Evolution of a Terrestrial Multiple Moon System
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The Surrender Software
Scientific image rendering for space scenes with the SurRender software Scientific image rendering for space scenes with the SurRender software R. Brochard, J. Lebreton*, C. Robin, K. Kanani, G. Jonniaux, A. Masson, N. Despré, A. Berjaoui Airbus Defence and Space, 31 rue des Cosmonautes, 31402 Toulouse Cedex, France [email protected] *Corresponding Author Abstract The autonomy of spacecrafts can advantageously be enhanced by vision-based navigation (VBN) techniques. Applications range from manoeuvers around Solar System objects and landing on planetary surfaces, to in -orbit servicing or space debris removal, and even ground imaging. The development and validation of VBN algorithms for space exploration missions relies on the availability of physically accurate relevant images. Yet archival data from past missions can rarely serve this purpose and acquiring new data is often costly. Airbus has developed the image rendering software SurRender, which addresses the specific challenges of realistic image simulation with high level of representativeness for space scenes. In this paper we introduce the software SurRender and how its unique capabilities have proved successful for a variety of applications. Images are rendered by raytracing, which implements the physical principles of geometrical light propagation. Images are rendered in physical units using a macroscopic instrument model and scene objects reflectance functions. It is specially optimized for space scenes, with huge distances between objects and scenes up to Solar System size. Raytracing conveniently tackles some important effects for VBN algorithms: image quality, eclipses, secondary illumination, subpixel limb imaging, etc. From a user standpoint, a simulation is easily setup using the available interfaces (MATLAB/Simulink, Python, and more) by specifying the position of the bodies (Sun, planets, satellites, …) over time, complex 3D shapes and material surface properties, before positioning the camera. -
Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Monte Carlo Methods to Calculate Impact Probabilities⋆
A&A 569, A47 (2014) Astronomy DOI: 10.1051/0004-6361/201423966 & c ESO 2014 Astrophysics Monte Carlo methods to calculate impact probabilities? H. Rickman1;2, T. Wisniowski´ 1, P. Wajer1, R. Gabryszewski1, and G. B. Valsecchi3;4 1 P.A.S. Space Research Center, Bartycka 18A, 00-716 Warszawa, Poland e-mail: [email protected] 2 Dept. of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden 3 IAPS-INAF, via Fosso del Cavaliere 100, 00133 Roma, Italy 4 IFAC-CNR, via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy Received 9 April 2014 / Accepted 28 June 2014 ABSTRACT Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik(1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill(1967, J. Geophys. Res., 72, 2429). Aims. We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods. We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. -
Phobos, Deimos: Formation and Evolution Alex Soumbatov-Gur
Phobos, Deimos: Formation and Evolution Alex Soumbatov-Gur To cite this version: Alex Soumbatov-Gur. Phobos, Deimos: Formation and Evolution. [Research Report] Karpov institute of physical chemistry. 2019. hal-02147461 HAL Id: hal-02147461 https://hal.archives-ouvertes.fr/hal-02147461 Submitted on 4 Jun 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Phobos, Deimos: Formation and Evolution Alex Soumbatov-Gur The moons are confirmed to be ejected parts of Mars’ crust. After explosive throwing out as cone-like rocks they plastically evolved with density decays and materials transformations. Their expansion evolutions were accompanied by global ruptures and small scale rock ejections with concurrent crater formations. The scenario reconciles orbital and physical parameters of the moons. It coherently explains dozens of their properties including spectra, appearances, size differences, crater locations, fracture symmetries, orbits, evolution trends, geologic activity, Phobos’ grooves, mechanism of their origin, etc. The ejective approach is also discussed in the context of observational data on near-Earth asteroids, main belt asteroids Steins, Vesta, and Mars. The approach incorporates known fission mechanism of formation of miniature asteroids, logically accounts for its outliers, and naturally explains formations of small celestial bodies of various sizes. -
