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6 Dec 2019 Is Interstellar Travel to an Exoplanet Possible?

6 Dec 2019 Is Interstellar Travel to an Exoplanet Possible?

arXiv:1308.4869v2 [.pop-ph] 6 Dec 2019 hsc Education Physics oueIseAtceNme www.physedu.in 1 Number Volume/Issue/Article h osbelmttos fay o such ever for humans any, could and be if travels, could interstellar limitations, What possible are: the here we explore be questions to could The want travel prohibitive. a immensely such for energy and requirements time the Consequently, space. interplanetary than the larger within encountered time those of thousands be could of system hundreds Solar the near- outside the of est some even reach to to covered has distances be the travel course Of reality. interplanetary a become the the on man after a of street, mind the gained in has impetus question further the this so, in or However, years 50 long. last for fiction Solar science realm of the our in been beyond have travels Such , system. a around some orbiting reach of to possibility travel the examine interstellar we article, this In Abstract 1 eateto hsc n etrfrFedTer n Partic and Theory Field for Center and Physics of Department sitrtla rvlt neolntpossible? exoplanet an to travel interstellar Is 2 srnm n srpyi iiin hsclRsac Lab Research Physical Division, Astrophysis and Astronomy ua nvriy hnhi203,China. 200433, Shanghai University, Fudan arnpr,Amdbd3009 India. 009, 380 Ahmedabad Navrangpura, amySingal Tanmay [email protected] [email protected] umte nxx-xxx-xxxx on Submitted 1 n so .Singal K. Ashok and tla itne soepsiiiy[] What [1]. possibility one is distances stellar inter- over communication they Radio assuming there? are extra-terrestrials, the contact physical in with get ever we Can hope- them. some of and on life them, intelligent of of existence the fully, fraction a life habit- of on the forms evolved some in with are possibly them zone, dis- able of been Many have system, covered. Solar stars our around beyond that of thousands , many decades three last the In Introduction 1 bet htgtrpre ntemedia the in time? reported to Flying time get from Unidentified that – – UFOs be Objects of could what reality near And a the future? in distant adventure even an or such for possible scenario a be a could hopefully What outcome? with positive voyage, a such undertake 2 ulcto Date Publication ePhysics, le oratory Physics Education Publication Date about the possibility of humans ever visiting Ganymede or Titan, as the planets them- “them”? Or an even more pertinent ques- selves are all gaseous, lacking a solid surface tion first – Is an interstellar space travel to to make a landing. an exoplanet around a star beyond our So- lar system possible? This begs a question: Could man possi- bly ever travel to distant stars to visit some In last 50-60 years, the mankind, first exoplanets, perhaps in a habitable zone, time in its history, has not only ventured to possibly encounter some extraterrestrial into , humans have successfully life? After all, a mere century back, a trip to stepped on the , the first time ever on the Moon, culminating in a human landing another celestial body. Rover explorations on it, looked as much impossible and such of the surface of Mars have been made accounts in science fiction seemed to be just many times, probes have landed on , a fig of imagination, as an and many other missions have been sent to to an exoplanet may appear now. Such other planets. The Galileo that analogies though may have their own jus- entered orbit around , made a num- tification grounds, but the fact remains that ber of close flybys to study Jupiter’s satel- the distances involved in interstellar travel lite Ganymede. In the Cassini-Huygens mis- are immensely larger. The nearest star out- sion, while Cassini orbited Saturn and stud- side the () is ies its rings before it plunged into Saturns at- as many times (∼ a hundred million times) mosphere, the Huygens probe successfully farther than the Moon, as the latter is com- landed on Saturn’s moon Titan. pared to distance between adjacent rooms In recent years, India too has sent two ((∼ 4 m) in a building. From a simple logic missions, Chandrayan-1 and Chandrayan- one could then expect that going to a star 2, to the Moon, and Mars Mission will at least be as much more difficult than (MOM), India’s first interplanetary mission, going to the Moon as the going-to-the-Moon has successfully reached Mars. A third mis- was with respect to a walk just next door sion to the Moon is now being planned, and within an office building. Of course, the other interplanetary missions are in the off- shortness of human lifetime makes things ing. Perhaps in a decade or so, India may all the more difficult. With the maximum also achieve a human landing on the the speeds achieved so far by the spaceships Moon. After that one could imagine such within the solar system, it will require about manned trips to Mars. Other countries are 80,000 years on a one-way journey to this also planning such expeditions in near fu- nearest star. Thus it may not look possi- ture. As for the Jovian planets like Jupiter ble to reach other stars within a human life- or Saturn, manned missions if any, will have time, although on a theoretical basis theory to have bases on one of their , e.g. of relativity could allow one to do so. For

