion of the image noted. Each point on the circumference of the Einstein ring averages The amount of light coming from an area inside a radius r is the light received from a stripe across the planet’s disk (with directly proportional to r. 50% of the light reaching the focal each stripe repeated twice at positions 180° around the disk). point comes from the area inside the 50% diameter; thus, 50% It is possible that the planet’s area can be reconstructed by comes from outside the 50% diameter (regardless of the fact these stripes. that the inner 50% of the diameter comes to only 25% of the area). Likewise, 10% of the light reaching the detector comes At any given position of the telescope at the focus of the from the central 10% of the diameter, accounting for 1% of the gravitational lens, there is a mirror ambiguity in reconstruct- planet’s area. Although, the central regions are weighed more ing the image of the planet from the intensity of points along heavily in the amplification, the outer parts have a proportion- the circumference of the Einstein ring, since this intensity ally larger area. Thus, if the focal blur is defined as the circle in- consists of equal contributions from opposite sides of the strip side, which half the light originates, the focal blur is exactly half across the planet. This ambiguity may be resolved by views the diameter of the planet, regardless of the size of the planet. from more than one location of the telescope at the gravita- Correcting the focal blur is possible if the telescope, at the tional focus or by allowing the moving image of the planet to focus, was able to resolve the width of the Einstein ring. How- pass across the telescope, thus changing the center spot. ever, because of the radial demagnification of the gravitational lens, the width of the Einstein ring is half the angular width More usefully, in general, the image of the planet will not of the planet; therefore, any telescope that could resolve the be fully illuminated. For a planet in half phase, the mirror am-

372 Vol 71 No.10 October 2018 JBIS A TELESCOPE AT THE SOLAR GRAVITATIONAL LENS: Problems and Solutions

This strip of the Einstein ring… …images this stripe on the planet

Fig.5 Mapping of the planet to the Einstein ring. Each section of the Einstein ring maps to a stripe across the image of the planet. (Not to scale). biguity is irrelevant, since the dark side of the planet does not stein ring is imaged separately. The signals from the different contribute. A planet in crescent phase would reduce the ambi- parts of the ring are then deconvoluted using an algorithm to guity even further. As the planet rotates, different areas of the reconstruct the planet. surface will rotate in and out of view. Multiple images of the planet may be required to distinguish the changes due to plan- 5 CONCLUSIONS etary rotation from the changing cloud patterns on the planet. Due to the bending of light by gravity, the gravity of Sun Since the Einstein ring being imaged has a radius of about forms a lens, which, in principle, can be used as a gravitational 1.75 arc seconds at the minimum focal distance, the resolu- lens telescope. A mission to the gravitational focus could use tion of the planet will depend on the resolution of the tele- the gravitational lens telescope to image an extrasolar plan- scope at the focal plane. The 2.4 m mirror of the Hubble Space et around a nearby star. The difficulties include the required Telescope, for example, has a diffraction-limited resolution of pointing, the size of the image on the focal plane, the speed of 0.05 arc seconds and an actual resolution of 0.1 arc seconds. motion of the image across the focal plane, the requirement Thus, if the Hubble telescope were used as the imager at the for an occulter to remove the brightness of the Sun itself from focal point, about 110 segments around the arc of the Einstein the image, the interference of the brightness of the primary ring could be resolved (since the stripe of the planet imaged star of the target planet, the signal to noise ratio produced by repeats 180° around the ring, this corresponds to 55 distinct the brightness of the solar corona and the fact that the inher- stripes). Thus, the resolution at the planet would, if the image ent aberration of the lens means that the focal blur of the im- could be deconvoluted, be on the order of about 1/110th of the age will be equal to half the diameter of the planet imaged. circumference (assuming that the planet is imaged in half or crescent phase, so only half the disk is imaged). In principle, as The difficulties are not necessarily fatal flaws; clever- ap the planet rotates, with this analysis technique an imager at the proaches may make it possible to use this large telescope and minimal focal distance might map the planet to a resolution of avoid some or all of the problems. In particular, an approach about 350 km. is pointed out whereby examining slices of the Einstein Ring, the surface of the planet might be reconstructed. However, it is This produces a completely different concept for imaging clear that a mission using the gravitational lens as a high mag- the planet: rather than making an image with multiple detec- nification telescope would be much more complicated than tors at the focal plane, as in a conventional telescope, a single simply sending a spacecraft equipped with an imaging plane telescope is used, but the light from different parts of the Ein- to the minimal focal distance of 550 AU from the Sun.

REFERENCES

1. A. Einstein, “Lens-Like Action of a Star by the Deviation of Light in the Discussion”, Mon. Not. R. Astron. Soc., 341, pp. 577–582, 2003. Gravitational Field”, Science, 84, p. 506, 1936. 6. G.A. Landis, “Mission to the Gravitational Focus of the Sun: A Critical 2. V.R. Eshleman, "Gravitational Lens of the Sun: Its Potential for Analysis”, AIAA-2017-1679, AIAA Science and Technology Forum and Observations and Communications Over Interstellar Distances", Exposition 2017, Grapevine, 2017. Science, 205, pp. 1133-1135, 1979. 7. “Robotic Interstellar Exploration in the Next Century: Workshop 3. C. Maccone, “Mission to Exploit the Gravitational Lens of the Sun Summary”, Jet Propulsion Laboratory, Pasadena, 1998. for Astrophysics and SETI”, 44th Congress of the International 8. G.L. Matloff, "Early Interstellar Precursor Solar Sail Probes",JBIS , 44, Astronautical Federation, Graz, Austria, 1993. pp. 367-70, (1991). 4. C. Maccone, The Sun as a Gravitational Lens: Proposed Missions, IPI 9. G. Vulpetti, “Sailcraft-based Mission to the Solar Gravitational Lens”, Press, 1997. AIP Conference Proceedings 504, Space Technology and Applications 5. S.G. Turyshev and B.G. Andersson, “The 550-AU Mission: A Critical International Forum 2000, Albuquerque, pp. 968-973, 2001.

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10. T. Elster, “Diffraction of Electromagnetic Waves in Schwarzschild’s 14. S.G. Turyshev and V.T. Toth, “Diffraction of Electromagnetic Waves in Space-time”, Astrophysics and Space Sci., 71, pp. 171-194, 1980. the Gravitational Field of the Sun”, Phys. Rev. D, 96, 024008, 2017. 11. R.J. Bontz and M.P. Haugan, "A Diffraction Limit on the Gravitational 15. G. Genta and G. Vulpetti, "Some Considerations on Sun Gravitational Lens Effect", Astrophysics and Space Sci., 78, pp. 199-200, 1981. Lens Missions", JBIS, 55, pp. 131-36, 2002. 12. T. T. Nakamura and S. Deguchi, “Wave Optics in Gravitational Lensing,” 16. M.J. Kuchner and W.A. Traub, “A Coronagraph with a Band-limited Progress of Theoretical Physics Supplement, 133, pp. 137-153, 1999. Mask for Finding Terrestrial Planets”, ApJ, 570, p. 900, 2002. 13. L. Koechlin, D. Serre, G.K. Skinner, P. Von Ballmoos and T. Crouzil, 17. R.J. Vanderbei, E. Cady and N.J. Kasdin, “Optimal Occulter Design for “Multiwavelength Focusing with the Sun as Gravitational Lens”, Exp. Finding Extrasolar Planets”, ApJ, 665, pp. 794-798, 2007. Astron., 20, pp. 307–315, 2005. 18. W. Cash, “Analytic Modeling of Starshades”, ApJ, 738, p. 76, 2011.

Received 31 July 2018 Approved 19 October 2018

374 Vol 71 No.10 October 2018 JBIS JBIS VOLUME 71 2018 PAGES 375-381

ET PROBES, NODES, AND LANDBASES: a Proposed Galactic Communications Architecture and Implied Search Strategies

JOHN GERTZ Foundation for Investing in Research on SETI Science and Technology (FIRSST). Correspondence: Zorro Productions, 125 University Avenue, Suite 101, Berkeley, CA, 94710. Tel: (510) 548-8700 USA email [email protected]

Land-based beacons, information laden probes sent into our solar system, and more distal communication nodes have each been proposed as the most likely means by which we might be contacted by ET. Each method, considered in isolation from ET’s point of view, has limitations and flaws. An overarching galactic communication architecture that tethers together probes, nodes, and land bases is proposed as a better overall solution. From this more efficient construct flows several conclusions: (a) Earth has been thoroughly surveilled, (b) Earth will be contacted in due course, (c) seti beyond half the distance that Earth’s EM has reached (~35-50 LY) is futile, and (d) the very quiescence of the galaxy paradoxically implies that that Drake’s N = many, and that there is a system of galactic governance. Search strategies are proposed to detect the described probe-node-land based communications network.

Keywords: SETI, ET, Nodes, Probes, Lurkers, Fermi’s Paradox

1 INTRODUCTION nicate in some fundamental way. If one speaks in words, as we understand the term, but the other speaks in colors or bee-like ET might be motivated to communicate with Earth in order to waggle dances, the chance of communicating anything more trade information; or ET might wish to disseminate its values, than “we also exist” is small. If ET is vastly more advanced than beliefs, history, art, religion, and so forth, without regard to re- us (a statistical likelihood, since what are the chances that, in ceiving anything in return; or ET’s main purpose might be to the billions of years in which it might have evolved, they also enlist us into a galactic alliance for the wellbeing of all member are in their first century of electronic technology?), then com- civilizations, i.e., law and order may be ET’s prime imperative. munication may be pointless from ET’s point of view. After all, would we feel the need to discuss literature or mathematics Any or all of these goals might be achieved by direct civiliza- with Australopithecus aferensis? tion-to-civilization communication by means of, for example, laser or radio transmissions. Such civilization-to-civilization There is then the problem of the immense danger facing transmissions are sometimes referred to in the literature as any civilization that decided to signal. Beacons are deadly dan- “beacons,” and the search for them (including the search for gerous (do not try this at home). A beacon would give away signals not intended for us, but acquired by us through eaves- ET’s exact location, as would Earth with its reply. Just in the dropping) constitutes the classic and still most common seti signal strength and type, ET will give away much about its research protocol [1, 2]. However, there are many reasons why level of advancement. An embedded message may have very ET might not choose to communicate with beacons. For exam- unintended consequences. For example, the Voyager plaque ple, a civilization must simultaneously deploy many beacons, showing a naked man and woman with the man’s hand raised each directed at a likely target star for eons in order to happen in a sign of peace, might convey that our species has no thorns, upon a receiver that might eventually turn to it. Alternatively, horns, shells or other obvious means of defense, and is there- if ET’s transmitter sequentially targets thousands of stars, while fore weak. Who knows but that a raised hand might have a Earth’s receiver sequentially targets thousands of stars then the similar meaning to ET as what a raised middle finger means chances of them aligning in time are nearly impossible unless in American culture. As good looking as we think we are, ET they are targeting the exact same set of stars (why would they?), might find our visage repulsive, vaguely resembling some ver- and even then the chances of alignment are tiny during any min on its planet. Our plaque sent in peace might actually in- one duty cycle. Additionally, there is the immense problem of vite a pre-emptive attack. receiving a return message. ET must either have an all-sky-all- the-time system or have a receiver dedicated to each and every If the beacon is very bright and very complicated, the re- star on its target list, since it will have no a priori idea which ceiving civilization may fear to respond. If ET communicates star might harbor a listening civilization or in which duty cycle with a flux that is a million times more powerful than our best its signal might be received, or how long the receiving civili- transmitter, Arecibo, dare we respond with Arecibo and there- zation might take to decode the message and decide upon its by let ET know just how feeble we are? If we try to bluff ET into response. However, this is only the start of the sending civiliza- believing that we are a mighty species with awesome powers, tion’s problems. The two civilizations must be able to commu- but that we merely choose not to use our own gargantuan ra-

