Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Small Solar System Bodies as granular media

Abstract

Asteroids and other Small Solar System Bodies (SSSBs) are of high general and scientific interest in many aspects. The origin, formation, and evolution of our Solar System (and other planetary systems) can be better understood by analysing the constitution and physical properties of small bodies in the Solar System. Currently, two space missions (Hayabusa2, OSIRIS-REx) have recently arrived at their respective targets and will bring a sample of the asteroids back to Earth. Other small body missions have also been selected by, or proposed to, space agencies. The threat posed to our planet by near-Earth objects (NEOs) is also considered at the international level, and this has prompted dedicated research on possible mitigation techniques. The DART mission, for example, will test the kinetic impact technique. Even ideas for industrial exploitation have risen during the last years. Lastly, the origin of water and life on Earth appears to be connected to asteroids. Hence, future space mission projects will undoubtedly target some asteroids or other SSSBs. In all these cases and research topics, specific knowledge of the structure and mechanical behaviour of the surface as well as the bulk of those celestial bodies is crucial. In contrast to large telluric planets and dwarf planets, a large proportion of such small bodies is believed to consist of gravitational aggregates (‘rubble piles’) with no—or low—internal cohesion, with varying macro-porosity and surface properties (from smooth regolith covered terrain, to very rough collection of boulders), and varying topography (craters, depressions, ridges). Bodies with such structure can sustain some plastic deformation without being disrupted in contrast to the classical visco-elastic models that are generally valid for planets, dwarf planets, and large satellites. These SSSBs are hence better described through granular mechanics theories, which have been a subject of intense theoretical, experimental, and numerical research over the last four decades. This being the case, it has been necessary to use the theoretical, numerical and experimental tools developed within soil mechanics, granular dynamics, celestial mechanics, chemistry, condensed matter physics, planetary and computer sciences, to name the main ones, in order to understand the data collected and analysed by observational astronomy (visible, thermal, and radio), and different space missions. In this paper, we present a review of the multi-disciplinary research carried out by these different scientific communities in an effort to study SSSBs.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Notes

  1. 1.

    http://www.unoosa.org/oosa/en/ourwork/spacelaw/treaties/introouterspacetreaty.html.

  2. 2.

    More precisely the macroscopic porosity.

  3. 3.

    Micro-porosity on the other hand is in the matrix of the grains or meteorites. Micro-porosity is a porosity that will survive entry in the atmosphere.

  4. 4.

    Possibly including relativistic effects, but this is not relevant in this paper on small bodies.

  5. 5.

    SpaceGrains ESA Topical Team from the European Space Agency https://spacegrains.org.

  6. 6.

    Sizes, when not measured directly, are estimated from the absolute magnitude H and by assuming an albedo of 0.2.

References

  1. Abe S, Mukai T, Hirata N, Barnouin-Jha OS, Cheng AF, Demura H, Gaskell RW, Hashimoto T, Hiraoka K, Honda T et al (2006) Mass and local topography measurements of Itokawa by Hayabusa. Science 312(5778):1344–1347

  2. Agnolin I, Roux JN (2007a) Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks. Phys Rev E 76(6):061302

  3. Agnolin I, Roux JN (2007b) Internal states of model isotropic granular packings III. Elastic properties. Phys Rev E Stat Nonlin Soft Matter Phys 76:061304

  4. Ahrens TJ, Harris AW (1992) Deflection and fragmentation of near-Earth asteroids. Nature 360(6403):429–433

  5. Ai J, Chen JF, Rotter JM, Ooi JY (2011) Assessment of rolling resistance models in discrete element simulations. Powder Technol 206(3):269–282. https://doi.org/10.1016/j.powtec.2010.09.030

  6. Alder BJ, Wainwright TE (1959) Studies in molecular dynamics. I. General method. J Chem Phys 31(2):459–466. https://doi.org/10.1063/1.1730376

  7. Alder BJ, Wainwright TE (1960) Studies in molecular dynamics. II. Behavior of a small number of elastic spheres. J Chem Phys 33(5):1439–1451. https://doi.org/10.1063/1.1731425

  8. Andert T, Rosenblatt P, Pätzold M, Häusler B, Dehant V, Tyler G, Marty J (2010) Precise mass determination and the nature of Phobos. Geophys Res Lett 37(9):L09202

  9. Andreotti B, Forterre Y, Pouliquen O (2013) Granular media: between fluid and solid. Cambridge University Press, Cambridge

  10. Aranson IS, Tsimring LS (2006) Patterns and collective behavior in granular media: theoretical concepts. Rev Mod Phys 78:641

  11. Asphaug E (2009) Growth and evolution of asteroids. Annu Rev Earth Planet Sci 37:413–448

  12. Asphaug E, Ostro SJ, Hudson R, Scheeres DJ, Benz W (1998) Disruption of kilometre-sized asteroids by energetic collisions. Nature 393(6684):437

  13. Asphaug E, Ryan EV, Zuber MT (2002) Asteroid interiors. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 463–484

  14. Azéma E, Sánchez P, Scheeres DJ (2018) Scaling behavior of cohesive self-gravitating aggregates. Phys Rev E 98:030901. https://doi.org/10.1103/PhysRevE.98.030901

  15. Azéma E, Estrada N, Preechawuttipong I, Delenne JY, Radjai F (2017) Systematic description of the effect of particle shape on the strength properties of granular media. EPJ Web Conf 140:06026. https://doi.org/10.1051/epjconf/201714006026

  16. Baer J, Chesley SR (2017) Simultaneous mass determination for gravitationally coupled asteroids. Astron J 154(2):76

  17. Bagatin AC, Petit JM, Farinella P (2001) How many rubble piles are in the asteroid belt? Icarus 149(1):198–209

  18. Ballouz R (2017) Numerical simulations of granular physics in the solar system. Ph.D. thesis, University of Maryland, College Park

  19. Ballouz RL, Richardson DC, Michel P, Schwartz SR, Yu Y (2015) Numerical simulations of collisional disruption of rotating gravitational aggregates: dependence on material properties. Planet Space Sci 107:29–35

  20. Bancelin D, Pilat-Lohinger E, Maindl TI, Ragossnig F, Schäfer C (2017) The influence of orbital resonances on the water transport to objects in the circumprimary habitable zone of binary star systems. Astron J 153(6):269

  21. Bardyn A, Baklouti D, Cottin H, Fray N, Briois C, Paquette J, Stenzel O, Engrand C, Fischer H, Hornung K et al (2017) Carbon-rich dust in comet 67P/Churyumov-Gerasimenko measured by COSIMA/Rosetta. Mon Not R Astron Soc 469(Suppl 2):S712–S722

  22. Barnes J, Hut P (1986) A hierarchical \(\text{ O }(N \log N)\) force-calculation algorithm. Nature 324:446–449. https://doi.org/10.1038/324446a0

  23. Belskaya I, Cellino A, Gil-Hutton R, Muinonen K, Shkuratov Y (2015) Asteroid polarimetry. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 151–163

  24. Ben-Naim E, Knight J, Nowak E, Jaeger H, Nagel S (1998) Slow relaxation in granular compaction. Phys D 123(1–4):380–385

  25. Benner LAM, Busch MW, Giorgini JD, Taylor PA, Margot JL (2015) Radar observations of near-Earth and main-belt asteroids. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 165–182. https://doi.org/10.2458/azu_uapress_9780816532131-ch009

  26. Binzel RP, Gehrels T, Matthews MS (eds) (1989) Asteroids II. University of Arizona Press, Tucson

  27. Biele J, Kesseler L, Grimm CD, Schröder S, Mierheim O, Lange M, Ho TM (2017) Experimental determination of the structural coefficient of restitution of a bouncing asteroid lander. arXiv:1705.00701

  28. Binzel RP, Morbidelli A, Merouane S, DeMeo FE, Birlan M, Vernazza P, Thomas CA, Rivkin AS, Bus SJ, Tokunaga AT (2010) Earth encounters as the origin of fresh surfaces on near-Earth asteroids. Nature 463(7279):331

  29. Board SS, Council NR et al (2010) Defending planet earth: near-Earth-object surveys and hazard mitigation strategies. National Academies Press, Washington

  30. Bockelée-Morvan D, Gil-Hutton R, Hestroffer D, Belskaya IN, Davidsson BJ, Dotto E, Fitzsimmons A, Kawakita H, Mothe-Diniz T, Licandro J et al (2016) Division F Commission 15: Physical study of comets and minor planets. Proc IAU 11(T29A):316–339

  31. Bottke WF Jr, Cellino A, Paolicchi P, Binzel RP (eds) (2002) Asteroids III. University of Arizona Press, Tucson

  32. Bottke WF Jr, Durda DD, Nesvornỳ D, Jedicke R, Morbidelli A, Vokrouhlickỳ D, Levison H (2005) The fossilized size distribution of the main asteroid belt. Icarus 175(1):111–140

  33. Bouzid M, Izzet A, Trulsson M, Clément E, Claudin P, Andreotti B (2015) Non-local rheology in dense granular flows. Eur Phys J E 38(11):125

  34. Braga-Ribas F, Sicardy B, Ortiz J, Snodgrass C, Roques F, Vieira-Martins R, Camargo J, Assafin M, Duffard R, Jehin E et al (2014) A ring system detected around the Centaur (10199) Chariklo. Nature 508(7494):72