Volume/Issue/Article Number 2 www.physedu.in Physics Education Publication Date instance, a spaceship accelerating continu- dream only. ously with a convenient value of g, that is In this article, we ignore the techni- the that we are used to on the cal aspects of the mission as technology surface of the , could travel to the most is bound to improve rapidly over time. distant parts of the universe within a human Further, we assume 100% efficiency of the lifetime, without violating the speed-limit of engine in converting fuel energy into c, the . In principle, interstellar of the exhaust, something travel may thus appear possible. that might not really be possible. We carry forth the possibility of our endeavour with- However, energies involved in such an out delving into many other equally im- endeavour would make it next to impossi- portant issues such as the long term effects ble. In a spaceship the fuel needed for the of cosmic radiation on the health of space later parts of the journey has to be carried travellers and their requirements for food, aboard and thus also needs to be acceler- medical and other life-sustaining needs. We ated till it is utilized. Therefore the initial consider mainly the minimum basics of the at the start of such a voyage is expo- travel, which are distance, time and energy. nentially larger than the final . With conventional chemical fuel such an arduous journey will need a fuel-mass of a whole 2 The story so far galaxy. Even within the best possible sce- nario, where almost 100% of mass is con- Till date there have been five spacecrafts that verted into energy (in a typical thermonu- have crossed the threshold of escape veloc- clear reaction only about 0.7% of mass is ity from the solar system and four of them converted into energy), one would require are already headed towards the interstellar initial mass to be millions of times the mass space. of the final payload and the energy required was launched in 1972, flew may be worth hundreds of years of total en- past Jupiter in 1973 and became the first ergy consumption of the whole world. If spacecraft to achieve from we imagine that the energy is beamed from the solar system. The contact was lost in power plants on the Earth to the spaceship, January 2003 and is heading in the direc- it will again require many hundred million tion of Aldebaran in Taurus. was megawatts of power throughout the dura- launched in 1973, flew past Jupiter in 1974 tion of such a trip, which might last for a and Saturn in 1979. The contact was lost in very long time. It therefore looks that at November 1995. The spacecraft is headed most we might travel to other planets within toward the constellation of Aquila. our solar system but the distant stars will Pioneer 10, as well as Pioneer 11, carry ever remain within the realm of a distant -anodized plaques in case

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most mysterious part of the whole message for them [2].

Voyager 1 was launched in September 1977, flew past Jupiter and Saturn, made a close approach to Saturn’s moon Titan and is now at a distance of about 145 (au), where one au (=1.5 × 108 km) is the average distance of the Earth from the . was launched in August 1977, Figure 1: The message, featuring human flew past Jupiter, Saturn, , figures along with several coded-symbols and is now at a distance of about 125 au. inscribed on the gold-anodized aluminium Both probes are already past heliopause, the plaques, carried aboard Pioneer and Voy- region where the interacts with ager spacecrafts. the at distances around 120 au from the Sun. Voyagers are thus either spacecraft is ever found by intelli- presently exploring the boundary between gent life-forms from another planetary sys- the Sun’s influence and interstellar space, tem. The plaques feature the human fig- where nothing from the Earth has flown be- ures along with several coded-symbols that fore, and are expected to return valuable are designed to provide information about data, hopefully, for another decade. Since the origin of the spacecraft, and the message the Pioneers were launched first, they had a may hopefully survive for hundreds of mil- head start on the Voyagers, but because they lions of years during its long travel through were travelling slower they were eventually the interstellar space. It is, thus, the artefact overtaken by Voyagers. of mankind with the longest expected life- , launched in 2006, made time [2]. a flyby of Jupiter in 2007, and then in 2015 it The content of the message should be made a flyby of Pluto, where it flew 12,500 clear to an advanced extraterrestrial civiliza- km above the surface of Pluto, making it the tion, which will have, of course, the entire first spacecraft to explore this dwarf . Pioneer 10 spacecraft itself at its disposal After that, New Horizons made a flyby of to examine as well. But being the product object 486958 Arrokoth, at ∼ of billions of years of independent biologi- 43 au from the Sun. New Horizons was cal evolution, they may not at all resemble launched with the largest-ever launch speed humans, nor may the perspective and line- for a man-made object. It will, however, drawing conventions be the same there as slow down to an escape velocity of only 2.5 here. The human beings will perhaps be the au per year as it moves away from the Sun,

Volume/Issue/Article Number 4 www.physedu.in Physics Education Publication Date and it will never overtake the Voyagers.