JBIS Vol 71 No.10 October 2018 375 JOHN GERTZ dio transmitter, do we perhaps invite the pre-emptive annihila- terms of hierarchical computing power, one might, by analogy tion we are trying to avert because they would fear us [3]? The only, imagine a probe as having the power of a laptop; a node as dangers may be so profound that ET civilizations that employ having the power of a supercomputer; while a land base might beacons (i.e., engage in METI) may not achieve the longevity host a server farm and multiple quantum supercomputers. For necessary for likely detection by Earth because they are soon conceptual purposes only, probes might orbit every star, and exterminated by others. therefore be spaced at ~3-6 light years (LY) in our region of the galaxy; nodes might be positioned at 25 LY intervals, and These and many other problems can be solved if ET simply land-based member civilizations might be located at an aver- sends a message to us in a probe [4,5,6,7,8,9], which is defined age distance of 250 LY from one another. It also might be that here as ET-derivative objects sent to any solar system for the nodes orbit most or all stars for the purpose of repeating and purposes of surveillance and/or communication with its resi- amplifying signals. Perhaps most of these are sub-nodes in that, dent technological species. Probes offer a variety of advantages while being signal repeaters, they otherwise lack comprehen- over beacons. As AI machines they can hide their planet of or- sive analytical abilities. igin, or reveal it as judgment might warrant. For all but nearby stars, the per bit cost of the information payload (e.g., con- 2 PROBES tained on something like a small thumb drive) is vastly cheaper than the cost to transmit the same information via continuous- 2.1 Probes as Surveillance Systems ly broadcasting beacons [10,11]. It is hard to be more specific than this, since an exact comparison would need to consider Flyby probes. In the first instance, nodes or land bases might such unknown factors as the mass of the probe, its speed, the send simple flyby probes through every stellar system for the gravity of its launch site and minimum escape velocity from its purposes of surveilling them. Breakthrough Starshot (BTS) is solar system versus the width of the informationally compara- designing just such a system to surveil nearby stars within the ble beacon’s beam at the point of reception (determining the current century [15]. One of the greatest challenges facing BTS amount of wasted flux) and the length of time a beacon must is in designing a robust communications system for sending continuously broadcast before being received. information back to Earth. However, assuming that ET’s probe is travelling at a low enough speed, it might dispense with this Probes would be able to surveil at close range, gathering data complexity by simply recording data as it flies through a plane- on their target solar systems even in the absence of communi- tary system on a trajectory that approaches its host star closely cation with a technological species. Probes nullify the limiting and accurately enough to be bent into a new trajectory aimed effect of Drake’s L, the length of time that an intelligent civili- directly at any node of convenience, that not necessarily being zation transmits beacons, since probes might long survive their the node that sent it. The flyby probe would simply upload its progenitor civilizations. However, these and other advantages data as it approaches that next node. That node would in turn of probes are for naught if ET wishes to receive a message in send that data on to adjacent nodes at the speed of light. return. Probes might pile up uselessly, waiting for such time, as ever, as a technological society might evolve in the solar system Speed is of the essence—i.e., slow speed. A major objection of their presence. They could spend those eons doing surveil- to the above is that by not transmitting the information it has lance and research, but without a gargantuan transmitter they gathered at the time of the flyby the probe has greatly length- would not be able to relay their findings home. ened the time of its mission, sacrificing light speed for physical travel time. This, then, would be a good moment to digress to This author [12,13] has argued that the problems inherent in a consideration of the question of time. In order to understand probes can be addressed by a system of nodes, defined as probes the proposed galactic communications architecture, it is im- that are not necessarily located within our solar system but that portant to understand that probes and nodes would likely be are explicitly designed to communicate among themselves, AI machines, for which human time scales are almost mean- as well as with technological civilizations within their area of ingless. Sol is not among the first generation of stars that might service. The fact that beacons are so inherently dangerous that have borne technological life. There is no known reason why no truly intelligent species would dare to deploy them may ac- the first ET civilization in the galaxy might not have arisen tually have given rise to a system of communication beacons more than five billion years ago (bya) [16]. ET’s entire library that are offset from the civilizations associated with them. Early might contain data on hundreds of billions of stars, and have ET civilizations may have sent beacons to orbit nearby stars, catalogued untold millions or billions of life-bearing planets. reasoning that if the respondent launches an attack it will be ET might have made contact with thousands or millions of against a decoy. Likewise, the first civilizations that responded technological societies and maintained the parochial libraries to those beacons would do so from their similarly offset trans- of those civilizations indefinitely, irrespective of whether any mitters. As a result, a proto-nodal communication system may particular civilization persists or has perished. be of the same age as the very first ET-to-ET transmissions. In deep time, the fact that a probe might take some addi- However, as this author has previously described them, tional tens of thousands of years to complete its mission may nodes also have distinct drawbacks. They would have only a be of trivial concern. Initial flybys might have been sent past limited capacity to surveil Earth if the nearest one is located a molten Earth 4 bya and found it to be lifeless, but the same at an interstellar distance. At even close interstellar distances, probe might have found life on Mars. As a consequence, per- Earth’s EM leakage damps down to incoherence from which haps the node sent follow up probes at 100 million year in- not much useful information might be gleaned other than per- tervals, soon discovering that Mars had turned lifeless, while haps that they are of artificial derivation [14]. Earth blossomed with microbial life. It would not have been until about 2.2 – 2.5 bya that it might have detected atmospher- Here it will be argued that the best solution may be a net- ic molecular oxygen and then presumed that multicellular life work of ET probes, nodes, and land-based systems tethered to- might have arisen. On such a 100 million year time scale, the gether into a comprehensive communications architecture. In speed of any one flyby mission would not be a major consid-

376 Vol 71 No.10 October 2018 JBIS ET PROBES, NODES, AND LANDBASES: a Proposed Galactic Communications Architecture and Implied Search Strategies eration. In fact, slow speed would be much preferred, because accomplish a full analysis of our civilization, nor the authority (a) it would cost much less in energy to accelerate a probe to to make contact. It may be passing information back to a node the desired speed; (b) the slower the speed, the less severe the or land based command and control center for a final determi- damage from collisions with interstellar dust or micrometeor- nation. In such an event, contact will be made in due course, ites (though cosmic rays would remain a problem—but one but that contact may be a century or more into our future. that is soluble through shielding and/or self-correcting data redundancy); (c) less energy would be required to decelerate • The local probe(s) or node is signaling us now, but we upon arrival at the target system using solar radiation and solar simply have not yet made the detection, or, we may actually wind (it could use the same solar wind and radiation to reaccel- have made a detection, but thrown it out as a hard to interpret erate out of our solar system); (d) at slower speeds the probe’s transient or as RFI (see below). trajectory can be more easily bent as it approaches the star; and (e) more data might be gathered at slower flyby speeds. • A probe might appropriate all the knowledge it could want from our EM leakage. However, the current hypothesis Orbiting probes. Once Earth had been determined to have may mean that Earth has a crucial role to play in the galactic entered its multicellular life form phase, one or more perma- communications architecture. In exchange for full member- nently orbiting probes might have been sent. If ET has a good ship in the galactic club, Earth might be required to dedicate idea of the average time between multicellularity and the emer- itself to building and launching nodes and probes. In effect, gence of a technological species, it might time its probe launch- Earth might assume responsibility for the maintenance of the es appropriately. Again, slow speed is of the essence to allow for local communication network. This, of course, would also be in the probe to be able to efficiently enter into an orbit without Earth’s own interest. the need to bring immense amounts of fuel along for deceleration. Permanent probes would be outfitted with interstellar 2.3 Where are they? class communication receivers and transmitters. Given that the signal, be it radio or optical, would likely be monochromatic If our solar system contains many probes, in the spirit of Fermi, and of an exactly known frequency to the receiving node, it can it should be asked why we cannot readily see evidence of them. be of relatively modest power. The very simple answer is that probes are probably fairly small, possibly no larger than an automobile, and perhaps as small as Just because we are being surveilled does not mean that a tennis ball or smaller. In our vast solar system, they would re- we live in a zoo. The probes hypothesized here are compatible main unnoticed were their discovery solely reliant upon seren- with, but different from, those hypothesized in the well-known dipity. We might only find them if they are actively signaling to “zoo hypothesis,” in that probes might be here to study us, but Earth, or if we catch them in the act of signaling to a node [18]. they also are hypothesized to have the capacity to communicate with us at some point. We are not necessarily merely a nature 3 NODES preserve. Upon a probe’s detection of our EM leakage, it might require a significant amount of time for it to analyze those sig- 3.1 What’s the rush? nals. Yet much more time would be required if the probe merely reformats and amplifies our leakage, focusing and transmitting As with probes, high speed is counterproductive. If nodes are it onwards to a node or land base for complete analysis and to launched into free orbit around the center of the Milky Way communicate instructions. This process might take centuries (MW), they would seem to be most functional when travelling or millennia. However, the net result is that when we do hear at about the same orbital speed as the star systems they serve. from our local probe(s) or node, it might be in fluent English, If nodes orbit stars (including possibly our own), then, as with or some other terrestrial language. probes, a slower entry speed into our solar system is necessary in order facilitate deceleration, and thereafter maneuver into 2.2 Probes as “Lurkers” an orbit. Moreover, a node that moves too quickly will be flung out of the MW. David Brin has postulated that probes reside in our solar system now, but actively decline to make their presence known 3.2 The Features of Nodes [17]. He calls them “lurkers,” in effect, spies. Brin offers a number of possible reasons for their refusal to make contact, among This author has elsewhere envisioned nodes as having com- which are (a) that they have seen our nightly news and either monalities with cell phone towers, the Internet, an escrow fear or loathe us; (b) they are waiting for us to pass some devel- service that ensures fair information exchange among civiliza- opmental milestone by which we might prove our worthiness; tions, and a lending library [12]. (c) they follow a strict policy of non-interference (i.e., the zoo hypothesis); or (d) they have no need to trade information with 3.3 Nodes as a Dating App us as they can simply steal it from our abundant EM communications streams, with no intention of reciprocating. To the above, this author would now add that nodes may provide the physical backbone for software that may be most akin However, there are other possibilities: to a dating app. There has been the tacit assumption among seti researchers that ET will transmit to us a uniform body of • Probes are studying us in order to understand how best knowledge. However, nodes may no more represent a homog- to make contact. Probes would only have had about a century enous galactic civilization than does the Internet. There may, to observe us through our EM leakage. We have studied dol- in fact, be no Encyclopedia Galactica (EG) embodying a sin- phins and whales for decades and still cannot speak with them. gle galactic culture. Nodes might instead resemble a dating site It may simply take a lot of analysis to understand us. that marries together civilizations with enough in common to intelligibly communicate. Our local node might recommend • The local probe(s) may not have the onboard capacity to specific civilizations to us. EG might actually be a collection of