Supplementary Information For
Supplementary Information for Vertical Angular Momentum Constraint on Lunar Formation and Orbital History ZhenLiang Tian and Jack Wisdom Z. Tian, J. Wisdom E-mail: [email protected], [email protected] This PDF file includes: Supplementary text Figs. S1 to S4 Table S1 References for SI reference citations www.pnas.org/cgi/doi/10.1073/pnas.2003496117 ZhenLiang Tian and Jack Wisdom 1 of 11 Supporting Information Text Model Comparison. Our model, which is the same as in (1), differs from the model of (2) in the following aspects: 1. Probably the most important difference is the tidal model. We use the conventional Darwin-Kaula constant Q model (3). In this model the tidal potential is expanded in a Fourier series and the response to each term is given a phase delay to model dissipation, by analogy to the damped harmonic oscillator. The explicit form builds in considerable constraints from orbital mechanics. There is little observational evidence to constrain the phase delays, but results from the analysis of lunar laser ranging (LLR) data are consistent with the Darwin-Kaula choice to set all the phase delays to be equal (4). Ćuk et al. (2) stated that there is a problem with the constant Q model: that it predicts a decay of orbital eccentricity that, to leading order, is independent of eccentricity. However, this is not true. Using the expressions in (3), one can show that the constant Q model gives a decay of eccentricity that is, to leading order, proportional to eccentricity. Nevertheless, given this misunderstanding of the constant Q model, Ćuk et al. -
Can Moons Have Moons?
A MNRAS 000, 1–?? (2018) Preprint 23 January 2019 Compiled using MNRAS L TEX style file v3.0 Can Moons Have Moons? Juna A. Kollmeier1⋆ & Sean N. Raymond2† 1 Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena, CA 91101 2 Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, all´eGeoffroy Saint-Hilaire, 33615 Pessac, France Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Each of the giant planets within the Solar System has large moons but none of these moons have their own moons (which we call submoons). By analogy with studies of moons around short-period exoplanets, we investigate the tidal-dynamical stability of submoons. We find that 10 km-scale submoons can only survive around large (1000 km-scale) moons on wide-separation orbits. Tidal dissipation destabilizes the orbits of submoons around moons that are small or too close to their host planet; this is the case for most of the Solar System’s moons. A handful of known moons are, however, capable of hosting long-lived submoons: Saturn’s moons Titan and Iapetus, Jupiter’s moon Callisto, and Earth’s Moon. Based on its inferred mass and orbital separation, the newly-discovered exomoon candidate Kepler-1625b-I can in principle host a large submoon, although its stability depends on a number of unknown parameters. We discuss the possible habitability of submoons and the potential for subsubmoons. The existence, or lack thereof, of submoons, may yield important constraints on satellite formation and evolution in planetary systems. Key words: planets and satellites – exoplanets – tides 1 INTRODUCTION the planet spins quickly or to shrink if the planet spins slowly (e.g. -
The Chaotic Rotation of Hyperion*
ICARUS 58, 137-152 (1984) The Chaotic Rotation of Hyperion* JACK WISDOM AND STANTON J. PEALE Department of Physics, University of California, Santa Barbara, California 93106 AND FRANGOIS MIGNARD Centre d'Etudes et de Recherehes G~odynamique et Astronomique, Avenue Copernic, 06130 Grasse, France Received August 22, 1983; revised November 4, 1983 A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the 1/2 and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and 1/2 states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional mo- tions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. -
Constraints on the Habitability of Extrasolar Moons 3 ¯Glob Its Orbit-Averaged Global Energy flux Fs