2.1 The Pale Blue Dot

The pale blue dot is a photograph of planet Earth taken in 1990 by the space- craft when the spacecraft reached ∼ 6 billion km, or about 40 au (the distance of Pluto), from the Sun. This is an actual photograph (Fig. 2) of the Earth, taken from the farthest distance till now, and it appears as a tiny pale blue dot against the background of an Figure 2: A panoramic (!) view of our Earth, apparent void (the faint brown band is due that appears as a pale bluish dot in the centre to the reflection of sunlight from camera op- of the image. The faint brown band across tics). This picture is very significant as a per- the image is due to the reflection of sunlight spective on our place in the cosmos as our from camera optics. blue planet literally pales into insignificance within the larger scheme of things. And this is the only actual image of the Earth ever and triumph they could become the mo- seen by anybody from such a vantage point. mentary masters of a fraction of a dot. Think It is both a chastening and humbling real- of the endless cruelties visited by the in- ization for us humans that our huge planet habitants of one corner of this pixel on the is such a tiny speck of dust seen from the scarcely distinguishable inhabitants of some distance of an outpost (Pluto!) of our plan- other corner. How frequent their misunder- etary system. If it could be photographed standings, how eager they are to kill one an- from near our nearest star [Proxima Cen- other, how fervent their hatreds. Our pos- tauri], its diameter will appear about 7000 turings, our imagined self-importance, the times smaller and it would be still fainter in delusion that we have some privileged po- brilliance by a factor of 50 million (with the sition in the universe, are challenged by this flux-density falling as a square of distance), point of pale light. Our planet is a lonely and that the Earth may not even qualify to speck in the great enveloping cosmic dark. be called “a tiny speck of dust” from our just In our obscurity - in all this vastness - there next-door neighbour star. is no hint that help will come from else- As Carl Sagan writes [3] “The Earth is where to save us from ourselves. The Earth a very small stage in a vast cosmic arena. is the only world known, so far, to harbour Think of the rivers of blood spilled by all life.” those generals and emperors so that in glory And to think further that somewhere

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Table 1: An idea of the cosmic distances involved Cosmic object Distance Moon 1.28 light seconds (384000 km) Sun 500 light seconds (150 million km) Proxima Centauri 4.24 light years Orion Nebula 1300 light years Centre of Milky-way 25,000 light years Andromeda Galaxy 2 million light years Size of Universe! 14 billion light years

on a far-off world perhaps some intelligent others or even kill and die for some totally being looking at this “not-even-a-speck-of- unfounded beliefs uttered or penned down dust” could amusedly imagine that some by someone perhaps with good intentions two-legged creatures, populating that ut- but based on the limited knowledge at that terly insignificant part of the universe, be- moment of time, or much worse, based on lieve that some of their ancestors (saints, gu- a pure whim and fancy, thrust upon other rus or prophets), confined to a minuscule gullible fellow beings. part of this tiniest of dots, had figured out the grandest design of the whole Universe 3 Cosmic distances involved or even of its so-called creator – and have the audacity to claim that the creator himself The main challenge facing interstellar travel or his some messenger had appeared in the is the vast distances that have to be covered, form of these very two-legged creatures on requiring very high speeds as well as long their own planet. It should also humble us travel times. The latter make it particularly and put into total insignificance the occur- difficult to design manned missions. rence of all our daily squabbles, aspirations, the desire to preserve our DNA through our 3.1 How far can a manned mission children and grandchildren, political up- travel from Earth? heavals, love-affairs, wars between nations, and above all it should show us the hollow- As one cannot travel faster than light, one ness of our religious beliefs – perhaps the might conclude that a human can never greatest folly of all – and our chauvinism make a round-trip farther than 20 light years that we are the best of all, with an utter con- (1 light year ≈ 9.5 × 1017, the distance trav- tempt for others who may not agree with elled by light in one year), assuming the us, and our willingness to condemn those traveller is active between the ages of 20 and

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60. Thus one would never be able to go be- tic effects of would have to yond a few star systems which exist within be taken into consideration. We know that the limit of ∼ 20 light years from the Earth. time passes relatively slower by a relativistic Even if we design a spaceship that can travel factor γ = 1/ 1 − (v/c)2 for an observer 10 at 0.99c, where c ≈ 3 × 10 cm/sec is the moving with ap relative speed v. Detailed cal- speed of light, which, from the theory of rel- culations show that by the time the space- ativity is the maximum possible speed an ship lands back on the Earth, the time t, object could ever attain, interstellar travel that would have passed on the Earth, would beyond some nearest stars seems impossi- be related to the time T, that passed on the ble. spaceship, as (see Appendix A) To survive for long years on a space- 4c gT t = sinh , (1) ship, it would be ideal to maintain a con- g 4c stant acceleration, g ≈ 9.8 × 102 cm sec−2, the acceleration due to that the hu- a factor of 4 in the formula appears because mans have evolved in and are accustomed of the four stages of the journey. During this to on the Earth, with the rocket continuously time, the maximum relative speed the space- accelerating the spaceship by this amount. ship would achieve, midway of the journey, Since we may want soft landings on the sur- is face of the exoplanet as well as on our re- v = c tanh(gT/c) (2) turn to the Earth, we divide our journey into four separate stages. In the onward Journey The maximum distance d, of the destina- while the spaceship is moving towards the tion that the spaceship would have arrived destination, it will be accelerated in the first at and returned from, will be given by half of the journey, while in the second half 2c2 gT it will have to be decelerated to attain an al- d = cosh − 1 . (3) g 4c most zero speed. In the same way during   the return journey, it will have to be accel- The destination distance D can be expressed erated in first half of the return journey and in terms of time t of the Earth, as then decelerated in the second half, for an 2 ultimate soft landing. 2c2 gt D = 1 + − 1 . (4) g s 4c    3.2 The relativity comes to the rescue –   It helps to remember that for g ≈ 9.8 × 102 time dilation cm sec−2, time c/g = 0.97 ≈ 1 year and the A constant acceleration of 1g for a year distance c2/g ≈ 1 light year. Table 2 gives would bring the speed of spaceship ap- us an idea of the time dilation involved from proximately close to c. Therefore relativis- the total duration and distance reached in a