  35. Brian Dade W, Huppert HE (1998) Long-runout rockfalls. Geology 26(9):803–806

  36. Brilliantov NV, Pöschel T (2010) Kinetic theory of granular gases. Oxford University Press, Oxford

  37. Brilliantov NV, Formella A, Pöschel T (2018) Increasing temperature of cooling granular gases. Nat Commun 9:797

  38. Brisset J, Heißelmann D, Kothe S, Weidling R, Blum J (2016) Submillimetre-sized dust aggregate collision and growth properties. experimental study of a multi-particle system on a suborbital rocket. Astron Astrophys 593:A3

  39. Brisset J, Heißelmann D, Kothe S, Weidling R, Blum J (2017) Low-velocity collision behaviour of clusters composed of sub-millimetre sized dust aggregates. Astron Astrophys 603:A66

  40. Britt DT, Consolmagno GJ (2001) Modeling the structure of high porosity asteroids. Icarus 152(1):134–139

  41. Britt DT, Yeomans D, Housen K, Consolmagno G (2002) Asteroid density, porosity, and structure. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 485–500

  42. Burtally N, King PJ, Swift MR (2002) Spontaneous air-driven separation in vertically vibrated fine granular mixtures. Science 295(5561):1877–1879. https://doi.org/10.1126/science.1066850

  43. Busch MW, Ostro SJ, Benner LAM, Brozovic M, Giorgini JD, Jao JS, Scheeres DJ, Magri C, Nolan MC, Howell ES, Taylor PA, Margot JL, Brisken W (2011) Radar observations and the shape of near-Earth asteroid 2008 EV5. Icarus 212:649–660. https://doi.org/10.1016/j.icarus.2011.01.013. arXiv:1101.3794

  44. Butcher JC (2016) Numerical methods for ordinary differential equations. Wiley, New York

  45. Campins H, Hargrove K, Pinilla-Alonso N, Howell ES, Kelley MS, Licandro J, Mothé-Diniz T, Fernández Y, Ziffer J (2010) Water ice and organics on the surface of the asteroid 24 Themis. Nature 464(7293):1320

  46. Campo Bagatin A, Alemañ RA, Benavidez PG, Richardson DC (2018a) Gravitational re-accumulation as the origin of most contact binaries and other small body shapes. Icarus 302:343–359. https://doi.org/10.1016/j.icarus.2017.11.024

  47. Campo Bagatin A, Alemañ RA, Benavidez PG, Richardson DC (2018b) Internal structure of asteroid gravitational aggregates. Icarus 302:343–359

  48. Cantelaube F, Bideau D (1995) Radial segregation in a 2d drum: an experimental analysis. Europhy Lett 30:3

  49. Caps H, Michel R, Lecoq N, Vandewalle N (2003) Long lasting instabilities in granular mixtures. Phys A 326:313

  50. Carry B (2012) Density of asteroids. Planet Space Sci 73(1):98–118

  51. Cattuto C, Marconi UMB (2004) Ordering phenomena in cooling granular mixtures. Phys Rev Lett 92:174502

  52. Chamberlin A (2018) NEO discovery statistics. http://neo.jpl.nasa.gov/stats. Accessed July 2018

  53. Chapman C (1977) The evolution of asteroids as meteorite parent-bodies. Comets, asteroids, meteorites: interrelations, evolution and origins. IAU Colloq 39:265–275

  54. Chapman C, Veverka J, Thomas P, Klaasen K, Belton M, Harch A, McEwen A, Johnson T, Helfenstein P, Davies M et al (1995) Discovery and physical properties of Dactyl, a satellite of asteroid 243 Ida. Nature 374(6525):783–785

  55. Cheng AF, Izenberg N, Chapman CR, Zuber MT (2002) Ponded deposits on asteroid 433 Eros. Meteorit Planet Sci 37:1095–1105. https://doi.org/10.1111/j.1945-5100.2002.tb00880.x

  56. Cheng AF, Michel P, Jutzi M, Rivkin AS, Stickle A, Barnouin O, Ernst C, Atchison J, Pravec P, Richardson DC et al (2016) Asteroid impact and deflection assessment mission: kinetic impactor. Planet Space Sci 121:27–35

  57. Chujo T, Mori O, Kawaguchi J, Yano H (2017) Categorization of Brazil nut effect and its reverse under less-convective conditions for microgravity geology. Mon Not R Astron Soc 474(4):4447–4459

  58. Cizeau P, Makse HA, Stanley HE (1999) Mechanisms of granular spontaneous stratification and segregation in two-dimensional silos. Phys Rev E 59:4408

  59. Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Model 26:89–111

  60. Clement E, Rajchenbach J, Duran J (1995) Mixing of a granular material in a bidimensional rotating drum. Europhy Lett 30:1

  61. Coulomb CA (1776) Essai sur une application des règles des maximis et minimis à quelques problèmes de statique relatifs à l’architecture. Mémoires de l’Académie Royale des Sciences 7:343–382

  62. Comito C (2012) Numerical \(N\)-body approach to binary asteroid formation and evolution. Ph.D. thesis, Università degli studi di Torino; Université Nice Sophia Antipolis

  63. Comito C, Thirouin A, Campo Bagatin A, Tanga P, Ortiz JL, Richardson DC (2011) Deformation and splitting of asteroids by YORP spin-up. In: EPSC-DPS joint meeting 2011, p 420

  64. Cotto-Figueroa D, Statler TS, Richardson DC, Tanga P (2015) Coupled spin and shape evolution of small rubble-pile asteroids: self-limitation of the YORP effect. Astrophys J 803(1):25

  65. Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

  66. Daniels KE (2013) Rubble-pile near Earth objects: insights from granular physics. In: Badescu V (ed) Asteroids: prospective energy and material resources. Springer, Berlin, Heidelberg, pp 271–286. https://doi.org/10.1007/978-3-642-39244-3_11

  67. Delbo M, Mueller M, Emery JP, Rozitis B, Capria MT (2015) Asteroid thermophysical modeling. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 107–128

  68. DeMeo F, Alexander C, Walsh K, Chapman C, Binzel R (2015) The compositional structure of the asteroid belt. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 13–41. https://doi.org/10.2458/azu_uapress_9780816532131-ch002

  69. Dijksman JA, Rietz F, Lõrincz KA, van Hecke M, Losert W (2012) Invited article: refractive index matched scanning of dense granular materials. Rev Sci Instrum 83(1):011301. https://doi.org/10.1063/1.3674173

  70. Dobrovolskis AR (1982) Internal stresses in Phobos and other triaxial bodies. Icarus 52(1):136–148

  71. Dohnanyi JS (1969) Collisional model of asteroids and their debris. J Geophys Res 74(10):2531–2554

  72. Donev A, Cisse I, Dand Sachs EA, Variano Stillinger FH, Connelly R, Torquato S, Chaikin PM (2004) Improving the density of jammed disordered packings using ellipsoids. Science 303:990–993

  73. Dove A, Anderson S, Gomer G, Fraser M, John K, Fries M (2018) Regolith stratification and migration in an asteroid-like environment. Lunar Planet Sci Conf 49:2993

  74. Drube L, Harris AW, Engel K, Falke A, Johann U, Eggl S, Cano JL, Ávila JM, Schwartz SR, Michel P (2016) The NEOT\(\omega \)IST mission (Near-Earth Object Transfer of angular momentum spin test). Acta Astronaut 127:103–111. https://doi.org/10.1016/j.actaastro.2016.05.009

  75. Durda DD, Bagatin AC, Alemañ RA, Flynn GJ, Strait MM, Clayton AN, Patmore EB (2015) The shapes of fragments from catastrophic disruption events: effects of target shape and impact speed. Planet Space Sci 107:77–83. https://doi.org/10.1016/j.pss.2014.10.006 (VIII workshop on catastrophic disruption in the solar system)

  76. Durech J, Carry B, Delbo M, Kaasalainen M, Viikinkoski M (2015) Asteroid models from multiple data sources. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 183–202. https://doi.org/10.2458/azu_uapress_9780816532131-ch010

  77. Dziugys A, Navakas R (2009) The role of friction in mixing and segregation of granular material. Granul Matter 11:403–416

  78. Eggl S, Hestroffer D, Thuillot W, Bancelin D, Cano JL, Cichocki F (2015) Post mitigation impact risk analysis for asteroid deflection demonstration missions. Adv Space Res 56:528–548. https://doi.org/10.1016/j.asr.2015.02.030

  79. Eggl S, Hestroffer D, Cano JL, Ávila JM, Drube L, Harris AW, Falke A, Johann U, Engel K, Schwartz SR, Michel P (2016) Dealing with uncertainties in asteroid deflection demonstration missions: NEOT\(\omega \)IST. In: Chesley SR, Morbidelli A, Jedicke R, Farnocchia D (eds) IAU symposium, vol 318, pp 231–238, https://doi.org/10.1017/S1743921315008698. arXiv:1601.02103

  80. Falcon E, Wunenburger R, Evesque P, Fauve S, Chabot C, Garrabos Y, Beysens D (1999) Cluster formation in a granular medium fluidized by vibrations in low gravity. Phys Rev Lett 83:440

  81. Falcon E, Bacri JC, Laroche C (2013) Equation of state of a granular gas homogeneously driven by particle rotations. Europhys Lett 103(64):004