JBIS Vol 71 No.10 October 2018 377 JOHN GERTZ parochial encyclopedias. If nodes help determine, for example, structs [19], but they may not exist. In addition to possibly be- that a given civilization might have enough in common with ing galactically illegal, they may be too difficult to construct Earth, it would send them our Wikipedia or Encyclopedia Bri- in practice. Imagine a replicator on an asteroid. It strains the tannica, and send us their equivalent. It might also translate imagination as to how it might fabricate computer chips in the from one language to another, or give us the Rosetta stone tools absence of any manufacturing facility; or how it would mine to enable us to do this ourselves. Then if mutually desired, it all necessary materials, say, the lithium and cobalt that might could put each of us in direct communication with the other be necessary for batteries. It might be far easier for land bases through the galactic node system, masking the exact location to be the mining and manufacturing hub for the probes and of each. This feature of the galactic communication network nodes that would be needed to service its local area. might allow for the following features: Land bases might also be the repository of the deepest store • We would be free to adopt the religion or art of one civili- of knowledge, and have the greatest computing sophistication. zation, while rejecting that of another civilization. Land bases should be considered broadly as having the natural resources to build probes, nodes, and supercomputers and • Instead of relying on the node’s judgment, we might be endowed with the intelligence to organize this, be that intelli- free to examine ET profiles, choosing for ourselves which civ- gence carbon based, AI or other. Small bodies, such as aster- ilizations we wish to further study. Our node might offer only oids, or artificial bodies, such as space stations, are not pre- a thumbnail at first, and then would download on request as cluded. If the proposed architecture is reliant upon land bases, much as we wanted from that civilization, subject perhaps to then our participation in the galactic order is necessary. This the rule that the node nearest that civilization would be au- will be Earth’s greatest bargaining chip. ET will not need us for thorized to download our full set of information as well (albeit, our knowledge, and in fact may get annoyed or bored if we try much later as limited by the speed of light). There might be no to impress it with how many prime numbers we know. As for point in putting us in contact with a cuttlefish-like color com- E=Mc2, they have heard that one too many times before also. municating civilization, or one that is a billion years in advance They may be mildly interested in Beethoven or Jackson Pollack, of us. By digging into our node’s databank, we would, in effect, but their real need is for us to assist in maintaining the galactic have a virtual conversation with any ET civilization of interest. communications network in Earth’s immediate neighborhood. The actual civilization could be quite remote, say, 50,000 LY Consequently, ET probes will not “lurk” indefinitely. The ga- away. It might also be the case that some, or even all, of the civ- lactic architecture needs us, and we are not therefore helplessly ilizations of most interest to us are no longer extant, or that we dependent upon ET’s merciful altruism. have made virtual contact with a civilization much earlier in its history, and that the same civilization is currently too advanced for meaningful direct communication. 5 THE GALACTIC COMMUNICATION ARCHECTECTURE AS LAWGIVER AND POLICE FORCE • Crucially, the proposed probe, node, and land base galactic architecture offers all involved anonymity, and therefore securi- Tipler has argued that we are alone, at least in the MW if not ty. Even if civilizations A and B decide to communicate in real in the entire visible universe, because if we were not alone, an time, limited only by light speed, they will never know each oth- earlier aggressive civilization would surely have created a von er’s locations. This is because their respective messages might go Neumann replicator, and that one solitary machine would pro- through dozens or hundreds of nodes, of whom only the first ceed to exponentially recreate itself ad nauseum until it had and last know the positions of the respective civilizations. Ano- gobbled up all matter in the galaxy [20]. Alternatively, had even nymity may be a vital and intended feature of the system not just one ordinary carbon-based life form set out to colonize the gal- for the safety and security of individual civilizations, but also for axy, due to its exponential growth, it too would have acted like the whole of the galaxy. Anonymity would serve as a break on a horde of locusts, per the classic interpretation of Fermi’s Par- would be attempts to form aggressive alliances or empires. adox. Either way, the result is a tragedy of the common. Since, obviously, this has not happened, it is deduced that we must be • The proposed architecture allows for multiple networks, alone. However, there are at least two other possible solutions just as many countries have competing cell phone systems or to the conundrum. It may be that Drake’s N does not = 1 (us), one might choose among various search engines. but that N = 2; us plus one other, a “berserker” civilization, that, like the first queen bee that emerges from her cell and immedi- 4 LAND-BASED COMMAND AND CONTROL CENTERS ately kills all other queens that would otherwise have hatched after her, this berserker civilization (or its AI creations) will de- It may be that probes report to nodes, and nodes report to stroy us as soon as it detects our EM leakage [21]. land-based command and control centers. Whereas probes and nodes are in all likelihood AI machines, the beings that inhabit There is, though, a third possibility, namely that the appar- the land bases may be life forms of recognizable organic chem- ent quietude of the galaxy paradoxically leads to the deduction istry, or they may be robotic AI beings, having been made by that N = at least a few and perhaps many, because a lack of col- but then replaced their natural predecessors. Land bases within onization must mean that there is a system of galactic govern- the proposed architecture would not be the capitals of empires ance in place, regulated by probes, nodes, and land bases, that any more than a server farm hosting an Internet cloud is an vigilantly guards against the type of tragedy of the common emperor. There may be no ruler anywhere in the galaxy, even implied by Tipler or the berserker hypothesis. In practice, seti though, as argued above, there must be rules. If simple enough, research is based on the premise that N = many, and therefore the rules can run on autopilot with rewards (membership in it presupposes a system of governance. the galactic architecture) and punishments (complete annihilation) that are simple to understand and administer. Haley, inventing the term “metalaw,” proposed a galactic rule book governing relations among its technological civiliza- Von Neumann replicators are interesting theoretical con- tions [22]. Others either elaborated upon or criticized the pu-

378 Vol 71 No.10 October 2018 JBIS ET PROBES, NODES, AND LANDBASES: a Proposed Galactic Communications Architecture and Implied Search Strategies tative corpus of laws [23,24,25]. Proponents argue in favor of that have had time to receive our EM leakage and to have re- a universal principle of “do unto others,” and “equality,” while sponded, i.e., stars ~<35 – 50 LY. Our local node may be in opponents tend to criticize on grounds that metalaw is anthro- orbit around any of them. Reasonable solutions to the Drake pomorphic with scant application to beings far more advanced Equation when applied to biologically based and transmitting or far different from humans, much less robotic life. In this civilizations yield a distance to the nearest such civilization as author’s view, laws must exist, but they must be equally appli- being much further than this. However, it is very reasonable cable to AI as well as naturally evolved life. This set of rules to assume that nodes may be much closer than the nearest or- might include: (a) severe limitations to colonization, perhaps ganic land based civilization, and that nearby stars are there- limited to a civilization’s immediate non-biological neighbor- fore prime candidates so long as they are closer than ~<35 – 50 hood, or even to one nearby star, and only then when neces- LY. Beyond that, it is recommended that the predominant seti sitated by the imminent death of one’s own star; (b) outlawing search paradigm be reversed, whereby stars are explicitly tar- of von Neumann replicators; and (c) outlawing of aggression geted and foreground probes or nodes would only be detect- against other civilizations, probes, nodes, and land bases. One ed by serendipity. The new paradigm would search for local might dispense with all the bodies of law that might govern probes and nodes, but be fully able to detect, by serendipity, non-aggressive behavior, brotherhood, equality and the like, background and distant beacons, say by preferentially targeting since under the proposed architecture, no civilization knows local objects such as asteroids or the area around the sun, when the whereabouts of any other, and therefore can do it no harm. they are transiting the plane of the MW. Since colonization is forbidden, there would be no border dis- putes. The galaxy’s entire rule book may consist of two words 6.2 Trade High Sensitivity for Wider Field of View (FOV) variously translatable as: “stay still” or “keep away.” Targeted star searches generally use a narrow beam with a small FOV and high sensitivity, as the signal they would detect The penalty for noncompliance would presumably be plan- is presumed to be weak because it comes from a great inter- etary destruction. It is speculated that the probes/nodes/land stellar distance. The preferred strategy for detecting intra-solar bases would have the means of disposing of aggressive civi- system probes/nodes would be to employ a wide FOV, since lizations as automatically as our immune system deals with an intra-solar system probe might be found in any direction. pathogens, without the need for judge or jury, as we would un- In exchange for this wide FOV, high sensitivity can be sacri- derstand those terms. This should not surprise us, as we our- ficed, since a probe in our own solar system is presumed to be selves are only a few years away from deploying autonomous transmitting at a power that any reasonably capable telescope automobiles and battlefield weapons whose algorithms will be might detect. Since telescopes generally have a fixed FOV, the fully empowered to make life and death ethical decisions. That effective recommendation is to use the existing FOV to mosaic said, probes could act as an early warning system that would areas of interest, sacrificing integration time, and with it sensi- presumably be able to determine far in advance whether a civi- tivity, to do so. lization is likely to go rogue, and might be able to take deterring actions short of annihilation. 6.3 Enlist Amateurs

Alternatively, and bleakly, probes might be currently sur- Amateur radio and optical astronomers might be recruited. If veilling us with the intent of deciding whether to engage with the sought-after signal is local, and therefore robust, amateurs us—or to destroy us. They may now be analyzing the data (e.g., might be able to successfully detect it. Given the plethora of violent newscasts versus feel-good movies like Forrest Gump). previous seti and non-seti sky surveys, it is unlikely that an am- The local probe(s) may be streaming data back to a local node, ateur would detect a persistent signal that had somehow been which in turn is passing it back to a command and control land missed. However, if a probe or node broadcasts to Earth very base, all in a grand determination of whether the galaxy should intermittently, say once a decade, perhaps from the surface of welcome us, leave us alone for the moment while more data is an asteroid, and then only for a short period of time, then an gathered, perhaps over the next several millennia, or destroy all-hands-on-deck strategy may be necessary in order to detect Earth forthwith. An algorithm that is as incapable of caring or its signal. mercy as we are when we pull a weed from our garden may even now be determining Earth’s fate. It may be that a local 6.4 Where to Look within Our Own Solar System probe, placed within the Solar System eons ago, is laced with a self-replicating toxin or nano-grey-goo that can be instruct- A probe that is transmitting to Earth could be orbiting the sun ed from afar to destroy life on Earth. If Judgment Day is well in any plane, forcing us to survey 360 degrees of sky. However, neigh, it will be by act of computer code rather than of a god. we can make some reasonable surmises that would narrow the search: 6 SEARCH STRATEGIES • Preferentially target the asteroid belt between Mars and The proposed probe/node/land base galactic communications Jupiter [2]. A probe might have landed on an asteroid where it architecture hypothesis leads to a set of recommended search might dig in for protection against micrometeorites and radia- strategies. Most of these assume that one or more probes or tion. There would be abundant sunlight for PV generation and nodes are transmitting to Earth now, but there might also be vi- useful materials for self-repair and the build out of capabilities. able strategies by which communications between an intra-solar system probe or node and a more remote node might be • Take a special look at Earth’s only known Trojan asteroid, intercepted. the ~30 km. wide 2010TK, located at Lagrange point, L4.

6.1 Emphasize Nearby Stars • Use the Large Synoptic Survey Telescope (LSST) to detect probes and nodes. When the LSST becomes fully operational Targeted star searches are recommended for nearby stars in 2022 it will conduct the most thorough visible wavelength

JBIS Vol 71 No.10 October 2018 379 JOHN GERTZ survey of the sky ever. It will have an exceptionally wide FOV, ladus or Europa proves to be Earth-like this may be evidence and is designed to repeatedly survey the entire sky visible to it. for panspermia. Panspermia between the Earth and the outer It will be ideally suited for optical seti (oseti) as traditionally Solar System, in turn, might be taken as prima facie evidence conceived as detecting a laser beacon originating from a re- for the past or present existence of probes that seeded them in mote star system. All that would be needed is a further set of common. algorithms capable of detecting a laser signal in non-sidereal motion as it moves through our own solar system, either in free 6.5 Probes and Nodes as Transients orbit around the Sun or Earth, or in solar orbit astride an object such as an asteroid or moon. Seti researchers should accept the possibility that ET signals may not be sidereally stationary. The greatest bane of seti re- • Preferentially target Lagrange points, especially the more search is the transient, a signal that mimics what might be ex- stable L4 and L5, including the Lagrange points around both pected from an extra-terrestrial beacon, but, if found in real Earth and the other planets, on the theory that probes would time, disappears before confirmation, or if found offline, is require less energy to maintain orbital stability. absent when researches return to the same fixed location. The 1977 WOW signal is the most famous example, but there are • The best solution for a probe entering our solar system many more. When a transient is recorded that is not obviously may be for it to enter into a highly eccentric orbit around our RFI, instead of assuming that it might have come from a star in Sun (a node might prefer a tight circular orbit around the Sun, the FOV, researchers should also examine the possibility that considered below). This would obviate the need for the addi- the source may be a foreground probe within our own solar tional gear necessary for it to land on an asteroid or moon, and system. They should determine whether an asteroid or moon it would require the least amount of energy relative to what was also in the FOV at the time of detection, and then observe would be needed to either land on a solar system object, such as at the then current position of that object. If no such object a moon or asteroid, or enter into a planet mimicking near-cir- was in the FOV at the time of original observation, or if that cular orbit either around the Earth or the Sun. A simple probe, confirmatory observation is negative, they should test to deter- one with no landing gear, and with a small communications mine whether the source might have been a free orbiting probe. system capable of reaching only the nearest stars, might not If the original detection was made in real time or not too long require the materials for build out and self-repair afforded by thereafter, the telescope should slowly slew in a spiral around asteroids. There would also be the added benefit to the probe the point of the detected transient. of being able to store the Sun’s energy as it closely approaches the Sun. It might also assume an orbit that allows it to close- 6.6 Eavesdropping on Probe-to-Node or Node-to-Node ly fly by Earth (the one obviously biological planet) once or Communications twice in each orbit for closer surveillance. This suggests that instead of searching the 360 x 360 = 129,600 square degrees of If a probe is not communicating with Earth, but in commu- sky, we might restrict the search to a more manageable ~100 - nication with nodes in nearby star systems (i.e., it is currently 200 square degrees of sky around the Sun, a region never yet in lurker mode), there may still be ways in which we might explored. Radio searches can be accomplished any time during eavesdrop on its signals: the day, while laser searches might be conducted just before sunrise and after sunset, as well as during solar eclipses. Re- • Whereas probes might be most efficiently placed in an ec- garding the latter, archival photos of total eclipses should be centric solar orbit, nodes might be best placed in close, nearly re-examined for lasers. It is possible that a laser was caught in circular solar orbits. Of course, there would be abundant en- the act but ignored as a lens or pixel malfunction. Were the very ergy available to it there. However, there may be more impor- first attempt to look for radio signals near the Sun to succeed, tant reasons for nodes to locate themselves in close solar orbits. it would either imply that probes in highly elliptical orbits must This would allow a sister node orbiting a nearby star to easily be legion, or that there is only one or a few probes, but they are locate the node and thereby allow for the use of a very narrow, in tight, almost circular, orbits around the Sun. A probe in a probably laser and probably phase arrayed beam. For exam- highly eccentric orbit would only travel a small fraction of its ple, a node in a solar orbit at 0.1 AU would unfailingly receive orbit within the 100 – 200 square degrees closest to the Sun. If 0.2 wide beamed communications from its sister if that beam probes are not legion, and the first observation fails, follow-up is centered on the Sun. This saves transmitter energy, while observations should be planned at regular intervals, certainly having the added benefit of being undetectable by life bearing not less than once per year. planets, except in the rare instances that the planet happens to transits that 0.2 AU space as seen from the perspective of the • If orbiting the Sun in a highly eccentric orbit, a probe transmitting node. For that reason, both the Sun and nearby might be found in any plane, necessitating a 360-degree search. stars should be viewed at times when the Earth transits between However, the search area might be reduced somewhat by deem- them. However, the better way to detect such a node, unless it is phasizing or ignoring altogether the ecliptic, reasoning that of intentionally transmitting to Earth, would be by placing one or all possible planes of orbit, the probe would be least likely to more receivers in solar orbits, in the hope of catching a node in be found in the debris-strewn ecliptic plane, through which it the act of transmitting. Because the probe or node may be ac- might otherwise be making hundreds of thousands or millions tively avoiding detection, the preferred orbit of our spacecraft of transits in the course of deep time. This strategy flies in the would be far away from the Earth, and would sample both the face of a strategy predicated on the hypothesis that local probes Sun and the direction exactly opposite the Sun. would choose to sit on asteroids. Astronomers might choose the paradigm they think more promising. • It is recommended to observe at the meridian at and around midnight. A probe or node in a tight orbit around the • Search for life within our own outer Solar System which Sun might be caught in the act of receiving a transmission from closely resembles Earth based life. Obviously, this is already a a node on the other side of Earth. This technique is particularly major goal of NASA and other space agencies. If life on Ence- recommended when a nearby star is in that position.