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Table 2: Effects of time dilation Time on spaceship Time on Earth Distance reached T (years) t (years) d (light years) 1 1.01 0.065 2 2.1 0.26 5 6.5 1.85 7 11.5 4.1 10 25 11 15 93 45 20 340 165 25 1,230 610 30 4,450 2,200 40 59,000 29,000 50 780,000 390,000 60 10,100,000 5,100,000 90 23,500,000,000 11,700,000,000

round trip, involving a constant acceleration ing back home is out of the question. Back of 1g for the crew. A future spacecraft, using on the Earth, millions of years would have technologies that we haven’t even dreamed passed and entire civilizations would have of, may use an engine that could sustain a come and gone, while the who constant acceleration of 1g. Travelling even left in their twenties would be still in their at the speed of light, visiting the stellar nurs- eighties. Table 2 gives time spent by the as- ery in Orion nebula would require at least tronaut, travelling in a rocket with a con- 2600 years on the earth time, while a cruise stant acceleration, as a function of time and to the centre of our Milky-way galaxy will distance seen from the Earth. take more than 50,000 years, and a round trip to Andromeda, the nearest spiral galaxy, will need at least 4 million years. But due to 4 The rocket equation the relativistic time dilation, for the traveller the time spent could be much smaller. With If the fuel needed for the journey has to be a 1g engine, a vacation trip to Andromeda carried aboard it also needs to be acceler- may be possible within a human lifetime! ated till it is utilized. Therefore the initial

mass, Mi, at the start of the journey is much For those astronauts, however, return- more than M f , the final payload mass. This

Volume/Issue/Article Number 8 www.physedu.in Physics Education Publication Date is given by the rocket equation, which gives or v c/u the final reachable speed v as a function of R = γ 1 + . (6) c the exhaust speed u of gas/ion/light emis- h  i For v ≪ u ≤ c, equation (6) reduces to the sion and R = Mi/M f , the ratio of the ini- tial mass (payload + fuel) to the final mass familiar non-relativistic equation (5). (only payload). From the momentum con- The power of the needed servation we have can be calculated from the required thrust of the rocket, which is nothing but the total dv dM M = − u, mass, M , of the spaceship (payload+fuel) dt dt i multiplied by its acceleration, g. The thrust We can integrate it of the rocket is obtained from the exhaust

v M f dM mass-flow rate times the exhaust veloc- dv = −u , M ity. For a non-relativistic case, the needed Z0 ZMi power, P, of the engine thus equals the which gives v mass-flow rate times one-half the square of = ln R. u the exhaust velocity. From that we get, P = or Mi gu/2. For a relativistic exhaust speed R = exp(v/u). (5) (u ∼ c) it becomes P = Mi gc. If at the maximum speed so far The exponential makes the required mass achieved, which is 16 km s−1 for the New ratio increase very fast with v/u. Horizons probe to Pluto, we could make a For example, return trip to the Moon in a little more than R = 1 , for v = 2.3u, half a (ignoring the slowing down due but to the Earth’s gravity), a similar return trip R = 1010 , for v = 23u. at this speed to Proxima Centauri, the star Thus, to obtain a final speed, v close to nearest to our solar system, will take about c, it is necessary for u to be of the order of 160,000 years which is over 6,000 human c as well, otherwise the required mass ratio generations, and this is of the order of time will be prohibitively large. that has passed since the homo sapiens (hu- In a relativistic case, the rocket equation mans) first appeared on the scene. One can becomes (see Appendix B) thus conclude that in order to reach these v 1 −R−2u/c interstellar destinations, one would have to = . c 1 + R−2u/c travel much faster, in fact with speeds close to that of light, c, which is the maximum For the mass ratio R, we then get attainable speed for any object. Otherwise (1 + v ) c/2u such a trip would be unimaginable. And to R = c , (1 − v ) get close to c, we need alternative fuels.  c  Volume/Issue/Article Number 9 www.physedu.in Physics Education Publication Date