  82. Fall A, Weber B, Pakpour M, Lenoir N, Shahidzadeh N, Fiscina J, Wagner C, Bonn D (2014) Sliding friction on wet and dry sand. Phys Rev Lett 112(175):502. https://doi.org/10.1103/PhysRevLett.112.175502

  83. Fan Y, Boukerkour Y, Blanc T, Umbanhowar P, Ottino JM, Lueptow RM (2012) Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps. Phys Rev E 86(051):305

  84. Faraday M (1831) On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos Trans R Soc London 121:299–340. http://www.jstor.org/stable/107936

  85. Farinella P, Paolicchi P, Tedesco E, Zappala V (1981) Triaxial equilibrium ellipsoids among the asteroids? Icarus 46(1):114–123

  86. Félix G, Thomas N (2004) Relation between dry granular flow regimes and morphology of deposits: formation of levées in pyroclastic deposits. Earth Planet Sci Lett 221(1–4):197–213

  87. Ferellec JF, McDowell GR (2010) A method to model realistic particle shape and inertia in DEM. Granul Matter 12:459–467

  88. Festou M, Keller HU, Weaver HA (2004) Comets II. University of Arizona Press, Tucson

  89. Finger T, von Rüling F, Lévay S, Szabó B, Börzsönyi T, Stannarius R (2016) Segregation of granular mixtures in a spherical tumbler. Phys Rev E 93:032903

  90. Fischer D, Finger T, Angenstein F, Stannarius R (2009) Diffusive and subdiffusive axial transport of granular material in rotating mixers. Phys Rev E 80:061302

  91. Fries M, Abell P, Brisset J, Britt D, Colwell J, Dove A, Durda D, Graham L, Hartzell C, Hrovat K, John K, Karrer D, Leonard M, Love S, Morgan J, Poppin J, Rodriguez V, Sánchez-Lana P, Scheeres D, Whizin A (2018) The Strata-1 experiment on small body regolith segregation. Acta Astronaut 142:87–94. https://doi.org/10.1016/j.actaastro.2017.10.025

  92. Fries M, Abell P, Brisset J, Britt D, Colwell J, Durda D, Dove A, Graham L, Hartzell C, John K, Leonard M, Love S, Sánchez DP, Scheeres DJ (2016) Strata-1: an international space station experiment into fundamental regolith properties in microgravity. In: Lunar and planetary science conference, LPI contributions, vol 1903, p 2799

  93. Fujiwara A, Kawaguchi J, Yeomans D, Abe M, Mukai T, Okada T, Saito J, Yano H, Yoshikawa M, Scheeres D et al (2006) The rubble-pile asteroid Itokawa as observed by Hayabusa. Science 312(5778):1330–1334

  94. Gaia-Collaboration Spoto F, Tanga P, Mignard F, Berthier J, Carry B, Cellino A (2018) Gaia data release 2: observations of solar system objects. Astron Astrophys 616:A13. https://doi.org/10.1051/0004-6361/201832900

  95. Galache J, Graps A, Asime 2016 Contributors (2017) ASIME 2016 white paper: answers to questions from the asteroid miners. In: European planetary science congress, vol 11, p 985

  96. Gao Z, Zhao J, Li XS, Dafalias YF (2014) A critical state sand plasticity model accounting for fabric evolution. Int J Numer Anal Methods Geomech 38:370–390

  97. Garcimartin A, Maza D, Ilquimiche JL, Zuriguel I (2002) Convective motion in a vibrated granular layer. Phys Rev E 65:031303

  98. Gehrels T, Matthews MS (eds) (1979) Asteroids. University of Arizona Press, Tucson

  99. Gehrels T, Drummond J, Levenson N (1987) The absence of satellites of asteroids. Icarus 70(2):257–263

  100. Godoy S, Risso D, Soto R, Cordero P (2008) Rise of a Brazil nut: a transition line. Phys Rev E 78:031301

  101. Goldhirsch I, Zanetti G (1993) Clustering instability in dissipative gases. Phys Rev Lett 70:1619

  102. Goldreich P, Tremaine S (1978) The velocity dispersion in Saturn’s rings. Icarus 34(2):227–239

  103. Gray JNMT, Ancey C (2011) Multi-component particle size-segregation in shallow granular avalanches. J Fluid Mech 678:535–558

  104. Gray JNMT, Thornton AR (2005) A theory for particle size segregation in shallow granular free-surface flows. Proc R Soc Lond Ser A 461:1447

  105. Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73(2):325–348. https://doi.org/10.1016/0021-9991(87)90140-9

  106. Guillard F, Forterre Y, Pouliquen O (2014) Lift forces in granular media. Phys Fluids 26(4):043301

  107. Gundlach B, Blum G (2013) A new method to determine the grain size of planetary regolith. Icarus 223:479–492

  108. Güttler C, von Borstel I, Schräpler R, Blum J (2013) Granular convection and the Brazil nut effect in reduced gravity. Phys Rev E 87:044201

  109. Haff P (1983) Grain flow as a fluid-mechanical phenomenon. J Fluid Mech 134:401–430

  110. Hajra SK, Khakhar DV (2011) Radial segregation of ternary granular mixtures in rotating cylinders. Granul Matter 13(4):475–486

  111. Harrington M, Weijs JH, Losert W (2013) Suppression and emergence of granular segregation under cyclic shear. Phys Rev Lett 111:078001. https://doi.org/10.1103/PhysRevLett.111.078001

  112. Harrington M, Lin M, Nordstrom KN, Losert W (2014) Experimental measurements of orientation and rotation of dense 3D packings of spheres. Granul Matter 16(2):185–191. https://doi.org/10.1007/s10035-013-0474-0

  113. Harris AW (1996) The rotation rates of very small asteroids: evidence for ‘rubble pile’ structure. In: Lunar and planetary science conference, vol 27

  114. Harris AW, Lagerros JS (2002) Asteroids in the thermal infrared. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson

  115. Harris AW, Fahnestock EG, Pravec P (2009) On the shapes and spins of ‘rubble pile’ asteroids. Icarus 199(2):310–318

  116. Harris A, Barucci M, Cano J, Fitzsimmons A, Fulchignoni M, Green S, Hestroffer D, Lappas V, Lork W, Michel P et al (2013) The European Union funded NEOShield project: a global approach to near-Earth object impact threat mitigation. Acta Astronaut 90(1):80–84

  117. Harth K, Kornek U, Trittel T, Strachauer U, Höme S, Will K, Stannarius R (2013) Granular gases of rod-shaped grains in microgravity. Phys Rev Lett 110:144102

  118. Harthong B, Jérier JF, Dorémus P, Imbault D, Donzé FV (2009) Modeling of high-density compaction of granular materials by the discrete element method. Int J Solids Struct 46(18):3357–3364

  119. Hartzell C, Carter D (2017) Electrostatic forces on grains near asteroids and comets. In: EPJ web conference, EDP sciences, vol 140, p 14009

  120. Heisselmann D, Blum J, Fraser HJ, Wolling K (2010) Microgravity experiments on the collisional behavior of Saturnian ring particles. Icarus 206:424–430

  121. Henych T, Holsapple KA (2018) Interpretations of family size distributions: the Datura example. Icarus 304:127–134. https://doi.org/10.1016/j.icarus.2017.05.018

  122. Herique A, Agnus B, Asphaug E, Barucci A, Beck P, Bellerose J, Biele J, Bonal L et al (2018) Direct observations of asteroid interior and regolith structure: science measurement requirements. Adv Space Res 62:2141–2162. https://doi.org/10.1016/j.asr.2017.10.020

  123. Hernquist L (1987) Performance characteristics of tree codes. Astrophys J Suppl Ser 64:715–734. https://doi.org/10.1086/191215

  124. Herrmann H, Luding S (1998) Modeling granular media on the computer. Contin Mech Thermodyn 10:189–231. https://doi.org/10.1007/s001610050089

  125. Hestroffer D (1998) Photocentre displacement of minor planets: analysis of Hipparcos astrometry. Astron Astrophys 336:776–781

  126. Hestroffer D, Dell’Oro A, Cellino A, Tanga P (2010) The Gaia mission and the asteroids. In: Souchay JJ, Dvorak R (eds) Dynamics of small solar system bodies and exoplanets. Springer, Berlin, pp 251–340. https://doi.org/10.2458/azu_uapress_9780816532131-ch012

  127. Hestroffer D, Agnan M, Segret B, Quinsac G, Vannitsen J, Rosenblatt P, Miau JJ (2017a) BIRDY—interplanetary CubeSat for planetary geodesy of small solar system bodies (SSSB). In: AGU fall meeting abstracts

  128. Hestroffer D, Bagatín AC, Losert W, Opsomer E, Sánchez P, Scheeres DJ, Staron L, Taberlet N, Yano H, Eggl S et al (2017b) Small solar system bodies as granular systems. EPJ Web Conf 140:14011. https://doi.org/10.105epjconf/201714014011

  129. Hill KM, Gioia G, Amaravadi D (2004) Radial segregation patterns in rotating granular mixtures: waviness selection. Phys Rev Lett 93:224301

  130. Hilton JL (2002) Asteroid masses and densities. In: Bottke WF Jr, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 103–112

  131. Hirabayashi M (2014) Structural failure of two-density-layer cohesionless biaxial ellipsoids. Icarus 236:178–180. https://doi.org/10.1016/j.icarus.2014.02.024