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• We might observe in a direction that is roughly in exact guished from UFOs along a number of parameters. UFOs have opposition to nearby stars. If a lurking probe is located on one been the subject of investigation for decades, but not one shred side of Earth and is signaling to a node on the other, we might of credible evidence has emerged in support of their existence. succeed in eavesdropping. To date, virtually no explicit search for probes or nodes has been undertaken. UFOs are often assumed to be piloted by liv- • Future space missions like LUCY, an upcoming NASA ing beings, the so-called “little green men.” Probes are hypoth- mission to several of Jupiter’s Trojan asteroids, as well as cur- esized to be artificial constructions impervious to the needs of rently flying missions to asteroids, Hayabusa2 (Japanese) and carbon life forms, such as ourselves. Therefore, they would not Oris-Rex (NASA) should train their radio receivers on their require the type of massive life support systems that carbon targeted asteroids to intercept possible probe-node communi- beings would require for multi-generational interstellar flight. cations. The asteroids should be observed from all directions, UFOs are presumed to have entered the atmosphere. Probes not assuming that its probe’s signal is directed toward Earth. are presumed to surveil Earth from space, from where they can readily monitor our EM transmissions. No special expertise is • Similarly, archival data from the Saturn probe, Cassini, required to study UFOs, only a video camera and a butterfly as well as asteroid probes, Hayabusa1, Rosetta and Dawn, and net to catch the little green men if they land. Being objects in Jupiter probe Galileo should be re-examined for evidence of outer space, the study of probes and nodes lies squarely within unaccounted for transmissions from asteroids or moons. In the the purview of astronomy. future, any NASA or other space agency probe to solar system Tens of thousands of individual stars have been surveyed objects should be outfitted with both radio and optical receiv- for radio or laser signals of technological origin. Breakthrough ers designed to detect ET signals. Listen is in the process of surveying one million more [27]. Perhaps the time has come to acknowledge the possibility that 7 CONCLUSIONS ET may no more be using star-to-star communications (except where nodes or land bases are orbiting nearby stars) than to A comprehensive search of our own solar system for evidence be using smoke signals. Instead, perhaps the time has come to of ET probes may have been stymied by a wholly unwarranted devote significant resources toward the comprehensive search association with UFOs [26]. Probes and nodes may be distin- of our own solar system for ET communications.

REFERENCES

1. A. Zaitsev, “Sending and Searching for Interstellar Messages,” Acta American, March, 2017, pp. 30-37. Astronautica, 63, pp. 614-617, 2008. 16. T.W. Hair, “Temporal Dispersion of the Emergence of Intelligence: An 2. G. Benford, J. Benford, D. Benford, “Searching for Cost Optimized Inter-arrival Time Analysis,” International Journal of Astrobiology, 10(2), Interstellar Beacons”, Astrobiology, 10, pp.491-498, 2010. 2011, pp. 131-135. 3. P.M. Todd & G.F. Miller wrote “The Evolutionary Psychology of 17. D. Brin, “An Open Letter to Alien Lurkers,” http://www.davidbrin.com/ Extraterrestrial Intelligence: Are There Universal Adaptations in Search, nonfiction/setiletter.html last accessed May 12, 2018. Aversion, and Signaling?” Biological Theory, 12, 2017. 18. J. Haqq-Misra and R.K. Kopparapu, “On the Likelihood of Non- 4. J. Gertz “E.T. Probes: Looking Here As Well As There”, JBIS, Vol. 69, pp. terrestrial artifacts in the Solar System,” ArXiv: 1111.1212v1, Nov. 4, 88-91, 2016. 2011. 5. R. N. Bracewell, The Galactic Club: Intelligent Life in Outer Space, W. W. 19. J. von Neumann, Theory of Self-Reproducing Automata, University of Norton & Company, New York, 1974. Illinois Press, Urbana, 1966. 6. R. Bracewell, “The Opening Message from an Extraterrestrial Probe”, 20. F.J. Tipler, “Extraterrestrial intelligent beings do not exist,” Journal of the Astronautics and Aeronautics, Vol. 11, pp.58-60, 1973. Royal Astronomical Society, 21, 1980, pp. 267-28. 7. R. Freitas, “A Self-Reproducing Interstellar Probe”, JBIS, Vol. 33, pp.251- 21. S. Webb, Where is Everybody? Fifty Solutions to the Fermi Paradox and 264, 1980. the Problem of Extraterrestrial Life, Springer, New York, 2002. 8. R. Freitas, “Interstellar Probes: A New Approach to SETI”, JBIS Vol. 33, 22. A.G. Haley, “Space Law and Metalaw—a Synoptic View,” Harvard Law pp.103-109, 1980. Record, November 8,1956. 9. R. Burke-Ward, “Possible Existence of Extra-Terrestrial technology in 23. E. Fasan, “Discovery of ETI: terrestrial and extraterrestrial legal the Solar System,” JBIS, Vol. 53, pp. 2-12, 2000. implications,” Acta Astronautica, 21(2), 131-135, 1990. 10. C. Rose, and G. Wright, “Inscribed Matter as an Energy-Efficient Means 24. R.A. Freitas, “Metalaw and interstellar relations,” Mercury, 6 (March- of Communication with an Extraterrestrial Civilization”, Nature, Vol. April), pp. 15-17. 431, pp.47-49, 2004. 25. A. Korbitz, “Altruism, Metalaw, and Celegistics: an Extraterrestrial 11. M. Hippke, P. Leyland, and J.G. Learned, “Benchmarking Inscribed Perspective on Universal Law-making,” in D.A. Vakoch (e.d), Matter Probes,” ArXiv:1712.10262v2, May 18, 2018, Extraterrestrial Altruism, Springer, 2014, pp. 231-247. 12. J. Gertz, ”Nodes: A Proposed Solution to Fermi’s Paradox,” JBIS, 70, 26. A. Tough, “How to Achieve Contact: Five Promising Strategies,” 2018, pp. 454-457. in When SETI Succeeds: The Impact of High-Information Contact, 13. B. McConnell, Beyond Contact, O’Reilly, 2001, pp. 375-379. Foundation for the Future, Bellevue, WA, 2000, pp. 115-125. 14. D.H. Forgan, R.S. Nichol, “A Failure of Serendipity: the Square 27. Isaacson, A.P.V. Siemion, G,W, Marcy, M. Lebofsky, D.C. Price, D. Kilometer Array Will Struggle to Eavesdrop on Human-like ETI,” MacMahon, S. Croft, D. Deboer, J. Hicksh, D. Werthimer, S. Sheik, G. International Journal of Astrobiology Vol.10, 2010, pp. 77-81. Hellbourg, and J.E. Enriquez, “The Breakthrough Listen Search for Intelligent Life: Target Selection of Nearby Stars and Galaxies” PASP, 15. A. Finkbeiner, “Near Light-speed Mission to Alpha Centuri,” Scientific 129(5), 054501, May 2017.

Received 12 June 2018 Approved 31 October 2018

JBIS Vol 71 No.10 October 2018 381 JBIS VOLUME 71 2018 PAGES 382-393

NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS from total energy expenditure on board, annual food production and space farming techniques

FRÉDÉRIC MARIN1, CAMILLE BELUFFI2, RHYS TAYLOR3 and LOÏC GRAU4 1Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France; 2CASC4DE, Le Lodge, 20, Avenue du Neuhof, 67100 Strasbourg, France; 3Astronomical Institute of the Czech Academy of Sciences, Bocni II 1401/1a, 141 00 Praha 4, Czech Republic; 4Morphosense, 18 allée du Lac Saint André, 73370 Le Bourget du Lac, France email [email protected]

In the first papers of our series on interstellar generation ships we have demonstrated that the numerical code HERITAGE is able to calculate the success rate of multi-generational space missions. Thanks to the social and breeding constraints we examined, a multi-generational crew can safely reach an exoplanet after centuries of deep space travel without risks of consanguinity or genetic disorders. We now turn to addressing an equally important question : how to feed the crew? Dried food stocks are not a viable option due to the deterioration of vitamins with time and the tremendous quantities that would be required for long-term storage. The best option relies on farming aboard the spaceship. Using an updated version of HERITAGE that now accounts for age-dependent biological characteristics such as height and weight, and features related to the varying number of colonists, such as infertility, pregnancy and miscarriage rates, we can estimate the annual caloric requirements aboard using the Harris-Benedict principle. By comparing those numbers with conventional and modern farming techniques we are able to predict the size of artificial land to be allocated in the vessel for agricultural purposes. We find that, for an heterogeneous crew of 500 people living on an omnivorous, balanced diet, 0.45 km2 of artificial land would suffice in order to grow all the necessary food using a combination of aeroponics (for fruits, vegetables, starch, sugar, and oil) and conventional farming (for meat, fish, dairy, and honey).

Keywords: Long-duration mission, Multi-generational space voyage, Space colonization, Space settlement, Space farming, Space genetics

1 INTRODUCTION of the code. This makes it possible to estimate the success rate and the associated uncertainties on the results for any kind of The first controlled, successful airship flights were made at the complex situation, such as the evolution of a space crew through end of the nineteenth century. A century later, humans are able several generations. Each iteration starts with a crew with given to launch unmanned interplanetary probes and crewed orbital biological and demographical input data, allowed to vary with space stations in low Earth orbit. The race towards the stars is time, and the code simulates the billions of interactions that accelerating and technologies are evolving to allow humanity can occur between breeding partners. This can thus determine to reach for neighbouring planets [1, 2, 3]. To reach more dis- if a ship with such initial crew can survive without inbreeding tant planets, i.e. planets orbiting around another star than the or genetic decay for several centuries [6]. We highlighted in Sun, means travelling much larger distances in deep space. To [7] that the most important parameters to monitor during the achieve such interstellar journeys in the scope of colonization, space travel are the inbreeding coefficient and the total popula- large spaceships will be necessary to transport human settlers. tion in the vessel. As a consequence, to maintain a genetically The question of the methods for ensuring a healthy popula- healthy community, the multi-generational crew must follow tion to reach its destination has been extensively covered in the adaptive social engineering principles, which means that each literature, and it was concluded that the only feasible scenar- year these principles should be revised in order to ensure the io relies on multi-generational spaceships [4, 5, 6]. The initial success of the mission. To achieve such goal, we found that an population would grow old and die, leaving their descendants initial ship with no less than 98 settlers is needed. Lower ini- to continue travelling. tial populations would lead to decreasing chances of mission success. We also found that it was mandatory to increase the The numerical tool HERITAGE was created in 2017 to in- allowed procreation window for women, with respect to [4], in vestigate the mathematical, biological, demographical and sta- order to keep a stable population level that can recover for cat- tistical feasibility of such an undertaking. HERITAGE is a code astrophic events that might occur during the interstellar trip. based on the Monte Carlo method, a mathematical approach that uses random draws to perform calculations, allowing tests We now turn our attention to the survivability of the pop- of all possible outcomes of a given scenario by repeat iterations ulation in terms of resources. Logically, our next step consists