5 Various rocket concepts nearest star would, however, require a min- imum of 170 years of travel time. Relativis- 5.1 Chemical fuel rocket tic effects of time dilation would be insignif- Till now the chemical energy being used icant at such speeds. comes from a mixture of liquid oxygen Fusion could provide ten times more and , which yields 100 MJ (Mega energy per unit fuel mass. Despite the fact Joules) per kg of fuel. The highest efficiency that controlled reactions of fusion of lighter is achieved if the end products of the chem- nuclei have not yet been very successful, we ical reactions themselves can be expelled for can imagine that the technology required propulsion with the energy produced. Then for it could be developed in the years to one will get an exhaust speed of u = 14 come. Banking on this assumption, one km/s. Attaining a modest maximum fi- could propose the energy required for inter- nal value of one thousandth of the speed of stellar travel to come from . ∼ light, would mean 17,000 years of travel Using fusion of lighter nuclei, an ex- time for a return trip to Proxima Centauri, haust speed of c/8.4 may become possible at a distance of 4.24 light years. This would (see Appendix C), and that we could attain a itself require, due to the four stages of the top speed of 0.3c, requiring for a return jour- R ∼ journey, an extremely high mass ratio ( ney a mass ratio more than 32,000. At these 4c/u ∼ × 37 (1.001) 1.6 10 ). This implies that a speeds a trip to the nearest star would re- ten ton payload (a minimum from any stan- quire for the return journey a minimum of ∼ × 44 dards) will need a fuel 1.6 10 ) gm, the 60 years of total travel time, slightly more ∼ mass equivalent of 100 billion or a than the average working life span of a sin- whole galaxy. Not at all a viable possibility, gle generation. Of course a ten ton payload considered from any angle. Perhaps nuclear will mean more than 320,000 tons of hydro- fuel might be a better option. gen to be carried aboard and to be converted into helium and propelled behind during 5.2 Nuclear fuel - fission or fusion? the journey. This will be ∼ 2 × 1017 MJ of en- Uranium yields about 6.5 × 107 MJ/kg of ergy, which is around 400 years worth of to- × 14 energy through fission, or about a million tal energy consumption (5 10 MJ for the times better than the chemical reactions. In year 2018) of the whole world! this case, we could get an exhaust velocity, The examples discussed so far were for 12,000 km/s or u = c/25, and we could pos- much lower than g, the accel- sibly attain a maximum travel speed, v = eration due to gravity on the Earth, an ideal 0.1c, which implies R ∼ 12 . Considering, value for journeys made by humans for long however, four stages of the journey, R > durations. In fact, an acceleration of 1g 20,000 will be needed. A round trip to the could make it possible to attain much higher

Volume/Issue/Article Number 10 www.physedu.in Physics Education Publication Date speeds for the spaceship and thus substan- terstellar spaceships as a way to help trigger tially cut down the travel time. However, as nuclear reactions. we will show later, the mass ratio, R, then snowballs to extremely high values, making 6 Non-rocket concepts even the nuclear fusion energy as a mode of locomotion for journey to other stars, not 6.1 A scoop on the way very promising. Thus a vision of interstel- lar space travel will be highly unrealistic, In a a huge scoop could col- if we were to depend only on these energy lect diffuse hydrogen from the interstellar sources. space and burn it on flight, using proton- proton fusion reaction and expel the fusion 5.3 product to get the thrust. The idea is attrac- tive as the fuel would be collected en route, An would have a far but all attempts to design some kind of a higher and specific impulse, scoop has the unfortunate effect of produc- i.e. total impulse (or change in momentum) ing more drag than you get back thrust. delivered per unit of propellant mass, than any other proposed class of rocket. When 6.2 Sailing away matter and anti-matter is made to fuse, the entire mass gets converted to radiation, but Solar sails are a form of spacecraft propul- the technology supporting such a mode of sion using the solar pressure, of a combi- energy production, would require matter nation of photons and solar wind from the and anti-matter to be stored at a safe dis- Sun, to push large ultra-thin mirrors to high tance from each other and to be able to com- speeds. tails are pushed away from bine them, a proper amount, at a proper the Sun by the same mechanism. time in order to be able to use the energy The momentum of a photon or an en- which is produced due to . tire flux is given by p = E/c, where E is The problem, however, is that all of the the photon or flux energy, p is the momen- current methods of manufacturing antimat- tum. At 1 au the flux density of solar ra- ter require enormous particle accelerators diation is 1.36 kW/m2, resulting in a pres- and produce antimatter in very small quan- sure of ∼ 4.5µPa. A perfectly reflecting sail tities, and to store antimatter, if we need with 1-sq. km area could thus yield a force a ton of magnets for one gram of antimat- ∼ 9 N, while the Sun’s gravitational force on ter, the entire idea of a lightweight way to one ton mass there is about 6 N. As both the store and carry immense amounts of energy radiation pressure and the gravity fall with remains no longer meaningful. Antimatter the square of distance from the Sun, a 1-ton could nevertheless perhaps find use in in- load attached to a sail of 1-sq. km area could