  132. Hirabayashi M, Scheeres DJ (2014) Analysis of asteroid (216) Kleopatra using dynamical and structural constraints. Astrophys J 780(2):160

  133. Hirabayashi M, Scheeres DJ (2015) Stress and failure analysis of rapidly rotating asteroid (29075) 1950DA. Astrophys J Lett 798(1):L8

  134. Hirabayashi M, Scheeres DJ, Sánchez DP, Gabriel T (2014) Constraints on the Physical properties of main belt comet P/2013 R3 from its breakup event. Astrophys J Lett 789(1):L12

  135. Hirabayashi M, Sánchez DP, Scheeres DJ (2015) Internal structure of asteroids having surface shedding due to rotational instability. Astrophys J 808(1):63

  136. Hirabayashi M, Scheeres DJ, Chesley SR, Marchi S, McMahon JW, Steckloff J, Mottola S, Naidu SP, Bowling T (2016) Fission and reconfiguration of bilobate comets as revealed by 67P/Churyumov-Gerasimenko. Nature 534(7607):352

  137. Hockney RW, Eastwood JW (1988) Computer simulation using particles. CRC Press, Boca Raton

  138. Holsapple KA (2001) Equilibrium configurations of solid cohesionless bodies. Icarus 154(2):432–448. https://doi.org/10.1006/icar.2001.6683

  139. Holsapple KA (2004) Equilibrium figures of spinning bodies with self-gravity. Icarus 172:272–303. https://doi.org/10.1016/j.icarus.2004.05.023

  140. Holsapple KA (2007) Spin limits of solar system bodies: from the small fast-rotators to 2003 EL61. Icarus 187(2):500–509. https://doi.org/10.1016/j.icarus.2006.08.012

  141. Holsapple K, Giblin I, Housen K, Nakamura A, Ryan E (2002) Asteroid impacts: laboratory experiments and scaling laws. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 443–462

  142. Hong DC, Quinn PV, Luding S (2001) Reverse brazil nut problem: competition between percolation and condensation. Phys Rev Lett 86:15

  143. Hou M, Liu R, Zhai G, Sun Z, Lu K, Garrabos Y, Evesque P (2008) Velocity distribution of vibration-driven granular gas in Knudsen regime in microgravity. Microgravity Sci Technol 20:73–80

  144. Hsieh HH, Jewitt D (2006) A population of comets in the main asteroid belt. Science 312(5773):561–563

  145. Huerta DA, Ruiz-Suarez JC (2004) Vibration-induced granular segregation: a phenomenon driven by three mechanisms. Phys Rev Lett 92:11

  146. Hut P, Makino J, McMillan S (1995) Building a better leapfrog. Astrophys J 443:L93–L96

  147. Jacobson SA, Scheeres DJ (2011) Dynamics of rotationally fissioned asteroids: source of observed small asteroid systems. Icarus 214:161–178. https://doi.org/10.1016/j.icarus.2011.04.009

  148. Jacobson R, Spitale J, Porco C, Beurle K, Cooper N, Evans M, Murray C (2007) Revised orbits of Saturn’s small inner satellites. Astron J 135(1):261

  149. Jaeger HM, Nagel SR, Behringer RP (1996a) Granular solids, liquids, and gases. Rev Mod Phys 68:1259–1273. https://doi.org/10.1103/RevModPhys.68.1259

  150. Jaeger HM, Nagel SR, Behringer RP (1996b) The physics of granular materials. Phys Today 49(4):32–38

  151. Jean M (1999) The non-smooth contact dynamics method. Comput Methods Appl Mech Eng 177(3–4):235–257

  152. Jenkins J, Richman M (1985) Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys Fluids 28(12):3485–3494

  153. Jenkins JT, Savage SB (1983) A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J Fluid Mech 130:187–202

  154. Jewitt D (2009) The active centaurs. Astron J 137:4296–4312. https://doi.org/10.1088/0004-6256/137/5/4296

  155. Jewitt D, Agarwal J, Weaver H, Mutchler M, Larson S (2013) The extraordinary multi-tailed main-belt comet P/2013 P5. Astrophys J Lett 778(1):L21

  156. Jewitt D, Agarwal J, Li J, Weaver H, Mutchler M, Larson S (2014) Disintegrating asteroid P/2013 R3. Astrophys J Lett 784(1):L8

  157. Jewitt D, Hsieh H, Agarwal J (2015) The active asteroids. In: Michel P, DeMeo FE, Bottke WF (eds) Asteroids IV. University of Arizona Press, Tucson, pp 221–241. https://doi.org/10.2458/azu_uapress_9780816532131-ch012

  158. John KK, Saucedo VL, Fisher KR, Fries MD, Dove AR, Leonard MJ, Graham LD, Abell PA (2018) Hermes microgravity research facility on the ISS. In: Lunar and planetary science conference, vol 49, p 1790

  159. Jones R, Chesley S, Connolly A, Harris A, Ivezic Z, Knezevic Z, Kubica J, Milani A, Trilling D, Collaboration LSSS et al (2009) Solar System science with LSST. Earth Moon Planets 105(2–4):101–105

  160. Jop P, Forterre Y, Pouliquen O (2006) A constitutive law for dense granular flows. Nature 441(7094):727

  161. Jutzi M, Michel P (2014) Hypervelocity impacts on asteroids and momentum transfer I. Numerical simulations using porous targets. Icarus 229:247–253

  162. Jutzi M, Michel P, Benz W, Richardson DC (2010) Fragment properties at the catastrophic disruption threshold: the effect of the parent body’s internal structure. Icarus 207(1):54–65. https://doi.org/10.1016/j.icarus.2009.11.016

  163. Kaasalainen M, Torppa J (2001) Optimization methods for asteroid lightcurve inversion. I. Shape determination. Icarus 153:24–36

  164. Kaasalainen M, Torppa J, Muinonen K (2001) Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem. Icarus 153:37–51

  165. Kaasalainen M, Mottola S, Fulchignoni M (2002) Asteroid models from disk-integrated data. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 139–150

  166. Kay JP, Dombard AJ (2018) Formation of the bulge of Iapetus through long-wavelength folding of the lithosphere. Icarus 302:237–244

  167. Kelfoun K (2011) Suitability of simple rheological laws for the numerical simulation of dense pyroclastic flows and long-runout volcanic avalanches. J Geophys Res 116:B08209. https://doi.org/10.1029/2010JB007622

  168. Kerr RA (1985) Could an asteroid be a comet in disguise; two asteroids of the inner solar system are strong candidates for once-active comets that now masquerade as inert hunks of rock. Science 227:930–932

  169. Khakhar DV, McCarthy J, Shinbrot T, Ottino JM (1997) Radial segregation of granular mixtures in rotating cylinders. Phys Fluids 9:3600

  170. Khakhar DV, Orpe VA, Hajra SK (2003) Segregation of granular materials in rotating cylinders. Phys A 318:126

  171. Kim T, Nam J, Yun J, Lee K, You S, (2009) Relationship between cohesion and tensile strength in wet sand at low normal stresses. In: Proceedings of 17th international conference on soil mechanics and geotechnical engineering, Olexandria, (2009) vol 367. JOS Press, Amsterdam, Berlin, Tokyo, Washington, p 364

  172. Klypin A (2017) Methods for cosmological \(N\)-body simulations. http://www.skiesanduniverses.org/resources/KlypinNbody.pdf. Accessed July 2018

  173. Knight JB, Jaeger HM, Nagel S (1993) Vibration-induced size separation in granular media: the convection connection. Phys Rev Lett 70:24

  174. Koeppe JP, Enz M, Kakalios J (1998) Phase diagram for avalanche stratification of granular media. Phys Rev E 58:R4104

  175. Kok JF, Parteli EJR, Michaels TI, Karam DB (2012) The physics of wind-blown sand and dust. Rep Progr Phys 75(10):106901

  176. Konopliv AS, Miller JK, Owen WM, Yeomans DK, Giorgini JD, Garmier R, Barriot JP (2002) A global solution for the gravity field, rotation, landmarks, and ephemeris of Eros. Icarus 160(2):289–299

  177. Kou B, Cao Y, Li J, Xia C, Li Z, Dong H, Zhang A, Zhang J, Kob W, Wang Y (2017) Granular materials flow like complex fluids. Nature 551(7680):360

  178. Kudrolli A (2004a) Size separation in vibrated granular matter. Rep Progr Phys 67(3):209

  179. Kudrolli A (2004b) Size separation in vibrated granular matter. Rep Progr Phys 67:209

  180. Lagrée PY, Staron L, Popinet S (2011) The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with a \(\mu \) (I)-rheology. J Fluid Mech 686:378–408

  181. Landau LD, Lifshitz E (1986) Theory of elasticity, course of theoretical physics, vol 7. Butterworth-Heinemann, Oxford

  182. Lauretta DS, Team Osiris-Rex et al (2019) The unexpected surface of asteroid (101955) Bennu. Nature 568(7750):55–60. https://doi.org/10.1038/s41586-019-1033-6

  183. Leconte M, Garrabos Y, Falcon E, Lecoutre-Chabot C, Palencia F, Evesque P, Beysens D (2006) Microgravity experiments on vibrated granular gases in a dilute regime: non-classical statistics. J Stat Mech 7:07012

  184. Lee V, Waitukaitis SR, Miskin MZ, Jaeger HM (2015) Direct observation of particle interactions and clustering in charged granular streams. Nat Phys 11:733–737