382 Vol 71 No.10 October 2018 JBIS NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS on the investigation of the food requirements to feed the crew. Astronauts on the International Space Station (ISS) require approximately 1.8 kilograms of food and packaging per day [8]. So if we were to feed the crew of an interstellar mission entirely from stored food, the mass required reaches millions of tonnes. Additionally, the amount of vitamins contained in the food significantly decreases with time, independently of the storage processes [9, 10, 11]. The prospect of storing the food supply required for the whole trip is therefore not viable. In contrast, space agriculture, which produces fresh food, recy- cles nutrients and faeces, generates oxygen, and continuously purifies the air is by far the best option to feed a large-scale population and avoid vitamin deficiency. In principle a space farm can transform the spaceship into a complete, closed eco- logical system. Studies of such systems already exists, like the Lada experiment on the ISS, running since 2002 [12, 13]. It Fig.1 New biological data included in HERITAGE. Solid black line: uses a greenhouse-like chamber to grow plants to investigate pregnancy probability over the course of one year; solid red line: the safety of space-grown crops, the micro-organisms they age-dependent infertility of a male population; dotted red line: might have to deal with, and how to optimize crop productivi- age-dependent infertility of a female population. Between age 13 ty. Meat production has not been considered yet, but the recent and 18 the data are only approximative. Before age 13 the child is developments of artificial meat grown from cultured cells in considered as non-pubescent. laboratories raises the possibility that astronauts could avoid a purely vegan diet without the enormous associated support network necessary for animal farming [14]. female infertility likelihood based on the work of [17], who explored the age-dependent correlation between age and fertility. We therefore begin our investigation into the required re- The resulting age-dependent biological values are presented in sources by examining the necessities of food production. How Fig. 1. As we can see the likelihood of pregnancy monotonous- big should be the surface of artificial land inside the vessel to ly decreases with time until it reaches zero at age 50. The infer- allow the whole population to survive with a balanced diet? tility rates are different between females and males, with female How is this dependent on the agricultural technique? We ded- fertility peaking before 30 while male’s fertility peaks right after icate our third paper of the series to bring a precise answer to 30. Both decrease with time but female infertility evolves fast- those questions. To examine such problems, we have improved er and reaches a 100% infertility rate by 52, while males are HERITAGE to include more physical data for the simulated fertile for a longer period. Between ages 18 and 13 data are in- crew in order to estimate how much food the settlers need to complete and we can only approximate the global behaviour of consume every year. Such investigation relies on a number of the curves. Before 13 women are considered as non-pubescent factors such as biological and demographical data, together (while this can vary from case-to-case, with extremes down to with their physical activity (see Section 2). The total energy 10 years old [18]) and for ethical and sociological reasons we expenditure of a given population size can then be translated do not explore this. in terms of food quantity to determine the area needed for food production within the spaceship ( Section 3). We examine a va- In Fig. 2, we show the evolution of the average pregnancy riety of scenarios and outcomes, and discuss our results before chance per woman considering a heterogeneous population of concluding in Section 4. several hundred by the end of the mission. We ran HERITAGE one thousand times in order to get statically significant results 2 IMPROVEMENTS TO THE HERITAGE CODE (see the Appendix, Section B). We observe that the global pregnancy chances are very unstable at the beginning of the in- The HERITAGE code underwent a series of improvements in terstellar flight due to the presence of well-defined demograph- order to better simulate realistic individuals and populations ic echelons with people clustering into discrete age groups. (see AppendixA). We now include in the blueprint of each numerical human biological data on age-dependent pregnancy chances, miscarriage rates and infertility likelihood (see Sec- tion 2.1). We further added anthropometric data such as the age-dependent height and weight (Section 2.2). By doing so it becomes feasible to determine with great precision the total energy expenditure of a stable, heterogeneous population (Section 2.3).

2.1 Biological data on human age-dependent pregnancy, miscarriage and infertility rates

In the previous version of HERITAGE, the infertility rate and pregnancy chances were age-independent, fixed values. This was a first-order approximation that we now discard for the benefit of more exact medical data. We include an age-dependent pregnancy rate based on reliable etiological sources that Fig.2 Evolution of the averaged pregnancy chances per woman discuss the causes of infertility and provide information on considering a heterogeneous population of several hundreds by the numerous treatments [15, 16]. We also include the male and end of the mission.

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(see, e.g., [19]). Miscarriages are more common for women under 18, in women over 35, and for patients with a history of miscarriage, see [20] and Fig. 4. On average, miscarriages occur in about 15% to 25% of pregnancies [21, 20].

Examining the number of miscarriages per year for a 2000 year-long journey in Fig. 5, we see that, similarly to previous plots, results are chaotic before the stabilization of the population that reaches ~ 400 humans. On average, there is only one or two miscarriage per year, which represents a very small risk of failure for the whole mission. This is due to the fact that sporadic miscarriages are not a disease. Less than 5% of women will experience two consecutive miscarriages and less than 1%, three or more [21, 20]. The sharp drop at 750 years is Fig.3 Evolution of the averaged infertility chances per man (in red) due, as in our previous investigations, to a catastrophic event and woman (in black) considering a heterogeneous population of that wipes out 30% of the population. Note that we restrain this several hundreds by the end of the mission. calamity to impact the crew and not the structure of the generation ship, so that the integrity of the vessel remains intact.

2.2 Anthropometric data on human age-dependent height and weight

In order to be more representative of real populations, we decided to include anthropometric data in the initial conditions of our numerical humans. This has the advantage of being a well documented subject and it is a necessary step to be able to calculate the food requirement aboard since the daily caloric consumption depends, among other things, on the age, height and weight (see Section 2.3). We first include the age-dependence of height. To do so, we followed the Dutch growth study presented in [22] to compute the height evolution. The authors used the infancy-childhood-puberty model (see [23]) to break Fig.4 Miscarriage chances as a function of woman age. down growth mathematically into three partly superimposed components:

When the age groups are too young (non-pubescent) and/or (1) too old (menopause), their likelihood of pregnancy drops to −1.56a 2 zero. However, when the population age becomes more evenly with H1 = 76.4-19.4e , H2 = -0.235a +9.5a-4.7, H3 = 16.1/ 16.4−1.2a −1.65a 2 spread, a global trend appears. The final population contains (1+e ) for males and H1 = 74.3-18.7e , H2 = -0.256a 12.4−1.1a about 200 women with different ages, hence different pregnan- +9.8a-4.8, H3 = 8.6/(1+e ) for females. In this equation H1 cy chances, and the median value for pregnancy likelihood sta- represents the infancy period (0 – 3 years), H2 the childhood bilizes around 50.5%. (3 – puberty) and H3 the puberty and onwards. The relative contributions of H1, H2 and H3 strongly vary with a, the age In Fig. 3, we investigate the evolution of the average infer- in years. The heights are given in centimeters. The resulting tility for males and females using the exact same population. stature Htot as a function of age is shown in Fig. 6. We see Data are statistically noisy at the beginning of the mission for that, on average, young boys and girls have a similar height the same reasons as presented above, and the curves stabilize until the onset of puberty. The final stature of both genders when the population becomes stable and heterogeneous in age. Male infertility is globally lower than female infertility due to slower decrease of fertility with time for men (see Fig. 1). The average infertility within the population is 10.7% for women and 4.7% for men (plus or minus 0.5%). Interestingly, we note that our preliminary approximations of age-independent pregnancy rate and infertility were valid but only for the case of a stable population. The values we used previously were 75% for pregnancy efficiency, and 10% and 15% for female and male infertility respectively. The final values we find using age-dependent medical data are lower but compensate each other, in the sense that globally the crew has lower pregnancy chances but is more fertile than previously estimated.

Another parameter that we now include in our Monte Carlo code is the possibility of miscarriages. Spontaneous interrup- Fig.5 Number of miscarriages per year among the starship for a tions of pregnancy often happen before the end of the first tri- 2000 year-long journey. Data stabilize when the population reaches mester of pregnancy and early miscarriages are mainly caused a growth stability level. The sharp drop at 750 years is due to a by a non-hereditary chromosomal abnormality of the embryo catastrophic event that wipes out 30% of the population.

384 Vol 71 No.10 October 2018 JBIS NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS

Fig.6 Female (solid black line) and male (dot-dashed black line) Fig.7 Ideal human body weight according to various authors (see stature as a function of age. text for formulas and references). A fifth order polynomial fit is shown in gray lines. stabilizes around 20 years old, where the curves are plateau- ing. We note that the stature of the Dutch population is slightly higher than the averaged height of other populations but it is within the worldwide human height interval [24, 25]. Within HERITAGE, we included a random 10% variation of height in order to account for a variety of statures and we checked that the height of a given human does not suddenly decrease due to this additional fluctuation. By doing so our population is an indiscriminate mix of short, medium and tall people.

Our second anthropometric addition is the inclusion of age-dependent weight. This is slightly more tricky as there are numerous methods to estimate body weight. In the case of children there are two main equations [26]. First the Leffler formula (similar to the equations used in the American Heart Fig.8 Female (solid black line) and male (dot-dashed black line) Association training program), which is used for children be- weight as a function of age using a fifth order polynomial fit from tween 0 and 10 years old: equations presented in Fig. 7.

(2) different anthropometric equations (Leffler, Theron, Devine Then there is the Theron formula that was developed to and Hamwi, see Fig. 7), we find that none of the curves over- improve the accuracy of weight estimation for overweight lap. This is particularly true for the transition between 8 and children: 12 years. Since we do not want to rely on a specific equation for HERITAGE, we decided to run a numerical fit to the data. (3) We extrapolated a fifth order polynomial function that is representative of the four equations. Our formula is shown in Fig. 7 with W the body weight in kilograms and a the age in years. and with greater details in Fig. 8. What is interesting with this We observe that the weight is the same for both male and fe- fit is that males are always heavier than females, even in the male children. In the case of adults the situation is different and childhood period. The difference is almost negligible during theoretical curves clearly separate men and women. Several infancy and increases with time. We thus included this formula equations have been published [27, 28, 29]. According to the in HERITAGE and we took into account that, in contrast to Devine formula [30], the ideal adult body weight is given by: height, weight can positively or negatively vary as a function of age. We thus allowed the randomly picked weight of each crew member to vary within an interval of 10% per year so an (3) individual can be underweight in his childhood and becomes overweight during adulthood. The median value is always cen- (4) tred on our fitted formula. This allows the population to have underweight, healthy, and overweight members. for men and women, respectively. W represents the weight in kg and H the height in cm. Another equation that is widely 2.3 Physical activity level and total energy expenditure used was presented by Hamwi [31] and takes the form: Now that we have developed our Monte Carlo code to account (5) for all necessary biological and anthropometric data, it becomes feasible to estimate the amount of food needed by the (6) crew during the journey. In order to do so, we must calculate total energy expenditure. The energy expenditure of the human Both formulas reach a plateau at age 20 but give quite dif- body is mainly a sum of two phenomena: the calories spent by ferent results for male weight. In fact, when we plot the four the metabolism to ensure the proper functioning of all the vital

JBIS Vol 71 No.10 October 2018 385 FRÉDÉRIC MARIN ET AL

TABLE 1 Physical activity level (PAL) for several lifestyles

Lifestyle Example PAL

Extremely inactive Cerebral Palsy patient < 1.40

Office worker getting little or no Sedentary 1.40 – 1.69 exercise

Construction worker or person Moderately active 1.70 – 1.99 running one hour daily