Volume/Issue/Article Number 11 www.physedu.in Physics Education Publication Date get pushed outward by the radiation pres- farther away. sure and thus escape the solar system. An idea similar to light sails could be Solar wind on the other hand exerts firing a particle beam at a spaceship that only a nominal dynamic pressure of about 3 would ride that energy. The problem with to 4 nPa, three orders of magnitude less than beams is that they disperse over dis- solar radiation pressure on a reflective sail, tance, so we could use particle beams. The and would not relatively have much effect. beam would have to have a neutral electrical A physically realistic approach would charge so as not to disperse itself over time. be to use the light from the Sun to acceler- ate. The ship would begin its trip away from 6.4 Bombs! the system using the light from the Sun to keep accelerating. Beyond some distance, Another idea for space travel would in- the ship would no longer receive enough volve riding explosions through space. Such light to accelerate it significantly, but would ”pulsed propulsion” would hurl bombs be- maintain its course due to inertia. When hind a ship, which is shielded with a giant nearing the target star, the ship could turn its plate. The explosions would push against sails toward it and begin to decelerate. Ad- the plate, propelling the ship. Nuclear ditional forward and reverse thrust could be pulsed propulsion works best for really big achieved with more conventional means of systems. If we want to send a colony of 1,000 propulsion such as rockets. people to space, this might be the way to do it

6.3 Laser sails or particle beams 7 Some other fanciful ideas Laser sails might be another way to go. Instead of relying just on the enormous 7.1 Interstellar travel by transmission amount of light given off by the Sun, laser sails to Proxima Centauri could also ride If physical entities could be decomposed as laser beams that the earthlings would fire “information”, then transmitted and then carefully at those ships to give an extra reconstructed at a destination, travel at boost, especially when sails were too far nearly the speed of light would be possi- away to catch much light from our Sun. The ble, which for the “travellers” would be in- problem with laser sails is that a lot of light stantaneous. However, sending an atom- needs to be used for a long time to get fast by-atom description of (say) a human body enough to get to Proxima Centauri within a would be a daunting task. Extracting and human lifetime. This means very powerful sending only a computer brain simulation is and extraordinarily large are needed a significant part of that problem. “Journey” in order to focus on sails that get farther and time would be the light-travel time plus the

Volume/Issue/Article Number 12 www.physedu.in Physics Education Publication Date time needed to encode, send and reconstruct time makes them not only extremely distant the whole transmission. from but, in terms of communication, also extremely isolated from the Earth. In fact 7.2 Generation-ships the communication issue could become the biggest problem. How will the people born A generation-ship is a kind of interstellar in an interstellar colony identify themselves ark in which crew that arrive at the desti- with no attachment to the Earth? Will they nation are descendants of those who started not feel literally excommunicated from the the journey. Generation ships are not cur- Earth? rently feasible, because of the difficulty of constructing a ship of the enormous re- quired scale, and the great biological and so- 8.2 Hard-hitting interstellar medium ciological problems that life aboard such a A major issue with traveling at extremely ship raises. high speeds is that interstellar dust and gas may cause considerable damage to the craft, 7.3 due to the high relative speeds and large Scientists and writers have postulated var- kinetic energies involved. A robust shield- ious techniques for suspended animation. ing method to mitigate this problem would These include human hibernation and cry- be needed. Larger objects (such as macro- onic preservation. While neither is cur- scopic dust grains) are far less common, but rently practical, they offer the possibility of would be much more destructive. The risks sleeper ships in which the passengers lie in- of impacting such objects, and methods of ert for the long years of the voyage, hope- mitigating these risks, will have to be ade- fully without many after-effects. quately addressed.

8 Other difficulties of interstellar 8.3 Manned missions

travel The mass of any craft capable of carry- ing humans would inevitably be substan- 8.1 Ex-communication! tially larger than that necessary for an un- The round-trip delay time is the minimum manned . The require- time taken for to-and-fro communication be- ments for food, water, medical and other tween the probe and the Earth. For Prox- life-sustaining needs of the crew will liter- ima Centauri this time would be 8.5 years. ally put huge burden on the mission. In Of course, in the case of a manned flight the case of interstellar missions, given the the crew can respond immediately to their vastly greater travel times involved, there emergencies. However, the round-trip delay will thus be the necessity of a closed-cycle