  185. Leinhardt ZM, Richardson DC, Quinn T (2000) Direct N-body simulations of rubble pile collisions. Icarus 146:133–151. https://doi.org/10.1006/icar.2000.6370. arXiv:astro-ph/9908221

  186. Levasseur-Regourd AC, Rotundi A, Bentley M, Della Corte V, Fulle M, Hadamcik E, Hilchenbach M, Hines D, Lasue J, Merouane S, et al (2015) Physical properties of dust particles in cometary comae: from clues to evidence with the Rosetta mission. In: European planetary science congress 2015, vol 10, p EPSC2015-932

  187. Li JY, Helfenstein P, Buratti B, Takir D, Clark BE (2015) Asteroid photometry. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 129–150. https://doi.org/10.2458/azu_uapress_9780816532131-ch007

  188. Liu AJ, Nagel SR (1998) Nonlinear dynamics: jamming is not just cool any more. Nature 396(6706):21–22

  189. Liu C, Nagel SR, Schecter DA, Coppersmith SN, Majumdar S, Narayan O, Witten TA (1995) Force fluctuations in bead packs. Science 269:513

  190. Lohse D, Bergmann R, Mikkelsen R, Zeilstra C, van der Meer D, Versluis M, van der Weele K, van der Hoef M, Kuipers H (2004) Impact on soft sand: void collapse and jet formation. Phys Rev Lett 93:198003. https://doi.org/10.1103/PhysRevLett.93.198003

  191. Losert W, Cooper DGW, Delour J, Kudrolli A, Gollub JP (1999) Velocity statistics in excited granular media. Chaos 9:682

  192. Louge MY, Jenkins JT, Xu H, Arnarson BÖ (2002) Granular segregation in collisional shearing flows. In: Aref H, Phillips JW (eds) Mechanics for a New Millennium. Springer, Dordrecht, pp 239–252

  193. Lu M, McDowell GR (2007) The importance of modelling ballast particle shape in the discrete element method. Granul Matter 9:69

  194. Lu XP, Cellino A, Hestroffer D, Ip WH (2016) Cellinoid shape model for hipparcos data. Icarus 267:24–33

  195. Lubachevsky BD (1991) How to simulate billiards and similar systems. J Comput Phys 94(2):255–283. https://doi.org/10.1016/0021-9991(91)90222-7

  196. Lucas A, Mangeney A, Ampuero JP (2014) Frictional velocity-weakening in landslides on Earth and on other planetary bodies. Nat Commun 5:3417

  197. Lucchitta BK (1979) Landslides in Valles Marineris. Mars. J Geophys Res 84(B14):8097–8113

  198. Ludewig F, Vandewalle N (2012) Strong interlocking of nonconvex particles in random packings. Phys Rev E 85:051307

  199. Maaß CC, Isert N, Maret G, Aegerter CM (2008) Experimental investigation of the freely cooling granular gas. Phys Rev Lett 100:248001

  200. Makse HA (1999) Continuous avalanche segregation of granular mixtures in thin rotating drums. Phys Rev Lett 83:3186

  201. Makse HA, Ball RC, Stanley HE, Warr S (1998) Dynamics of granular stratification. Phys Rev Lett 58:3357

  202. Marchis F, Hestroffer D, Descamps P, Berthier J, Bouchez AH, Campbell RD, Chin JC, Van Dam MA, Hartman SK, Johansson EM et al (2006) A low density of \(0.8\,\text{ g } \text{ cm }^{-3}\) for the Trojan binary asteroid 617 Patroclus. Nature 439(7076):565

  203. Margot JL, Pravec P, Taylor P, Carry B, Jacobson S (2015) Asteroid systems: binaries, triples, and pairs. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 355–374

  204. Masiero JR, Grav T, Mainzer AK, Nugent CR, Bauer JM, Stevenson R, Sonnett S (2014) Main-belt Asteroids with WISE/NEOWISE: near-infrared Albedos. Astrophys J 791:121. https://doi.org/10.1088/0004-637X/791/2/121. arXiv:1406.6645

  205. Masiero JR, Nugent C, Mainzer AK, Wright EL, Bauer JM, Cutri RM, Grav T, Kramer E, Sonnett S (2017) NEOWISE reactivation mission year three: asteroid diameters and albedos. Astron J 154(4):168

  206. Matsumura S, Richardson DC, Michel P, Schwartz SR, Ballouz RL (2014) The Brazil nut effect and its application to asteroids. Mon Not R Astron Soc 443:3368–3380

  207. Mattson W, Rice BM (1999) Near-neighbor calculations using a modified cell-linked list method. Comput Phys Commun 119(2–3):135–148

  208. Maurel C, Ballouz RL, Richardson DC, Michel P, Schwartz SR (2017) Numerical simulations of oscillation-driven regolith motion: Brazil-nut effect. Mon Not R Astron Soc 464:2866–2881. https://doi.org/10.1093/mnras/stw2641

  209. McCarthy DF, McCarthy DF (1977) Essentials of soil mechanics and foundations. Reston Publishing Company, Reston

  210. McMahon J, Scheeres D, Hesar S, Farnocchia D, Chesley S, Lauretta D (2018) The OSIRIS-REx radio science experiment at Bennu. Space Sci Rev 214(1):43. https://doi.org/10.1007/s11214-018-0480-y

  211. McNamara S, Young WR (1994) Inelastic collapse in two dimensions. Phys Rev E 50:R28–R31. https://doi.org/10.1103/PhysRevE.50.R28

  212. Meech KJ, Weryk R, Micheli M, Kleyna JT, Hainaut OR, Jedicke R, Wainscoat RJ, Chambers KC, Keane JV, Petric A et al (2017) A brief visit from a red and extremely elongated interstellar asteroid. Nature 552(7685):378

  213. Mehta A (1994) Granular matter: an interdisciplinary approach. Springer, New York. https://doi.org/10.1007/978-1-4612-4290-1

  214. Merline WJ, Close L, Dumas C, Chapman C, Roddier F, Menard F, Slater D, Duvert G, Shelton C, Morgan T (1999) Discovery of a moon orbiting the asteroid 45 Eugenia. Nature 401(6753):565

  215. Merline WJ, Weidenschilling SJ, Durda DD, Margot JL, Pravec P, Storrs AD (2002) Asteroids do have satellites. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona, Tucson, pp 289–312

  216. Metzger MJ, Remy B, Glasser BJ (2011) All the Brazil nuts are not on top: vibration induced granular size segregation of binary, ternary and multi-sized mixtures. Powder Technol 205:42–51

  217. Michel P, Richardson DC (2013) Collision and gravitational reaccumulation: possible formation mechanism of the asteroid Itokawa. Astron Astrophys 554:L1

  218. Michel P, Benz W, Tanga P, Richardson DC (2001) Collisions and gravitational reaccumulation: forming asteroid families and satellites. Science 294(5547):1696–1700

  219. Michel P, Tanga P, Benz W, Richardson DC (2002) Formation of asteroid families by catastrophic disruption: simulations with fragmentation and gravitational reaccumulation. Icarus 160:10–23. https://doi.org/10.1006/icar.2002.6948

  220. Michel P, Richardson DC, Durda DD, Jutzi M, Asphaug E (2015a) Collisional formation and modeling of asteroid families. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 341–354

  221. Michel P, DeMeo FE, Bottke WF (eds) (2015b) Asteroids IV. University of Arizona Press, Tucson. https://doi.org/10.2458/azu_uapress_9780816532131

  222. Michel P, Kueppers M, Sierks H, Carnelli I, Cheng AF, Mellab K, Granvik M, Kestilä A et al (2018) European component of the AIDA mission to a binary asteroid: characterization and interpretation of the impact of the DART mission. Adv Space Res 62:2261–2272. https://doi.org/10.1016/j.asr.2017.12.020

  223. MiDi-GDR, (2004) On dense granular flows. Eur Phys J E 14:341–365. https://doi.org/10.1140/epje/i2003-10153-0

  224. Miyamoto H, Yano H, Scheeres DJ, Abe S, Barnouin-Jha O, Cheng AF, Demura H, Gaskell RW, Hirata N, Ishiguro M, Michikami T, Nakamura AM, Nakamura R, Saito J, Sasaki S (2007) Regolith migration and sorting on asteroid Itokawa. Science. https://doi.org/10.1126/science.1134390

  225. Möbius M, Lauderdale BE, Nagel SR, Jaeger HM (2001) Brazil-nut effect: size separation of granular particles. Nature 414:270

  226. Morbidelli A, Chambers J, Lunine J, Petit JM, Robert F, Valsecchi G, Cyr K (2000) Source regions and timescales for the delivery of water to the Earth. Meteorit Planet Sci 35(6):1309–1320

  227. Moreau JJ (1994) Some numerical methods in multibody dynamics: application to granular materials. Eur J Mech A 13:93–114

  228. Mouret S, Hestroffer D, Mignard F (2007) Asteroid masses and improvement with Gaia. Astron Astrophys 472:1017–1027. https://doi.org/10.1051/0004-6361:20077479

  229. Movshovitz N, Asphaug E, Korycansky D (2012) Numerical modeling of the disruption of comet D/1993 F2 Shoemaker-Levy 9 representing the progenitor by a gravitationally bound assemblage of randomly shaped polyhedra. Astrophys J 759(2):93