Agricultural worker (non mechanized) Vigorously active 2.00 – 2.40 or person swimming two hours daily Fig.9 Physical activity level (PAL) scenarios for four different Extremely active Competitive cyclist > 2.40 populations: sedentary (in red), moderately active (in purple), vigorously active (in blue), and extremely active (in black). operations (breathing, digestion, regulation of body tempera- in a starship during their whole life, as it may depend on their ture) and the calories burnt during physical effort associated occupation inside the vessel. Also, some public health rules with external work. The energy consumed by vital organs and might be implemented to insure everyone has a sufficient ac- the resulting heat production is called the basal metabolic rate tivity level to avoid health issues related to obesity [35]. In (BMR). The BMR is strongly correlated with age, height and order to explore a large parameter phase space, we have con- body mass, hence the necessity to include anthropometric for- sidered several scenarios where the individual PAL varies as a mulas in our code. The Harris-Benedict principle [32], revised function of the settler’s age. We assume that colonists are not by [33], is a method used to estimate an individual’s BMR for very active in their early years, then there is an increase of the both men and women: activity level that peaks between 25 and 45 years old, and finally the PAL decreases with old age. We varied the peak of ac- (8) tivity as a function of the scenario we wanted to test, including sedentary, moderately active, vigorously active, and extremely (9) active populations. The four scenarios are illustrated in Fig. 9. with W the weight in kg, H the height in cm and A the age in The product of BMR and PAL gives the approximate dai- years. ly kilo-calorie intake needed to maintain current body weight, also known as the total energy expenditure (TEE). The TEE The second cause of calorie loss, i.e. the external work, can has been computed for the four different PAL scenarios pre- be evaluated by measuring the physical activity level (PAL) sented in Fig. 9 and the results are shown in Fig. 10. We find of the individual. This is the ratio of energy expenditure to that the total TEE increases as the number of people in the BMR and it can be quantified as the sum of obligatory and generation ship increases, from 98 at the beginning of the jour- discretionary physical activities. Obligatory activities include ney to about 400 people at the end. The population (and the daily activities such as going to school, tending to the home TEE) stabilizes after 600 years, decreases sharply due to a cat- and family, and other demands made on children and adults astrophic event that wipes out 30% of the population at year by their economic, social and cultural environment, while dis- 750, then increases again to reach the same maximal level after cretionary physical activities are related to health, well-being and quality of life in general. Five categories of PAL have been identified by the World Health Organization, the United Nations University, and the Food and Agriculture Organiza- tion of the United Nations [34]. They are summarized in Table 1. An extremely inactive PAL corresponds to no exercise at all. A sedentary PAL corresponds to intensive exercise for 30 to 60 minutes once to three times a week. This may include activities such as cycling, jogging or swimming, or may also corresponds to a busy life style with frequent walks for long periods. A moderately active PAL corresponds to intensive exercise for 60 minutes or greater five to seven days a week (same activities as above). Labour-intensive occupations including construction work, general labour, farming, or land- scape work enter this category. The fourth category, vigorously active PAL, corresponds to people with very demanding jobs, such as mining. Finally, the fifth category corresponds to ex- Fig.10 Total energy expenditure (TEE, in kilo-calories) per year in ceedingly active and/or very demanding activities such as ath- the vessel for the four different PAL scenarios presented in Fig. 9. letes with an almost unbroken training schedule corresponding The crew is composed of 98 people at the beginning of the mission to multiple training sessions throughout the day. and the population slowly rises to ~ 400 people by the end. The sharp drop at 750 years is due to a catastrophic event that wipes out It is difficult to predict the individual PAL for people living 30% of the population.

386 Vol 71 No.10 October 2018 JBIS NUMERICAL CONSTRAINTS ON THE SIZE OF GENERATION SHIPS a few hundred years. It is interesting to note that the extremely active population requires only 36% more calories than the sedentary population. In the extreme case where all the 400 settlers are Olympic athletes during their 20s and 30s, one can assume that a maximum of 4.47 × 108 kilo-calories have to be produced every year to correctly feed the whole vessel. This values gives us an upper limit for food production within the starship. Taking into account a more reasonable yet vigorously active population, the total energy expenditure for 400 settlers is about 3.57 ± 0.52 × 108 kilo-calories a year. We expended our simulations to smaller and larger populations and plotted in Fig. 11 the total energy expenditure per year as a function of the crew size, given that the population is both stable and heterogeneous. The required TEE increases continuously with the population size and can be easily interpolated for larger crews. Fig.11 Total energy expenditure (TEE, in kilo-calories) per year as a function of the crew size. The crew is representative of a vigorously 3 Evaluating the size of artificial land for agriculture active, stable and heterogeneous population that includes children, adults and elders, together with skinny, fat, small or tall persons. Our simulations of the TEE per year as a function of the crew The 95% confidence range is shown in grey. size enables us to estimate the amount of food required by the population, given the constraints of maintaining ideal body weight, avoid cardiovascular risks and sustain a healthy life- above ground. The soil is then replaced by an inert and sterile style. Thanks to Fig. 11, we can now estimate the size of ar- substrate, such as coconut fibers, sand, perlite, coir peat or clay tificial land required in the starship for agricultural purposes. balls. In order to overcome the lack of nutrients usually con- We proceed in three steps. First we review in Section 3.1 the tained in horticultural land, it is necessary to regulate the com- different farming techniques that currently exist, including position of nutrient solutions using automatized engines. An conventional farming, hydroponic and aeroponic methods. additional improvement with respect to conventional farming Then, we evaluate the surface of artificial land to feed any size is that this technology is not subject to weather conditions or of population, and finally we apply the different agricultural the seasons. A study conducted at the John F. Kennedy Space procedures to a single-food diet. By focusing on the highest ca- Center by [41] have shown that it is possible to grow Triticum loric density food in Section 3.2 we can provide a clear lower aestivum (common wheat) using a growth chamber at 23°C, limit on the agricultural surface. In Section 3.3 we examine a 65% relative humidity, 1000 ppm CO2 , continuous light, with more balanced diet that includes fresh fruits, fresh vegetables, a continuous flow, thin film nutrient delivery system. 24 trays meat, whole grains, nuts, lean proteins and a few other ani- of wheat were planted and harvested. The grain yields aver- mal-based products to be grown/raised aboard. aged 520 g.m−2 and had an average edible biomass of 32%. More recent studies [42] have shown that tuber production 3.1 Current and experimental farming methods from a staggered harvest in hydroponics was 286% greater than in the bed and pot systems for Monalisa and Agata cvs If we discard agriculture techniques based on an archaic tech- potatoes. This means that, under the hypothesis of function- nology with very low productivity, there are essentially three al terrestrial gravity inside the spacecraft, hydroponics could modern farming techniques. improve the food production of cereals, starch, and a variety of fruits and vegetables by almost 300% with respect to con- The first one is industrial, conventional, geoponic farming. ventional farming. This form of agriculture follows agronomic innovations, uses chemical, biological and pesticide fertilizers, uses improved In order to get rid of the constraints brought by the use of crop varieties and heavy machinery. All of these factors com- soil or an aggregate medium, one can explore aeroponic farm- bine to yield better productivity. Intensive farming, such as ing methods. Aeroponics is the process of growing plants sus- needed to feed a population in a starship, comes with serious pended in a closed or semi-closed environment by spraying side effects such as soil compaction, soil erosion, and declines the plant’s dangling roots and lower stem with an atomized in overall soil fertility [36]. To maintain a high productivity, or sprayed, nutrient-rich water solution. The project lead by it will be necessary to let the soil fallow. Fallowing will help [43] has shown that this high performance food production the soil to restore organic carbon, nitrogen, phosphorus, and technology rapidly grows crops using 99% less water and 50% potassium among the principal soil nutrients. It was observed less nutrients in 45% less time than geoponic agriculture. The that their concentrations significantly increase with increasing major improvements of aeroponics is that crops can be planted fallow duration up to 7 years [37]. To account for fallowing, it and harvested year-round without interruption and it is insen- is then necessary to consider a resting period of about a third sitive to gravity. A more recent aeroponics study of the vege- of the time, which means that two artificial land surfaces will tative growth and minituber yield in three potato varieties has produce food while a third surface will lie fallow in order to shown that the number of minitubers per plant increased by restore the soil organic matter, including water and microbial 277.2% compared to hydroponics [44]. This found that aer- activity and diversity [38]. To do so, the most efficient method oponic farms are by far more efficient than the other farming is to sow non-edible plant species and use bacterial and fungal techniques, and the associated technologies are under intense organisms to restore the fertility of degraded land [39]. development [45].

The second farming technique one can consider is hydro- One major concern is for the production of animal proteins. ponic agriculture. Hydroponics is, in fact, a very old horticul- Hydroponics and aeroponic are capable of growing crops in tural technique [40] that makes it possible to cultivate a crop space but the space needed to raise a living being cannot be

JBIS Vol 71 No.10 October 2018 387 FRÉDÉRIC MARIN ET AL compressed below the limit of the physical size of the animal. TABLE 2 Average energy production of selected aliments in According to the Housing and Space Guidelines for Livestock kcal/ha/day published by the New Hampshire Department of Agriculture, the minimum space requirements for, e.g., a beef or dairy cow Aliment Edible energy Ref. is 6.97–9.29 m2. A pig requires a minimum living surface of 2 2 2 4.46 m , a sheep 1.86–2.32 m , and a turkey 0.56 m . Those Sweet potato 70 000 [46] estimates account for decent living conditions, not barren battery cages. It is also feasible to dedicate an exercise yard Potato 54 000 [46] for the animals in order to release both their own and the human colonists stress of living in a confined space. The animal Rice, paddy 49 000 [46] that requires the largest exercise area is the horse (18.58 m2). However, the larger the area, the larger and more complex Yam 47 000 [46] the spacecraft. In the following we will only account for the necessary decent living conditions for the required livestock Wheat 40 000 [46] and thus only calculate the agricultural area required on the spaceship. Groundnut in shell 36 000 [46] 3.2 First-order approximation: a single-food diet Cassava 27 000 [46]

In order to efficiently feed the population of the vessel, one Lentil 23 000 [46] can consider – as a first-order approximation – a single-food diet. According to the Food and Agriculture Organization of Carrots 20 500 [47] the United Nations [46], a single-food diet based on sweet potatoes would be the most efficient hypothesis for our pre- Milk 17 400 [48] liminary analysis. For comparison, we report in Table 2 the edible energy (in kcal/ha/day) for a variety of crops, fruits, Orchard 16 900 [49] vegetables, animals and animal-based products. We see in Fig. 12 the required agricultural surface area (in square kilometers) Meat: pork 16 500 [48] as a function of the crew size for a sweet potato diet. Using conventional farming techniques, a crew of 500 would require Cheese 10 400 [48] an agricultural area of 0.230–0.315 km2 to grow food. Using hydroponics, this surface is reduced to 0.042–0.055 km2. With Butterfat 8 700 [48] aeroponics farms, growing enough sweet potatoes would only 2 require 0.012–0.015 km . Meat: mutton 3 300 [48]

3.3 Second-order approximation: a balanced diet Meat: beef 3 200 [48]

Our previous results are a useful first step, but a society eating Eggs1 1 900 [48] nothing (or almost nothing) but sweet potatoes would likely be riddled with disease. In order to overcome deficiencies in pro- Meat: poultry1 1 700 [48] teins, vitamins, carbohydrates, fat, iron, calcium and other elements, it is necessary to construct a balanced diet. To achieve Honey 1 400 [47] this goal we follow the dietary advice from Public Health Eng- land [50]. They recommend to eat each day a selection of fruits 1Assuming that poultry are kept under ordinary poultry farm conditions, the and vegetables (39%), meat and fish (12%), dairy (8%) and pullets being raised and the old hens and young males being used for meat. starch (37%) at the proportions given in parentheses. About 1% of the dietary content should be used for oils and spreads and 3% in food high in salt, sugar and fat. Based on Table 2 and on the constraints established in Section 3.1, it is possible to evaluate the average energy production of each food category to sustain a healthy diet.

In Fig. 13, we computed the required agricultural surface area as a function of the crew size for a balanced diet that comprises fruits, vegetables, meat, fish, dairy, and starch. As stated previously, the animals that are used for proteins, dairy or honey are kept under decent living conditions with enough space to move. We see that, overall, the space needed to ful- fill a balanced diet has drastically increased with respect to a single-food diet. This is because the average edible energy per product is lower than for sweet potatoes. For a crew of 500, the different farming techniques require, on average, a surface of 1.01 km2, 0.53 km2, and 0.45 km2, for conventional farming, Fig.12 Required agricultural surface area (in square kilometers) as hydroponics and aeroponics respectively. The 1.01 km2 geo- a function of the crew size for a single-food diet, see Sect. 3.2. The ponic value (i.e. 0.2 of a hectare per person) compares very colors highlight the different, farming techniques used. well with the minimum amount of agricultural land necessary

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pling, one should minimize the habitat’s angular velocity. A threshold of Ω ≤ 3 is recommended to avoid disabling motion sickness [54].

The tangential velocity V is the velocity measured at any point tangent to the spaceship rotating surface. As humans will move within a rotating habitat, they will be subject to Coriolis accelerations that distort the apparent gravity. For relative motion in the plane of rotation, the ratio of Coriolis to centripetal acceleration is twice the ratio of the relative velocity to the habitat’s tangential velocity. This ratio can be minimized by maximizing the habitat’s tangential velocity.