Volume/Issue/Article Number 13 www.physedu.in Physics Education Publication Date life support system, which would last over the deceleration and the return journey as decades. In generation ships, will there be well, the scenario becomes impossible as the a large enough gene pool for healthy future mass ratio for the nuclear fusion case swells generations? There will be the ethical ques- to R ∼ (4.7 × 106)4 ≈ 5 × 1026. So for a tions – Should a new-born be condemned to 10 ton payload, we will need a fuel mass of a life-time of journey in which he or she may ∼ 5 × 1033 gm, that is, equivalent to more have no choice whatsoever. Then there is the than two suns. Thus one will have to tug possibility that the new generations aboard along fuel mass equivalent to two suns or might change their mind and abandon the more, in order to accomplish a return trip mission or go elsewhere, keeping no contact to the nearest star beyond the Solar system. with the Earth. The fuel requirement could be reduced sub- stantially if we are able to somehow achieve nuclear fusion of hydrogen into iron, the ul- 9 A hypothetical journey! timate stage in the nuclear fusion, where the maimum exhaust speed becomes u = c/7.4 Let us make a hypothetical journey to Prox- (Appendix C). In that case the fuel needed ima Centauri, the star closest to the Solar for a return journey to Proxima Centauri, system, at a distance of 4.24 light years. For with a 10 ton payload, reduces to ∼ 3 × 1030, this we expand on a scenario created by Pur- equivalent to the mass of ∼ 500 . Still cell [1], with the crew always under an accel- an impossible amount of fuel. eration of 1g, the acceleration due to gravity, so that the they “feel at home”. From Equa- Though recently an earth-size planet tion (4) we find that the return trip will take has been found orbiting around α-Centauri a total of 12 years of the earth time, with the B, but it seems too close to the parent star top speed (Equation (2)) reaching 0.95c mid- and would be very hot and perhaps not hab- way point of the journey. However, from itable. It is estimated that to visit a habit- Equation (3), the traveller would age only by able planet and hopefully encounter some about 7 years. We already saw that a chem- extraterrestrial life, we may have to probe ical fuel cannot provide enough thrust as it stars up to about 12 light years. For in- does not give rise to large enough exhaust stance, b, a confirmed Earth-sized speed. So let us try nuclear fusion of hy- exoplanet, orbiting within the inner habit- drogen into helium, for which the best pos- able zone of the Ross 128, lies sible exhaust speed is u = c/8.4 (see Ap- at a distance of about 11 light years from pendix C). Then assuming a 100% efficiency, the Earth. Another exoplanet, , or- the equation (5) yields a biting within the habitable zone of the red mass ratio R ∼ 4.7 × 106 to reach a maxi- dwarf Luyten’s Star, is at a distance of 12.2 mum speed 0.95c. However, if we consider light years from our Solar system. With this

Volume/Issue/Article Number 14 www.physedu.in Physics Education Publication Date in mind, let us make a hypothetical return snowballs to R = (14)4 = 40,000 for the trip to an exoplanet, say, at a distance of 12 complete journey in four stages, implying light years. From Equation (4) we find that 200,000 tons of matter and antimatter each. the return trip will take a total of 28 years of For the early part of the journey we will the earth time, with the top speed (Equation need ∼ 1.2 × 1012 MW, about seven times (2)) reaching 0.99c midway point of the jour- more than the radiation that the Earth re- ney. However, from Equation (3), the trav- ceives from the Sun. But with all that in eller would age only by about 10 years. For gamma-rays, our problem will be not only the best possible exhaust speed is u = c/7.4, to shield the payload but also to shield the to reach 0.99c, the mass ratio for the nuclear Earth. Again, not a very promising scenario! fusion case swells to R ∼ 2 × 1034. So for a 10 ton payload we will need a fuel mass of ∼ 2 × 1041 gm, that is, equivalent to ∼ 100 10 Could we? Or should we? million suns. This would imply consum- ing, throughout the journey of 10 years on So far no one has created technology that is board, on the average, fuel mass about one widely agreed upon as capable of caring for third of the sun every second. This means or preserving humans across the lifetimes it the energy that the Sun produces during its might take to get to even Proxima Centauri; life time of ∼ 1010 years, would be con- it might easily take more than one lifetime to sumed every three seconds to accelerate the reach any ! If that is so, mission spaceship. In fact the fuel consumption will designers might have to take procreation be orders of magnitude higher in the initial and family into account so that offspring of the original crew would get properly edu- stages, being at a rate Mi g/u, that is ∼ 25 suns per second. A scenario not imaginable cated and trained to manage the ship in due even in the wildest of our fantasies. course. Thus a trip to our nearest star requires Thus forgetting the chemical fuel, even not only ingenious methods of propulsion the nuclear fusion could not be the source and a minimum of decades en route, but of energy for interstellar travel. And that also a sophisticated system of life support too when we restricted travels to only a few for the human crew to survive the journey. light years within the reach of the Solar Sys- Not only the costs and difficulties are al- tem. It is quite clear that, one would need an most insurmountable, but they would also exhaust speed, u ≈ c and matter-antimatter require almost unparalleled public and gov- annihilation only may provide it. To reach ernmental support. The ultimate question 0.99c, the mass ratio in such a case may ap- then might change from – Could we to pear to be manageable, R = 14, at least should we? for one leg of the journey, which however, Even if the constraints imposed by the