Formation, detection, and characterization of extrasolar habitable planets Proceedings IAU Symposium No. 293, 2012 c 2012 International Astronomical Union Nader Haghighipour DOI: 00.0000/X000000000000000X Constraints on the habitability of extrasolar moons Ren´eHeller1 and Rory Barnes2,3 1Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam email: [email protected] 2University of Washington, Dept. of Astronomy, Seattle, WA 98195, USA 3Virtual Planetary Laboratory, NASA, USA email: [email protected] Abstract. Detections of massive extrasolar moons are shown feasible with the Kepler space telescope. Kepler’s findings of about 50 exoplanets in the stellar habitable zone naturally make us wonder about the habitability of their hypothetical moons. Illumination from the planet, eclipses, tidal heating, and tidal locking distinguish remote characterization of exomoons from that of exoplanets. We show how evaluation of an exomoon’s habitability is possible based on the parameters accessible by current and near-future technology. Keywords. celestial mechanics – planets and satellites: general – astrobiology – eclipses 1. Introduction The possible discovery of inhabited exoplanets has motivated considerable efforts towards estimating planetary habitability. Effects of stellar radiation (Kasting et al. 1993; Selsis et al. 2007), planetary spin (Williams & Kasting 1997; Spiegel et al. 2009), tidal evolution (Jackson et al. 2008; Barnes et al. 2009; Heller et al. 2011), and composition (Raymond et al. 2006; Bond et al. 2010) have been studied. Meanwhile, Kepler’s high precision has opened the possibility of detecting extrasolar moons (Kipping et al. 2009; Tusnski & Valio 2011) and the first dedicated searches for moons in the Kepler data are underway (Kipping et al. -
Positioning: Drift Orbit and Station Acquisition
Orbits Supplement GEOSTATIONARY ORBIT PERTURBATIONS INFLUENCE OF ASPHERICITY OF THE EARTH: The gravitational potential of the Earth is no longer µ/r, but varies with longitude. A tangential acceleration is created, depending on the longitudinal location of the satellite, with four points of stable equilibrium: two stable equilibrium points (L 75° E, 105° W) two unstable equilibrium points ( 15° W, 162° E) This tangential acceleration causes a drift of the satellite longitude. Longitudinal drift d'/dt in terms of the longitude about a point of stable equilibrium expresses as: (d/dt)2 - k cos 2 = constant Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF EARTH ASPHERICITY VARIATION IN THE LONGITUDINAL ACCELERATION OF A GEOSTATIONARY SATELLITE: Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN & MOON ATTRACTION Gravitational attraction by the sun and moon causes the satellite orbital inclination to change with time. The evolution of the inclination vector is mainly a combination of variations: period 13.66 days with 0.0035° amplitude period 182.65 days with 0.023° amplitude long term drift The long term drift is given by: -4 dix/dt = H = (-3.6 sin M) 10 ° /day -4 diy/dt = K = (23.4 +.2.7 cos M) 10 °/day where M is the moon ascending node longitude: M = 12.111 -0.052954 T (T: days from 1/1/1950) 2 2 2 2 cos d = H / (H + K ); i/t = (H + K ) Depending on time within the 18 year period of M d varies from 81.1° to 98.9° i/t varies from 0.75°/year to 0.95°/year Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN RADIATION PRESSURE Due to sun radiation pressure, eccentricity arises: EFFECT OF NON-ZERO ECCENTRICITY L = difference between longitude of geostationary satellite and geosynchronous satellite (24 hour period orbit with e0) With non-zero eccentricity the satellite track undergoes a periodic motion about the subsatellite point at perigee. -
Lecture 12 the Rings and Moons of the Outer Planets October 15, 2018
Lecture 12 The Rings and Moons of the Outer Planets October 15, 2018 1 2 Rings of Outer Planets • Rings are not solid but are fragments of material – Saturn: Ice and ice-coated rock (bright) – Others: Dusty ice, rocky material (dark) • Very thin – Saturn rings ~0.05 km thick! • Rings can have many gaps due to small satellites – Saturn and Uranus 3 Rings of Jupiter •Very thin and made of small, dark particles. 4 Rings of Saturn Flash movie 5 Saturn’s Rings Ring structure in natural color, photographed by Cassini probe July 23, 2004. Click on image for Astronomy Picture of the Day site, or here for JPL information 6 Saturn’s Rings (false color) Photo taken by Voyager 2 on August 17, 1981. Click on image for more information 7 Saturn’s Ring System (Cassini) Mars Mimas Janus Venus Prometheus A B C D F G E Pandora Enceladus Epimetheus Earth Tethys Moon Wikipedia image with annotations On July 19, 2013, in an event celebrated the world over, NASA's Cassini spacecraft slipped into Saturn's shadow and turned to image the planet, seven of its moons, its inner rings -- and, in the background, our home planet, Earth. 