Finally the centripetal acceleration A (measured in units Fig.13 Required agricultural surface area (in square kilometers) as a of gravitational force g), is a measurement of the type of ac- function of the crew size for a balanced diet, see Sect. 3.3. The colors celeration that causes a perception of weight. For example, 1 g highlight the different farming techniques used. is the acceleration due to gravity at the Earth’s surface. While the minimum g required to preserve health remains unknown, the maximum A should generally not exceed 1 g for comfort for sustainable food security, with a diversified diet similar to reasons [55]. A safe range of g-values lies between 0.3 and 1 those of North America and Western Europe (hence includ- according to [55, 56, 57]. ing meat), that is 0.5 of a hectare per person according to the Food and Agriculture Organization of the United Nations [51]. Knowing the surface of farmland in the spaceship, it is then We see that the decrease in required land area due to hydro- possible to calculate possible ship architectures under the hy- ponics is only a factor 2 with respect to conventional farming. pothesis of centripetal gravity. To do so, we used the open-ac- The reduction factor is even lower between hydroponics and cess spin calculator SpinCalc developed by Theodore W. Hall. aeroponics because of the physical constraints brought by the We present in Table 3 a representative set of spaceship radii R animals. Successful further improvement in crop production (and their associated length L), in meters, to maintain a surface would not help to decrease the size of artificial land needed for of 0.45 km2 of farmland under different centripetal acceler- agriculture by a large factor because of the presence of animal ations. We varied the values of A and maintained Ω close to proteins and dairy in a balanced diet. The presence of animals 2. We see that, for decreasing artificial gravity, the tangential on board the spacecraft determines the limit of the land size velocity V and R decrease, resulting in increasing values of L. required for agriculture. We will discuss alternative methods A cylindrical generation ship with an Earth-like gravity could for protein production in Section 3. have a radius of 224 m and a length of 320 m in order to maintain a surface of 0.45 km2 of farmland, whilst minimizing the 3.4 Ship’s architecture various uncomfortable effects of rotational gravity. The length of the spaceship is, of course, a simple approximation. It seems We saw that a minimum of 0.45 km2 of farmland, using a mix reasonable to assume that plant and food crops may tolerate of aeroponics (for fruits, vegetables, starch, sugar, and oil) and a lower level of gravity. Thus if we allow the ship to contain conventional farming (for meat, fish, dairy, and honey), is to be allocated in the spaceship. While aeroponics is insensitive to gravity, animals and humans suffer deleterious health effects TABLE 3 Ship’s architecture for a crew of 500 humans and the from long periods without (Earth-like) gravity – for example 0.45 km2 of farmland needed to feed them1 bone demineralization, with bone density dropping at over 1 1% per month (about 12 times faster than for elderly people A (g) Ω (rotations/min.) V (m/s) R (m) L (m) on Earth [52]). Microgravity also influences muscles, the heart and brain, and increases cancer risk. To prevent such problems, 1.0 1.998 46.87 224 320 some form of Earth-like gravity is necessary. Artificial gravity can be created using a centripetal force [53]. In this case, the re- 0.9 1.996 42.22 202 355 sulting ‘gravity’ is the inertial reaction to the centripetal acceleration that acts on a body in circular motion. There are four in- 0.8 1.999 37.47 179 400 terdependent parameters that are used to constraint the system: the radius R from the center of rotation, the angular velocity 0.7 1.997 32.83 157 456 Ω, the tangential velocity V, and the centripetal acceleration A. 0.6 1.994 28.18 135 531 The radius R corresponds to the distance from the centre of rotation. A natural geometry for the spaceship is a cylinder that 0.5 1.998 23.43 112 639 is rotating like a rigid body. Since the nominal artificial gravity is directly proportional to R, inhabitants will experience a 0.4 1.994 18.79 90 796 head-to-foot gravity gradient. To minimize this, one should maximize the radius. 0.3 1.986 14.14 68 1053 The angular velocity Ω is the rate at which the spaceship 1The length L of the starship is calculated from the usual surface area of rotates around its centre. The cross-coupling of normal head a cylinder: 2πRL. The ship’s radius and length do not account for other movements (i.e. rotation) with the habitat rotation can lead to facilities besides farming. dizziness and motion sickness, so, to minimize this cross-cou-

JBIS Vol 71 No.10 October 2018 389 FRÉDÉRIC MARIN ET AL multiple floors, each with a different radius, the required area An important and still untouched question regards water. can be maintained while significantly reducing the length of The National Academy of Medicine suggests that an average the cylinder. Assuming the depth of each level to be 3 m, if male adult should drink 3.7 litres of water daily, while an av- we allow food crops on levels down to 0.9 g, the length of the erage female adult should drink 2.7 liters per day in order to 224 m-radius cylinder could be reduced to 106 m, or 25 m if maintain body functions [61]. Of course, water needs vary tre- we allow them down to 0.5 g. Of course other facilities besides mendously from individual to individual, and are dependent farming are necessary – human habitation, control rooms, on numerous factors such as the activity level or the environ- power generation, reaction mass and engines, the requirements mental temperature. Most people will be adequately hydrated of which we leave to future papers. at levels well below these recommended volumes. It must be noted that these amounts include water from food consump- 3 Conclusions and further development tion. About 20% of the daily total water intake can be found in food [62]. If we consider a gender-balanced crew of 500 In this paper, we have improved our Monte Carlo code in order persons, approximately 468,000 litres of water will be required to account for all the necessary biological and anthropometric every year. This represents a storage of volume 468 m3 and, data to compute the yearly energy expenditure aboard a mul- apart from this volume, one also needs to take into account the ti-generational spacecraft. We tested a complete phase space mass of the containers. of scenarios that simulated different crew activity levels that directly impact the caloric budget. By doing so, we determined Since water refuelling will not be possible during the jour- the required amount of kilo-calories to be consumed per year ney, a recycling system should be installed in the spaceship. in the spaceship in order to maintain the ideal body weight Such system is currently used aboard the ISS. Astronaut’s of a stable, heterogeneous crew. The final relation between waste water is captured, such as urine, sweat, and even the the yearly kilo-calorie expenditure and the size of the crew moisture from their breath. Then impurities and contaminants is established. This allows us to easily determine the amount are filtered out. The final product is potable water whichis of food to be produced aboard. We investigated the problem cleaner than what most Earthlings drink. However, the sys- through the prism of different farming techniques: convention- tem is not 100% efficient: water is lost by the space station in al agriculture, hydroponic farms, and aeroponic systems. The several ways: a small amount of urine cannot be purified; the latest is the most efficient method to harvest large quantities of oxygen-generating system consumes water; air that is lost in crops with minimum space requirement. It also works under the air locks takes humidity with it; the CO2 removal systems low gravity conditions and does not require soil. We used those leach some water out of the air, to name a few [63]. So the three techniques to determine the minimum size of artificial amount of water to be stored at the beginning of the journey land to be saved in the spacecraft for agricultural purposes. has to take into account the water recycling systems efficiency First considering a single-food diet, we determined that aero- in order to have enough water for all the colonists inside the ponic farms could produce enough food to feed a population vessel during the whole trip. of 500 with only 0.012 km2 of farming area. Improving the diet to include dairy, meat and a large variety of starch, vegeta- Finally, estimating the amount of water required for plant bles and fruits, the final land surface is larger. An area of 0.45 growth is extremely complex since it is species-dependent. It km2 is required to grow all the food, but also to raise animals is impossible, as this stage, to give a precise number of how in decent living conditions for protein and dairy production. much water should be embarked, but this number is expect- Working with the hypothesis of centripetal artificial gravity, ed to be very large. Clearly, the best but difficult to resolve this surface put strong constraints on the ship’s architecture. option would rely on finding alternative water sources along the ship’s journey, e.g. from comets, asteroids, and other large We have seen in Section 3.3 that the limiting factor to the sources while still in the Solar System. Similarly, the issue of agricultural surface is the presence of animals. Hydroponics and how efficiently plant and animal nutrients can be recycled will aeroponics are able to reduce the size of vegetable crop cultures strongly affect the amount of mass required for sustainable but reducing the space associated with protein intake is a much farming aboard the ship. more complicated task. However potential solutions exist. In particular, there is a growing research area on edible insects as In conclusion, we have put strong constraints on the mor- an alternative protein source for human food and animal feed. phological structure of future multi-generational spacecraft. Insects are highly nutritious and thus represent an interesting By improving our simulation tool, we have opened a new field alternative to animal meat. A list of insects to be used in gastron- of investigation for HERITAGE. There are still many more omy is presented in [58], together with a discussion on the risks steps to be taken in order to provide a realistic simulation of and benefits of insects as a human food source. The harvesting a global generation ship and we aim at pushing our numerical of insects is also much simpler than for cows or poultry, and it tool to higher grounds by including population genetics and requires much less space. According to [59], an average of 7,500 mutation in the next paper of this series. metric tonnes of insects is annually produced for home consumption and markets in Thailand. In fact, roasted mealworms have a Acknowledgment higher protein content than chicken, pork or beef [60]. The author of the aforementioned paper calculated that about 160,000 The authors would like to thank Theodore W. Hall for his Ja- mealworms per day must be eaten by a gender-balanced crew vaScript applet “SpinCalc” (https://www.artificial-gravity. of 160 people in order to fulfil their daily protein requirement. com/sw/SpinCalc/) that was used to calculate the various ar- This, of course, opens a whole new window as it could help to tificial-gravity environments. R. Taylor was supported by the decrease the size of artificial land used in the spacecraft, but in- Albert Einstein Centre for Gravitation and Astrophysics via sects can also be used to improve biodiversity, regenerate soils, the Czech Science Foundation project 14-37086G, the insti- and destroy organic wastes while providing extra fertilizers. In- tutional project RVO 67985815, and the Czech Ministry for sect consumption, however, is not frequent in all countries and a Education, Youth and Sports research infrastructure grant LM psychological barrier must be crossed. 2015067.

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APPENDICES

A Input parameters for HERITAGE TABLE 4 Input parameters of the simulation

In Table 4, we remind the reader about the list of parameters Parameters Values Units that must be determined by the user before starting the simulation. Extensive explication, details and description of the Number of space voyages to simulate 1000 – parameters are given in [6] and [7]. Duration of the interstellar travel 2000 years

B How many iterations needed? Colony ship capacity 500 humans

Overpopulation threshold 0.9 fraction All simulations presented in this paper have been achieved by Inclusion of Adaptive Social Engineering looping our Monte Carlo code one thousand times. The reader 1 – may wonder if this number is sufficient to have statistically Principles (0 = no, 1 = yes) significant results. Number of initial women 49 humans Number of initial men 49 humans We explored this issue and present in Fig. 14 four realisa- tions of the same simulation using a different number of iter- Age of the initial women 20 years Standard deviation for the age of the initial ations. The total energy expenditure per year in the vessel for 1 years a vigorously active population is plotted as a function of the women number of iterations. In the case of a single loop, the results are Age of the initial men 20 years Standard deviation for the age of the initial noise-dominated and uncertainties prevail over the real median 1 years outcome. When the simulation is looped ten times the results men start to stabilize and specific features (such as the sudden de- Number of child per woman 2 humans Standard deviation for the number of child per crease in population at 750 years due to the catastrophic event 0.5 humans on-board) start to appear. Looping the simulation one hundred woman times gives us a median value that is no longer subject to high Twinning rate 0.015 fraction statistical fluctuations, except at the beginning of the journey Life expectancy for women 85 years where the population is smaller than in the end, hence initial statistics are still poor. Nevertheless the results at the end of Standard deviation for women life expectancy 15 years the interstellar trip are already significant. Finally, looping the Life expectancy for men 79 years simulation one thousand times gives us access to a very smooth Standard deviation for men life expectancy 15 years median outcome. Statistical fluctuations are almost non-exist- ent and we can safely conclude that one thousand iterations are Mean age of menopause 45 years perfectly sufficient. Start of permitted procreation 30 years

To better understand what this represents, looping this sim- End of permitted procreation 40 years ulation a thousand times means that about one million humans have been simulated. The total number of humans simulated Initial consanguinity 0 fraction to obtain Fig. 11 corresponds to approximately two hundred Allowed consanguinity 0 fraction million, three times the current population of France [64]. Life reduction due to consanguinity 0.5 fraction Possibility of a catastrophic event (0 = no, 1 1 – = yes) Fig.14 (below) Total energy expenditure (TEE, in kilo-calories) Fraction of the crew affected by the 0.3 fraction per year in the vessel for a vigorously active population (see Figs. catastrophe 9 and 10 for details about the crew and the journey). Each panel Year at which the disaster will happen (year; 0 750 years presents the same simulation achieved with a different number of = random) iterations. More loops means a better statistical estimation of the representative result. Chaotic element of any human expedition 0.001 fraction

(a) 1 interstellar trip sampled (1 iteration) (b) 10 interstellar trips sampled (10 iterations)

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Received 10 October 2018 Approved 6 December 2018

JBIS Vol 71 No.10 October 2018 393 JBIS VOLUME 71 2018 PAGES 394-396

EFFECTS OF ENHANCED GRAPHENE REFLECTION on the Performance of Sun-launched Interstellar Arks

GREGORY L. MATLOFF Physics Department, New York City College of Technology, CUNY, Brooklyn, NY 11201, USA email [email protected]

Graphene, a carbon molecular monolayer, has an essentially zero reflectivity to visible light that can be increased to 0.05 if alkali atoms are intercalated with carbon atoms. Recently published theoretical work considers methods of selectively altering graphene optical properties. This paper considers the effects of increasing graphene fractional reflectivity on the performance of a previously considered Sun-launched interstellar ark. The ark considered has a payload mass of 5×106 kg and a maximum population of 20-50. The hollow-body sail, with a radius of 764 km, is unfurled (or inflated) at the 0.1-AU perihelion of an initially parabolic solar orbit. A multiple-layer structure of graphene and molybdenite is used to increase sail fractional absorption of visible light to 0.4. Fractional reflectivity is varied incrementally between 0.05 and 0.4. Final interstellar cruise velocity, peak acceleration and perihelion temperature are examined as functions of sail reflectivity to sunlight. It is shown that even small increases in reflectivity significantly increases interstellar cruise velocity.