Volume/Issue/Article Number 15 www.physedu.in Physics Education Publication Date technology are ignored, the requirement of mediate stellar neighbourhood, as each such energy plays a huge constraint by itself. A excursion will exhaust the resources of their huge amount of fuel would have to be put to home planet so much that those will dwin- use for such an endeavour and many gener- dle rather fast and there might not be much ations of earthlings would have to work on left for the further scientific and technolog- such a project. ical advancements. So the science-fiction There is a very strong likelihood that fancy of a Galactic Empire may ever remain the mission would fail due to many other in our fantasies only. And as for the mythi- factors. We have ignored the requisites of cal UFOs, whose quiet appearances do get food and water and other medicinal require- reported in the press once in a while, re- ments for the crew. There is also the ef- cent explorations have shown no evidence fect of the harmful radiation such as cosmic that any such thing could have an origina- rays and impacts with other larger bodies. tion within our own solar system itself, a What if some deadly disease strikes? It is “quiet” return trip from a distant star is al- unlikely that living beings will be able to most impossible as it could not be so quiet as survive such ordeals for time periods of the the exhaust in any such trip will dazzle the order of decades. sky like many suns or perhaps more like a Further we have not even considered burst occurring, but not in a dis- the time and resources needed for possible tant part of the universe, instead going off research and conduction of experiments at right in our own solar backyard. the place of the destination, without which such a trip would not be of much advantage Appendix A: The distance-time to us, anyway. relation for an accelerated motion with relativistic speeds 11 Conclusions We can compute time T of a spaceship trav- Taking these severe limitations into account, eller, undergoing a proper acceleration g to we can conclude that space travel, even in achieve relativistic speeds, in terms of the the most distant future, will remain confined time t and distance x, as measured by a set to our own , and a similar of observers stationary with respect to the conclusion will hold forth for any other civ- launching station. We assume it to be a 1- ilization, no matter how advanced it might dimensional motion, say, along the x-axis, be, unless those extraterrestrial species have taking x = 0 and t = 0 at the start of the life spans order of magnitude longer than journey at T = 0. From relativistic transfor- ours. Even in such a case it is unlikely that mations, we have the time dilation formula, they will travel much farther than their im- dt = γ dT while for the longitudinal accel-

Volume/Issue/Article Number 16 www.physedu.in Physics Education Publication Date eration we have, dv/dt = g γ−3 [4]. Appendix B: The relativistic The equation of motion then is rocket equation

γ3dv = g dt = gγ dT. If in the instantaneous rest frame of the rocket, a fuel mass ∆m is consumed dur- We can integrate it ing a proper time ∆T, to generate energy that causes the expulsion of the propellent v T dv with an exhaust speed u, with a correspond- 2 = g dT. 0 1 − (v/c) 0 2 Z Z ing γu = 1/ 1 − (u/c) , For a constant proper acceleration g, we thus from the energy conservationp we have, ∆ ′ 2 ∆ 2 ∆ ′ get γu m c = mc , where m is the mass in the expelled fuel’s rest frame. The expelled v ∆ ′ ∆ = tanh(gT/c), mass carries a momentum, γu m u = mu c and from momentum conservation, we get which gives γ = cosh(gT/c). dM Mg = − u, From this we can get a relation between dT t and T as Using dT = dt/γ and g = γ3 dv/dt from t T T gT Appendix A, we get dt = γ dT = cosh dT, 0 0 0 c dv dM Z Z Z Mγ2 = − u, dt dt or or dv dM c gT = − u. t = sinh . − 2 g c 1 (v/c) M We can integrate it The distance covered is v dv M f dM = −u , x t T 2 gT 0 1 − (v/c) Mi M dx = v dt = c sinh dT, Z Z c Z0 Z0 Z0 to get v u or tanh−1 = ln R, c c c2 gT x = cosh − 1 . which can be written as g c   v Ru/c −R−u/c = tanh[ln Ru/c]= . Distance x can be expressed in terms of t as c Ru/c + R−u/c The relativistic rocket equation then is c2 gt 2 x = 1 + − 1 . v 1 −R−2u/c g s c  = ,   c 1 + R−2u/c   Volume/Issue/Article Number 17 www.physedu.in Physics Education Publication Date or References

c/2u (1 + v ) v c/u R = c = γ 1 + . [1] Purcell, E., Interstellar Communica- (1 − v ) c  c  h  i tion, ed. Cameron, A. G. W., Benjamin For a constant proper acceleration g, we sub- This yields for a nuclear fusion rocket, the stitute for v and γ from Appendix A, to get best possible values for the exhaust speed, u = c/8.4 , for ǫ = 0.71% R c/u = [cosh(gT/c)+ sinh(gT/c)] and = exp(gT/u). u = c/7.4 , for ǫ = 0.92%.

Appendix C: The exhaust velocity limit for a nuclear fusion rocket Inc. (1963), p. 121-143. In a nuclear fusion reaction of hydrogen into helium, an amount ǫ = 0.71% of the fuel [2] Sagan, C., Carl Sagan’s Cosmic mass gets converted into energy, while for Connection - An Extraterrestrial Per- a conversion from hydrogen to iron, the ulti- spective, Cambridge University Press mate stage in the nuclear fusion, the amount (2000). is ǫ = 0.92% [5]. The energy released by this amount [3] Sagan, C., Pale Blue Dot: A Vision of could be converted into the kinetic energy the Human Future in Space, Ballantine ′ 2 Books (1997). [(γu − 1)∆m c ] of the expelled fuel mass, giving [4] Jackson, J.D.: Classical Electrodynam- ′ 2 2 (γu − 1)∆m c = ǫ∆mc . ics, 2nd edn., Wiley, New York (1975).

′ Using γu∆m = ∆m (Appendix B), we get [5] von Hoerner, S., Interstellar Commu- nication, ed. Cameron, A. G. W., Ben- (1 − 1 − (u/c)2)= ǫ. jamin Inc. (1963), p. 144-159. q

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