  230. Müller TG, Marciniak A, Kiss C, Duffard R, Alí-Lagoa V, Bartczak P, Butkiewicz-Ba̧k M, Dudziński G, et al (2018) Small bodies near and Far (SBNAF): a benchmark study on physical and thermal properties of small bodies in the solar system. Adv Space Res 62:2326–2341. https://doi.org/10.1016/j.asr.2017.10.018

  231. Murdoch N, Michel P, Richardson DC, Nordstrom K, Berardi CR, Green SF, Losert W (2012) Numerical simulations of granular dynamics II: particle dynamics in a shaken granular material. Icarus 219(1):321–335

  232. Murdoch N, Rozitis B, Green S, Lophem TL, Michel P, Losert W (2013a) Granular shear flow in varying gravitational environments. Granul Matter 15(2):129–137. https://doi.org/10.1007/s10035-013-0395-y

  233. Murdoch N, Rozitis B, Green S, Michel P, de Lophem TL, Losert W (2013b) Simulating regoliths in microgravity. Mon Not R Astron Soc 433(1):506–514

  234. Murdoch N, Rozitis B, Nordstrom K, Green S, Michel P, de Lophem T, Losert W (2013) Granular convection in microgravity. Phys Rev Lett 110(1):018307. https://doi.org/10.1103/PhysRevLett.110.018307

  235. Murdoch N, Sánchez P, Schwartz SR, Miyamoto H (2015) Asteroid surface geophysics. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 767–792. https://doi.org/10.2458/azu_uapress_9780816532131-ch039

  236. Murdoch N, Avila Martinez I, Sunday C, Zenou E, Cherrier O, Cadu A, Gourinat Y (2017a) An experimental study of low-velocity impacts into granular material in reduced gravity. Mon Not R Astron Soc 468(2):1259–1272

  237. Murdoch N, Hempel S, Pou L, Cadu A, Garcia RF, Mimoun D, Margerin L, Karatekin O (2017b) Probing the internal structure of the asteroid Didymoon with a passive seismic investigation. Planet Space Sci 144:89–105

  238. Murdoch N, Cadu A, Mimoun D, Karatekin O, Garcia R, Carrasco J, Garcia de Quiros J, Vasseur H, Ritter B, Eubanks M, et al (2016) Investigating the surface and subsurface properties of the Didymos binary asteroid with a landed CubeSat. In: EGU general assembly conference abstracts, vol 18, p 12140

  239. Neuffer D, Schultz R (2006) Mechanisms of slope failure in Valles Marineris. Mars. Q J Eng Geol Hydrogeol 39(3):227–240

  240. Noirhomme M, Fand Ludewig N, Vandewalle Opsomer E (2017) Cluster growth in driven granular gases. Phys Rev E 95(022):905

  241. Noll KS, Grundy WM, Chiang EI, Margot JL, Kern SD (2008) Binaries in the Kuiper belt. In: Barucci MA, Boehnhardt H, Cruikshank DP, Morbidelli A (eds) The solar system beyond neptune. University of Arizona Press, Tucson, pp 345–363

  242. O’Brien DP, Walsh KJ, Morbidelli A, Raymond SN, Mandell AM (2014) Water delivery and giant impacts in the ’Grand Tack’ scenario. Icarus 239:74–84

  243. Ogawa S (1978) Multitemperature theory of granular materials. In: Proceedings of the US–Japan seminar on continuum mechanical and statistical approaches in the mechanics of granular materials, Gakajutsu Bunken Fukyu-Kai, pp 208–217

  244. Opsomer E, Ludewig F, Vandewalle N (2011) Phase transitions in vibrated granular systems in microgravity. Phys Rev E 84(051):306

  245. Opsomer E, Vandewalle N, Noirhomme M, Ludewig F (2014) Clustering and segregation in driven granular fluids. Eur Phys J E 37:115. https://doi.org/10.1140/epje/i2014-14115-1

  246. Opsomer E, Noirhomme M, Vandewalle N, Falcon E, Merminod S (2017) Segregation and pattern formation in dilute granular media under microgravity conditions. npj Microgravity 3:1

  247. Orpe A, Khakhar DV (2001) Scaling relations for granular flow in quasi-two-dimensional rotating cylinders. Phys Rev E 64:031302

  248. Ortiz JL, Santos-Sanz P, Sicardy B, Benedetti-Rossi G, Bérard D, Morales N, Duffard R, Braga-Ribas F, Hopp U, Ries C et al (2017) The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation. Nature 550(7675):219

  249. Ostro SJ, Hudson RS, Benner LAM, Giorgini JD, Magri C, Margot JL, Nolan MC (2002) Asteroid radar astronomy. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 151–168

  250. Ottino JM, Khakhar DV (2000) Mixing and segregation of granular materials. Annu Rev Fluid Mech 32(1):55–91. https://doi.org/10.1146/annurev.fluid.32.1.55

  251. Oyama Y (1939) Axial segregation of granular materials. Bull Inst Phys Chem Res (Tokyo) Rep 5 18:600

  252. Paetzold M (2017) Mass determination of small bodies in the solar system. In: AGU fall meeting abstracts

  253. Pähtz T, Herrmann HJ, Shinbrot T (2010) Why do particle clouds generate electric charges? Nat Phys 6:364. https://doi.org/10.1038/nphys1631

  254. Patrick R, Nicodemi M, Delannay R, Ribiere P, Bideau D (2005) Slow relaxation and compaction of granular systems. Nat Mat 4(2):121

  255. Peale S, Canup R (2015) The origin of the natural satellites. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 559–604. https://doi.org/10.1016/B978-0-444-53802-4.00177-9

  256. Pelton JN, Allahdadi F (eds) (2015) Handbook of cosmic hazards and planetary defense. Springer, Cham. https://doi.org/10.1007/978-3-319-03952-7

  257. Pena AA, Garcia-Rojo R, Herrmann HJ (2007) Influence of particle shape on sheared dense granular media. Granul Matter 9:279–291

  258. Perera V, Jackson AP, Asphaug E, Ballouz RL (2016) The spherical Brazil nut effect and its significance to asteroids. Icarus 278:194–203

  259. Perna D, Dotto E, Ieva S, Barucci MA, Bernardi F, Fornasier S, De Luise F, Perozzi E, Rossi A, Mazzotta Epifani E, Micheli M, Deshapriya JDP (2016) Grasping the nature of potentially hazardous asteroids. Astron J 151:11. https://doi.org/10.3847/0004-6256/151/1/11

  260. Pletser V (2004) Short duration microgravity experiments in physical and life sciences during parabolic flights: the first 30 ESA campaigns. Acta Astronaut 55:829–854

  261. Polishook D, Moskovitz N, Binzel R, Burt B, DeMeo F, Hinkle M, Lockhart M, Mommert M, Person M, Thirouin A et al (2016) A 2 km-size asteroid challenging the rubble-pile spin barrier–a case for cohesion. Icarus 267:243–254

  262. Pöschel T, Brilliantov NV (2003) Granular gas dynamics, lecture notes in physics, vol 624. Springer, Berlin. https://doi.org/10.1007/b12449

  263. Pouliquen O, Cassar C, Jop P, Forterre Y, Nicolas M (2006) Flow of dense granular material: towards simple constitutive laws. J Stat Mech 07:P07020

  264. Poux M, Fayote P, Bertrand J, Bridons D, Bousquet J (1991) Strong interlocking of nonconvex particles in random packings. Powder Technol 8:63

  265. Pravec P, Harris AW (2000) Fast and slow rotation of asteroids. Icarus 148(1):12–20. https://doi.org/10.1006/icar.2000.6482

  266. Pravec P, Harris AW, Michalowski T (2002) Asteroid rotations. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 113–122

  267. Pravec P, Vokrouhlickỳ D, Polishook D, Scheeres DJ, Harris AW, Galad A, Vaduvescu O, Pozo F, Barr A, Longa P et al (2010) Formation of asteroid pairs by rotational fission. Nature 466(7310):1085

  268. Procopio AT, Zavaliangos A (2005) Simulation of multi-axial compaction of granular media from loose to high relative densities. J Mech Phys Solids 53(7):1523–1551

  269. Radjai F (2015) Modeling force transmission in granular materials. C R Phys 16:3–9

  270. Radjaï F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley-ISTE, New York

  271. Radjai F, Richefeu V (2009a) Bond anisotropy and cohesion of wet granular materials. Philos Trans R Soc A 367:5123–5138

  272. Radjai F, Richefeu V (2009b) Contact dynamics as a nonsmooth discrete element method. Mech Mater 41(6):715–728

  273. Radjai F, Jean M, Moreau JJ, Roux S (1996) Force distributions in dense two-dimensional granular systems. Phys Rev Lett 77(2):274

  274. Radjai F, Schäfer J, Dipple S, Wolf D (1997) Collective friction of an array of particles: a crucial test for numerical algorithms. J Phys I 7(9):1053–1070

  275. Richardson DC (1993) A new tree code method for simulation of planetesimal dynamics. Mon Not R Astron Soc 261:396–414. https://doi.org/10.1093/mnras/261.2.396

  276. Richardson DC (1994) Tree code simulations of planetary rings. Mon Not R Astron Soc 269:493. https://doi.org/10.1093/mnras/269.2.493

  277. Richardson DC, Quinn T, Stadel J, Lake G (2000) Direct large-scale \(N\)-body simulations of planetesimal dynamics. Icarus 143(1):45–59. https://doi.org/10.1006/icar.1999.6243