Keywords: Interstellar Ark, Graphene, Interstellar Travel, Photon Sails

1 INTRODUCTION: GRAPHENE AND ITS APPLICATION TO fractional visible-light reflectivity of 0.05 and a fractional vis- INTERSTELLAR SOLAR SAILING ible-light absorption of 0.4. The sail is configured as a hollow-body (inflatable) structure with the payload mounted Graphene, a one-atom thick carbon-lattice monolayer, has a on the anti-Sun face of the sail. The areal mass density of the thickness of 0.335 nm and its areal mass density is 7.4 × 10-7 multi-layer sail is 5×10-6 kg/m2, including hollow-body fill gas. -6 kg/m2. Pure graphene has an essentially zero reflectance (R) The areal mass thickness of the entire spacecraft (σs/c) is 8×10 to visible light. Reflectance can be increased to 0.05 if alkali kg/m2. Perihelion distance (Dau) is taken as 0.1 Astronomical atoms are intercalated with grapheme. The fractional visible Units (AU). The spacecraft departs the solar system at about light absorption (A) of a pure graphene monolayer has been 922 km/s. Travel time to Alpha Centauri is about 1,400 years. measured as approximately 0.023. Other interesting properties Peak perihelion acceleration (ACCpeak) is 2.9 g and peak tem- of graphene include impermeability to many gases and a very perature at perihelion (Tperi) is 1021 K. high tensile strength—about 130 GPa [1]. The melting point of graphene is reported to be in excess of 4,000 K [2]. These values are slightly refined in a follow-on paper. Physi- cal properties of the ark are also discussed in that paper and the If one creates a two-layer structure consisting of graphene population of the spacecraft is estimated at 20-50 people [3]. and molybdenite, fractional absorption of visible light can be increased to 0.37. Sandwiching graphene between two appro- 2 SOME ANALYTICAL TOOLS priate layers may increase fractional absorption of visible light to >0.5 [1]. One significant parameter in the consideration of Sun- launched interstellar ark performance is the lightness number, In Ref. [1], three possible applications of graphene so- η. This is defined as the ratio of solar radiation pressure force lar-photon sails to interstellar travel are considered. One is a on the sail to solar gravitational force on the spacecraft. The thin-film, high-acceleration probe accelerated by Sunlight after Lightness Number can be expressed [1]: the sail is unfurled at the perihelion of an initially parabolic solar orbit. The second is a robotic interstellar probe. The third (1) is a small interstellar ark with a payload of 5×106 kg. This paper further considers the baseline interstellar-ark scenario in Ref. The Lightness Number can next be used to calculate the in- [1] with fixed fractional absorption of visual spectral-range terstellar cruise velocity of the spacecraft, finV . This is expressed light and variable reflection. using Eq. (3) of Ref. [1]:

The baseline disc sail in Ref. [1] has a radius of 733 km, a (2)

This paper was presented at the Foundations of Interstellar Studies where Dau is the perihelion distance in Astronomical Units Workshop at CUNY City Tech, New York City, 13-15 June 2017. (AU).

394 Vol 71 No.10 October 2018 JBIS EFFECTS OF ENHANCED GRAPHENE REFLECTION on the Performance of Sun-launched Interstellar Arks

The solar gravitational acceleration at 1 AU is 6.04 × 10-4 g. TABLE 1 Effects of Varying Sail Reflectivity (R) on Interstellar Therefore, peak solar-radiation-pressure acceleration at peri- Ark Performance helion can be calculated [1]: R η Vfin(km/s) ACCperi (g) ε Tperi (K) (3) 0.05 49.67 938 3.0 0.44 1022 To evaluate ark thermal properties at perihelion, it is worth noting that sail fractional transmission of sunlight, T, can be expressed as T = 1- A - R. Emissivity of this non-opaque sail 0.1 59.60 1032 3.6 0.47 1006 can now be defined [1,4]:

(4) 0.2 79.47 1192 4.8 0.52 981

Emissivity and the grey-body equation can be used with the value of the Solar Constant (1366 W/m2) to estimate sail abso- 0.4 119.20 1454 7.2 0.52 981 lute temperature at perihelion, Tperi. Application of Eq. (7) of

Ref. [1] results in: η = lightness number, Vfin = final velocity,ACC peri = peak acceleration, ε = emissivity, Tperi = peak sail temperature. (5) In all cases: As discussed above, it is assumed that the payload is mount- sail visible light absorption = 0.4 sail radius = 764 km ed on the anti-Sunward face of the inflated hollow-body sail. perihelion distance = 0.1 AU Maximum allowable sail stress can be defined using Eq. (8) of sail mass = 9.16×106 kg Ref. [1]: payload mass = 5×106 kg

(6) mine the value of emissivity (ε) using Eq. (4). Peak perihelion temperature, from Eq. (5), varies with the fourth root of (A/ε) where σpay is the areal mass density of the payload and accel- for the case of constant perihelion distance. eration is in MKS units. In all cases considered, stress is not an issue because of the very high tensile strength of graphene. Table 1 summarizes these results for fractional sail visible-light reflectivity varies between 0.05 and 0.4. In all cases, 3 RESULTS: EFFECTS OF REFLECTION VARIATION the sail radius, payload mass, sail fractional absorption, payload mass, sail areal mass density and perihelion distance are Before considering the effects of reflection variation on inter- maintained constant as discussed above. Consideration of the stellar ark performance, it is worth reviewing the baseline case results presented in Table 1 reveals that increased sail visi- from Ref. [3] and discussing parameters that are fixed for all ble-light reflectivity increases both interstellar cruise velocity cases considered in this analysis. This is done below. and peak acceleration at perihelion. Increased reflectivity results in slightly lower perihelion temperatures. 3.1 The Baseline Case (R=0.05) and Fixed Parameters 4 CONCLUSIONS In all cases, the sail radius is 764 km. Sail fractional absorption (A) to visible light is 0.4. Fractional reflectivity of visible light is If the occupants of the ark are organic lifeforms similar or iden- 0.05. The payload mass is fixed at 5×106 kg and the areal mass tical to humans, it may not be possible to fully take advantage density of the multi-layer sail is 5×10-6 kg/m2. The spacecraft of the higher performance possible with increased sail reflec- areal mass density is therefore (σs/c) is 7.73×10-6 kg/m2. At per- tivity. This is because, as discussed in Ref. [3], the maximum ihelion, the total spacecraft mass is 1.42×107 kg. tolerable acceleration by humans during the multi-hour acceleration period is about 3 g. As shown in Table 1, peak acceler- From Ref. [3], the emissivity of the baseline sail is 0.44; peak ation increases more rapidly than interstellar cruise velocity as perihelion temperature is 1022 K. The spacecraft lightness sail reflectivity is increased. number (η) is 49.67. The peak acceleration is 3g and the interstellar cruise velocity is 938 km/s. The interstellar transit time One possibility is to depart from a higher perihelion dis- to Alpha/Proxima Centauri is about 1375 years. tance to maintain a 3 g maximum acceleration. A second possibility is to increase payload mass as sail reflectivity is increased. 3.2 Effects of Increasing Reflectivity (R) This will decrease lightness number and acceleration as well as the interstellar cruise velocity. Possibilities of altering graphene optical properties, including reflection, are discussed in the literature [5]. To consider the Acknowledgements effects of increasing sail reflectivity upon ark performance, -re fer to Eqs. (1)-(5). The spacecraft lightness number (η) varies Although the author serves as an advisor to Breakthrough Ini- with (A+2R) from Eq. (1). Applying Eq. (2), interstellar cruise tiative Project Starshot, the scenarios investigated here have no velocity (Vfin) varies with the square root of (A+2R). Peak ac- direct relation to the probe and sail concepts under considera- celeration at perihelion, from Eq. (3), varies with the lightness tion by that project. Discussions with Oleg Berman and Roman number. Kezerashvili of New York City College of Technology, CUNY and Godfrey Gumbs of Hunter College, CUNY, are greatly ap- To calculate thermal properties, it is first necessary to deter- preciated.

JBIS Vol 71 No.10 October 2018 395 GREGORY L. MATLOFF

REFERENCES

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Received 7 April 2018 Approved 16 October 2018

396 Vol 71 No.10 October 2018 JBIS DIARY FORTHCOMING LECTURES & MEETINGS OF THE BIS

THE TOOLS OF APOLLO 22 January 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London, SW8 1SZ Mark Yates looks at three artefacts from the Apollo programme, each with a fascinating story behind them. APOLLO MISSIONS: THE MECHANICS OF RENDEZVOUS & DOCKING BY DAVID BAKER 20 February 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London, SW8 1SZ Starting with Apollo 9 launched on 3 March 1969, a key feature of the Apollo missions was the ability to rendezvous and dock in orbit – a capability that NASA had evolved over the preceding four years. SpaceFlight Editor David Baker describes the process in detail and casts an expert eye over the different options considered by mission planners in the run-up to the lunar landing missions. APOLLO 9 – TESTING THE LUNAR MODULE 6 March 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London, SW8 1SZ Jerry Stone continues his series of talks to celebrate the 50th anniversary of the Apollo missions with a uniquely personal take on the story of Apollo 9 – the first test of the full lunar landing package and only the second outing of the Lunar Module. WEST MIDLANDS BRANCH: A NEW SPACE RACE? & PROJECT CHEVALINE 16 March 2019, 1.45pm VENUE: BIS, 27/29 South Lambeth Road, London SW8 1SZ Gurbir Singh posits the beginning of a new space race between India and China, while John Harlow and Paul Jackman look back to the days of Project Chevaline and the famed Twin Chamber Propulsion Unit. ARTISTS IN SPACE: THE EARLY YEARS 3 April 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London SW8 1SZ David A. Hardy FBIS, the “longest established astronomical artist”, uses art from Lucian Rudaux, Chesley Bonestell and our own R.A.Smith, plus other ‘lesser-known’ artists (and of course his own!) to trace the genre of space art from its inception in 1874. APOLLO 10 – DRESS REHEARSAL FOR THE MOON LANDING 22 May 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London SW8 1SZ Jerry Stone continues his coverage of Apollo with the first flight to carry both the Apollo spacecraft and the Lunar Module on a full dress rehearsal of a landing. Call for Papers RUSSIAN-SINO FORUM 1-2 June 2019, 9.30 am to 5pm (tbc) VENUE: BIS, 27/29 South Lambeth Road, London SW8 1SZ The BIS has now scheduled its 39th annual Russian-Sino Forum – one of the most popular and longest running events in the Society's history. Papers are invited. Watch this space for further details. APOLLO MISSIONS: LANDING ON THE MOON BY DAVID BAKER 12 June 2019, 7.00pm VENUE: BIS, 27/29 South Lambeth Road, London, SW8 1SZ SpaceFlight's editor looks at the systems evolved by NASA for calculating optimum lunar landing trajectories, and at the descent procedures needed to achieve the maximum chance of success while preserving emergency abort and safety considerations. Journal of the British Interplanetary Society

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