8 Newly Discovered Saturnian Ring • Nearly invisible ring in the plane of the moon Pheobe’s orbit, tilted 27° from Saturn’s equatorial plane • Discovered by the infrared Spitzer Space Telescope and announced 6 October 2009 • Extends from 128 to 207 Saturnian radii and is about 40 radii thick • Contributes to the two-tone coloring of the moon Iapetus • Click here for more info about the artist’s rendering 9 Rings of Uranus • Uranus -- rings discovered through stellar occultation – Rings block light from star as Uranus moves by. -
Predictable Patterns in Planetary Transit Timing Variations and Transit Duration Variations Due to Exomoons
Astronomy & Astrophysics manuscript no. ms c ESO 2016 June 21, 2016 Predictable patterns in planetary transit timing variations and transit duration variations due to exomoons René Heller1, Michael Hippke2, Ben Placek3, Daniel Angerhausen4, 5, and Eric Agol6, 7 1 Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany; [email protected] 2 Luiter Straße 21b, 47506 Neukirchen-Vluyn, Germany; [email protected] 3 Center for Science and Technology, Schenectady County Community College, Schenectady, NY 12305, USA; [email protected] 4 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; [email protected] 5 USRA NASA Postdoctoral Program Fellow, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA 6 Astronomy Department, University of Washington, Seattle, WA 98195, USA; [email protected] 7 NASA Astrobiology Institute’s Virtual Planetary Laboratory, Seattle, WA 98195, USA Received 22 March 2016; Accepted 12 April 2016 ABSTRACT We present new ways to identify single and multiple moons around extrasolar planets using planetary transit timing variations (TTVs) and transit duration variations (TDVs). For planets with one moon, measurements from successive transits exhibit a hitherto unde- scribed pattern in the TTV-TDV diagram, originating from the stroboscopic sampling of the planet’s orbit around the planet–moon barycenter. This pattern is fully determined and analytically predictable after three consecutive transits. The more measurements become available, the more the TTV-TDV diagram approaches an ellipse. For planets with multi-moons in orbital mean motion reso- nance (MMR), like the Galilean moon system, the pattern is much more complex and addressed numerically in this report. -
Abstracts of the 50Th DDA Meeting (Boulder, CO)
Abstracts of the 50th DDA Meeting (Boulder, CO) American Astronomical Society June, 2019 100 — Dynamics on Asteroids break-up event around a Lagrange point. 100.01 — Simulations of a Synthetic Eurybates 100.02 — High-Fidelity Testing of Binary Asteroid Collisional Family Formation with Applications to 1999 KW4 Timothy Holt1; David Nesvorny2; Jonathan Horner1; Alex B. Davis1; Daniel Scheeres1 Rachel King1; Brad Carter1; Leigh Brookshaw1 1 Aerospace Engineering Sciences, University of Colorado Boulder 1 Centre for Astrophysics, University of Southern Queensland (Boulder, Colorado, United States) (Longmont, Colorado, United States) 2 Southwest Research Institute (Boulder, Connecticut, United The commonly accepted formation process for asym- States) metric binary asteroids is the spin up and eventual fission of rubble pile asteroids as proposed by Walsh, Of the six recognized collisional families in the Jo- Richardson and Michel (Walsh et al., Nature 2008) vian Trojan swarms, the Eurybates family is the and Scheeres (Scheeres, Icarus 2007). In this theory largest, with over 200 recognized members. Located a rubble pile asteroid is spun up by YORP until it around the Jovian L4 Lagrange point, librations of reaches a critical spin rate and experiences a mass the members make this family an interesting study shedding event forming a close, low-eccentricity in orbital dynamics. The Jovian Trojans are thought satellite. Further work by Jacobson and Scheeres to have been captured during an early period of in- used a planar, two-ellipsoid model to analyze the stability in the Solar system. The parent body of the evolutionary pathways of such a formation event family, 3548 Eurybates is one of the targets for the from the moment the bodies initially fission (Jacob- LUCY spacecraft, and our work will provide a dy- son and Scheeres, Icarus 2011).