  278. Richardson DC, Leinhardt ZM, Melosh HJ, Bottke WF Jr, Asphaug E (2002) Gravitational aggregates: evidence and evolution. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 501–515

  279. Richardson JE, Melosh HJ, Greenberg R (2004) Impact-induced seismic activity on asteroid 433 Eros: a surface modification process. Science 306(5701):1526–1529

  280. Richardson D, Michel P, Walsh K, Flynn K (2009) Numerical simulations of asteroids modelled as gravitational aggregates with cohesion. Planet Space Sci 57(2):183–192

  281. Richardson DC, Walsh KJ, Murdoch N, Michel P (2011) Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests. Icarus 212(1):427–437

  282. Rietz F, Stannarius R (2008) On the brink of jamming: granular convection in densely filled containers. Phys Rev Lett 100(7):078002. https://doi.org/10.1103/PhysRevLett.100.078002

  283. Rivkin AS, Emery JP (2010) Detection of ice and organics on an asteroidal surface. Nature 464(7293):1322

  284. Rocchetti N, Frascarelli D, Nesmachnow S, Tancredi G (2018) Performance improvements of a parallel multithreading self-gravity algorithm. In: Mocskos E, Nesmachnow S (eds) High performance computing (CARLA 2017). Springer, Cham, pp 291–306. https://doi.org/10.2458/azu_uapress_9780816532131-ch038

  285. Rognon P, Einav I (2010) Thermal transients and convective particle motion in dense granular materials. Phys Rev Lett 105(218):301. https://doi.org/10.1103/PhysRevLett.105.218301

  286. Rosato A, Starndburg KJ, Prinz F, Swendsen RH (1987) Why the brazil nuts are on the top: size segregation of particulate matter by shaking. Phys Rev Lett 58:1038

  287. Rosenblatt P, Lainey V, Le Maistre S, Marty J, Dehant V, Pätzold M, Van Hoolst T, Häusler B (2008) Accurate Mars Express orbits to improve the determination of the mass and ephemeris of the Martian moons. Planet Space Sci 56(7):1043–1053

  288. Rosenblatt P, Charnoz S, Dunseath KM, Terao-Dunseath M, Trinh A, Hyodo R, Genda H, Toupin S (2016) Accretion of Phobos and Deimos in an extended debris disc stirred by transient moons. Nat Geosci 9(8):581–583

  289. Roux S, Radjai F (1998) Texture-dependent rigid-plastic behavior. In: Herrmann HJ, Hovi JP, Luding S (eds) Physics of dry granular media. Springer, Dordrecht, pp 229–236

  290. Rouyer F, Menon N (2000) Velocity fluctuations in a homogeneous 2D granular gas in steady state. Phys Rev Lett 85:3676

  291. Rozitis B, MacLennan E, Emery JP (2014) Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA. Nature 512(7513):174–176. https://doi.org/10.1038/nature13632

  292. Rubincam DP (2000) Radiative spin-up and spin-down of small asteroids. Icarus 148(1):2–11. https://doi.org/10.1006/icar.2000.6485

  293. Russell HN (1906) On the light-variations of asteroids and satellites. Astrophys J 24:1–18. https://doi.org/10.1086/141361

  294. Saito J, Miyamoto H, Nakamura R, Ishiguro M, Michikami T, Nakamura A, Demura H, Sasaki S, Hirata N, Honda C et al (2006) Detailed images of asteroid 25143 Itokawa from Hayabusa. Science 312(5778):1341–1344

  295. Salo H (2001) Numerical simulations of the collisional dynamics of planetary rings. In: Pöschel T, Luding S (eds) Granular gases. Springer, Berlin, Heidelberg, pp 330–349

  296. Sánchez DP, Scheeres DJ (2015) Scaling rule between cohesive forces and the size of a self-gravitating aggregate. In: 46th lunar and planetary science conference, LPI contributions, vol 1832, p 2556

  297. Sánchez P (2015) Asteroid evolution: role of geotechnical properties. Proc IAU 10(S318):111–121. https://doi.org/10.1017/S1743921315008583

  298. Sánchez P, Scheeres DJ (2011) Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. Astrophys J 727(2):120

  299. Sánchez DP, Scheeres DJ (2012) DEM simulation of rotation-induced reshaping and disruption of rubble-pile asteroids. Icarus 218(2):876–894. https://doi.org/10.1016/j.icarus.2012.01.014

  300. Sánchez P, Scheeres DJ (2014) The strength of regolith and rubble pile asteroids. Meteorit Planet Sci 49(5):788–811. https://doi.org/10.1111/maps.12293

  301. Sánchez P, Scheeres DJ (2016) Disruption patterns of rotating self-gravitating aggregates: a survey on angle of friction and tensile strength. Icarus 271:453–471. https://doi.org/10.1016/j.icarus.2016.01.016

  302. Sánchez P, Scheeres DJ (2018) Rotational evolution of self-gravitating aggregates with cores of variable strength. Planet Space Sci. https://doi.org/10.1016/j.pss.2018.04.001

  303. Sanchez P, Colombo C, Vasile M, Radice G (2009) Multicriteria comparison among several mitigation strategies for dangerous near-Earth objects. J Guid Control Dyn 32(1):121–142

  304. Sánchez P, Scheeres DJ (2009) Granular mechanics in asteroid regolith: simulating and scaling the Brazil nut effects. In: Lunar and planetary science conference, LPI contributions, vol 40, p 2228

  305. Savage SB (1989) Flow of granular materials. In: Theoretical and applied mechanics. Elsevier, pp 241–266

  306. Savage SB (1993) Banding or pattern formation in horizontal drum mixers. In: Bideau D, Hansen A (eds) Disorder and granular media. North-Holland, Amsterdam, pp 255–285

  307. Savage S, Lun C (1988) Particle size segregation in inclined chute flow of dry cohesionless granular solids. J Fluid Mech 189:311–335

  308. Scheeres DJ, Team Osiris-Rex et al (2019) The dynamic geophysical environment of (101955) Bennu based on OSIRIS-REx measurements. Nat Astron 3:352–361. https://doi.org/10.1038/s41550-019-0721-3

  309. Scheeres DJ (2015) Landslides and mass shedding on spinning spheroidal asteroids. Icarus 247:1–17. https://doi.org/10.1016/j.icarus.2014.09.017

  310. Scheeres DJ, Hartzell CM, Sánchez P, Swift M (2010) Scaling forces to asteroid surfaces: the role of cohesion. Icarus 210(2):968–984. https://doi.org/10.1016/j.icarus.2010.07.009

  311. Scheeres DJ, Britt D, Carry B, Holsapple KA (2015) Asteroid interiors and morphology. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 745–766. https://doi.org/10.2458/azu_uapress_9780816532131-ch038

  312. Scholz C, Pöschel T (2017) Velocity distribution of a homogeneously driven two-dimensional granular gas. Phys Rev Lett 118:198003

  313. Schorghofer N (2008) The lifetime of ice on main belt asteroids. Astrophys J 682(1):697

  314. Schröter M, Ulrich S, Kerft J, Swift JB, Swinney HL (2006) Mechanisms in the size segregation of a binary granular mixture. Phys Rev E 74:011307

  315. Schwamb ME, Jones RL, Chesley SR, Fitzsimmons A, Fraser WC, Holman MJ, Hsieh H, Ragozzine D, Thomas CA, Trilling DE, Brown ME, Bannister MT, Bodewits D, de Val-Borro M, Gerdes D, Granvik M, Kelley MSP, Knight MM, Seaman RL, Ye QZ, Young LA (2018) Large synoptic survey telescope solar system science roadmap. arXiv:1802.01783

  316. Schwartz SR, Richardson DC, Michel P (2012) An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granul Matter 14(3):363–380

  317. Schwartz SR, Michel P, Richardson DC (2013) Numerically simulating impact disruptions of cohesive glass bead agglomerates using the soft-sphere discrete element method. Icarus 226(1):67–76

  318. Schwartz SR, Michel P, Jutzi M, Marchi S, Zhang Y, Richardson DC (2018) Catastrophic disruptions as the origin of bilobate comets. Nat Astron 2:379–382. https://doi.org/10.1038/s41550-018-0395-2

  319. Seiden G, Thomas PJ (2011) Complexity, segregation, and pattern formation in rotating-drum flows. Rev Mod Phys 83:1323

  320. Serero D, Noskowicz SH, Tan ML, Goldhirsch I (2009) Binary granular gas mixtures: theory, layering effects and some open questions. Eur Phys J Spec Top 179:221–247

  321. Shäfer J, Dippel S, Wolf D (1996) Force schemes in simulations of granular materials. J Phys I 6(1):5–20

  322. Sharma I (2013) Structural stability of rubble-pile asteroids. Icarus 223(1):367–382

  323. Sharma I, Jenkins JT, Burns JA (2009) Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids. Icarus 200(1):304–322. https://doi.org/10.1016/j.icarus.2008.11.003

  324. Shimokawa M, Suetsugu Y, Hiroshige R, Hirano T, Sakaguchi H (2015) Pattern formation in a sandpile of ternary granular mixtures. Phys Rev E 91(062):205

  325. Shinbrot T, Duong NH, Kwan L, Alvarez MM (2004) Dry granular flows can generate surface features resembling those seen in Martian gullies. Proc Natl Acad Sci 101(23):8542–8546. https://doi.org/10.1073/pnas.0308251101

  326. Sierks H, Lamy P, Barbieri C, Koschny D, Rickman H, Rodrigo R, A’Hearn MF, Angrilli F, Barucci MA, Bertaux JL, Bertini I, Besse S, Carry B, Cremonese G, Da Deppo V, Davidsson B, Debei S, De Cecco M, De Leon J, Ferri F, Fornasier S, Fulle M, Hviid SF, Gaskell RW, Groussin O, Gutierrez P, Ip W, Jorda L, Kaasalainen M, Keller HU, Knollenberg J, Kramm R, Kührt E, Küppers M, Lara L, Lazzarin M, Leyrat C, Moreno JJL, Magrin S, Marchi S, Marzari F, Massironi M, Michalik H, Moissl R, Naletto G, Preusker F, Sabau L, Sabolo W, Scholten F, Snodgrass C, Thomas N, Tubiana C, Vernazza P, Vincent JB, Wenzel KP, Andert T, Pätzold M, Weiss BP (2011) Images of asteroid 21 Lutetia: a remnant planetesimal from the early solar system. Science 334:487. https://doi.org/10.1126/science.1207325

  327. Spahn F, Schmidt J (2006) Hydrodynamic description of planetary rings. GAMM-Mitteilungen 29(1):118–143

  328. Stadel JG (2001) Cosmological \(N\)-body simulations and their analysis. Ph.D. thesis, University of Washington, Washington, DC

  329. Stansberry J, Grundy W, Brown M, Cruikshank D, Spencer J, Trilling D, Margot J (2008) Physical properties of kuiper belt and centaur objects: constraints from the Spitzer Space Telescope. In: Barucci MA, Boehnhardt H, Cruikshank DP, Morbidelli A (eds) The solar system beyond Neptune. University of Arizona Press, Tucson, pp 161–179

  330. Staron L (2016) Segregation mechanisms in granular systems: role of gravity and velocity fluctuations. In: EGU general assembly conference abstracts, vol 18, p 8047

  331. Staron L, Lagrée PY, Popinet S (2012) The granular silo as a continuum plastic flow: the hour-glass vs. the clepsydra. Phys Fluids 24(10):103301

  332. Sugimoto Y, Radice G, Ceriotti M, Sanchez JP (2014) Hazardous near Earth asteroid mitigation campaign planning based on uncertain information on fundamental asteroid characteristics. Acta Astronaut 103:333–357. https://doi.org/10.1016/j.actaastro.2014.02.022

  333. Sugita S et al (2019) The geomorphology, color, and thermal properties of Ryugu: implications for parent-body processes. Science 364:252–252. https://doi.org/10.1126/science.aaw0422

  334. Sunday C, Murdoch N, Cherrier O, Serrano SM, Nardi CV, Janin T, Martinez IA, Gourinat Y, Mimoun D (2016) A novel facility for reduced-gravity testing: a setup for studying low-velocity collisions into granular surfaces. Rev Sci Instrum 87(8):084504. https://doi.org/10.1063/1.4961575

  335. Syal MB, Dearborn DS, Schultz PH (2013) Limits on the use of nuclear explosives for asteroid deflection. Acta Astronaut 90(1):103–111. https://doi.org/10.1016/j.actaastro.2012.10.025

  336. Tancredi G, Maciel A, Heredia L, Richeri P, Nesmachnow S (2012) Granular physics in low-gravity environments using discrete element method. Mon Not R Astron Soc 420(4):3368–3380

  337. Tanga P, Comito C, Paolicchi P, Hestroffer D, Cellino A, Dell’Oro A, Richardson DC, Walsh K, Delbo M (2009a) Rubble-pile reshaping reproduces overall asteroid shapes. Astrophys J Lett 706(1):L197

  338. Tanga P, Hestroffer D, Delbo M, Richardson DC (2009b) Asteroid rotation and shapes from numerical simulations of gravitational re-accumulation. Planet Space Sci 57(2):193–200

  339. Tanga P, Campo Bagatin A, Thirouin A, Cellino A, Comito C, Ortiz J, Hestroffer D, Richardson D (2013) Possible routes to spin up fission for the formation of asteroid binaries and pairs. In: European planetary science congress, vol 8

  340. Tardivel S, Sánchez P, Scheeres DJ (2018) Equatorial cavities on asteroids, an evidence of fission events. Icarus 304:192–208. https://doi.org/10.1016/j.icarus.2017.06.037

  341. Tatsumi S, Murayama Y, Hayakawa H, Sano M (2009) Experimental study on the kinetics of granular gases under microgravity. J Fluid Mech 641:521–539

  342. Taylor PA, Howell ES, Nolan MC, Thane AA (2012) The shape and spin distributions of near-Earth asteroids observed with the arecibo radar system. In: AAS meeting abstracts #220, vol 220. American Astronomical Society, p 128.02

  343. Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice. Wiley, New York

  344. Thomas P (2010) Sizes, shapes, and derived properties of the Saturnian satellites after the Cassini nominal mission. Icarus 208(1):395–401

  345. Thomas PA, Bray JD (1999) Capturing nonspherical shape of granular media with disk clusters. J Geotechnol Geoenviron Eng 125:169–178

  346. Thuillet F, Maurel C, Michel P, Biele J, Ballouz RL, Richardson DC (2017) Numerical simulations of surface package landing on a low-gravity granular surface: application to the landing of MASCOT onboard Hayabusa2. In: Lunar and planetary science conference, LPI contributions, vol 1964, p 1810

  347. Tiscareno MS, Murray CD (2018) Planetary ring systems: properties, structure, and evolution, vol 19. Cambridge University Press, Cambridge

  348. Toiya M, Stambaugh J, Losert W (2004) Transient and oscillatory granular shear flow. Phys Rev Lett 93(8):088001

  349. van der Hucht KA (2008) Proceedings of the twenty sixth general assembly Prague 2006: transactions of the international astronomical union XXVIB, vol 26. Cambridge University Press, Cambridge

  350. Verlet L (1967) Computer ‘experiments’ on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys Rev 159(1):98

  351. Von Kampen P, Kaczmarczik U, Rath HJ (2006) The new drop tower catapult system. Acta Astronaut 59:278–283

  352. Vu-Quoc L, Zhang X, Walton OR (2000) A 3-D discrete-element method for dry granular flows of ellipsoidal particles. Comput Methods Appl Mech Eng 187:483–528

  353. Wadsley JW, Stadel J, Quinn T (2004) Gasoline: a flexible, parallel implementation of TreeSPH. New Astron 9:137–158. https://doi.org/10.1016/j.newast.2003.08.004. arXiv:astro-ph/0303521

  354. Walker R, Binns D, Carnelli I, Kueppers M, Galvez A (2016) CubeSat opportunity payload intersatellite network sensors (COPINS) on the ESA asteroid impact mission (AIM). In: 5th interplanetary CubeSat workshop (iCubeSat)

  355. Walsh KJ, Team Osiris-Rex et al (2019) Craters, boulders and regolith of (101955) Bennu indicative of an old and dynamic surface. Nat Geosci 12:242–246. https://doi.org/10.1038/s41561-019-0326-6

  356. Walsh KJ, Jacobson SA (2015) Formation and evolution of binary asteroids. In: Michel P, DeMeo F, Bottke W (eds) Asteroids IV. University of Arizona Press, Tucson, pp 375–393

  357. Walsh KJ, Richardson DC (2006) Binary near-Earth asteroid formation: rubble pile model of tidal disruptions. Icarus 180(1):201–216

  358. Walsh K, Richardson D (2008) A steady-state model of NEA binaries formed by tidal disruption of gravitational aggregates. Icarus 193(2):553–566

  359. Walsh KJ, Richardson DC, Michel P (2008) Rotational breakup as the origin of small binary asteroids. Nature 454(7201):188

  360. Walsh KJ, Richardson DC, Michel P (2012) Spin-up of rubble-pile asteroids: disruption, satellite formation, and equilibrium shapes. Icarus 220(2):514–529. https://doi.org/10.1016/j.icarus.2012.04.029

  361. Warner BD, Harris AW, Pravec P (2009) The asteroid lightcurve database. Icarus 202:134–146. 10.1016/j.icarus.2009.02.003. http://www.minorplanet.info/lightcurvedatabase.html. Accessed 24 June 2018

  362. Watanabe S et al (2019) Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu–a spinning top-shaped rubble pile. Science 364(6437):268–272. https://doi.org/10.1126/science.aav8032

  363. Weidenschilling SJ, Paolicchi P, Zappala V (1989) Do asteroids have satellites? In: Binzel R, Gehrels T, Matthews M (eds) Asteroids II. University of Arizona Press, Tucson, pp 643–658

  364. Weissman PR, A’Hearn MF, McFadden L, Rickman H (2002) Evolution of comets into asteroids. In: Bottke WF, Cellino A, Paolicchi P, Binzel RP (eds) Asteroids III. University of Arizona Press, Tucson, pp 669–686

  365. Wilkening LL, Matthews MS (1982) Comets. University of Arizona Press, Tucson

  366. Will CM (2014) The confrontation between general relativity and experiment. Living Rev Relativ 17:4. https://doi.org/10.12942/lrr-2014-4. arXiv:1403.7377

  367. Wisdom J, Tremaine S (1988) Local simulations of planetary rings. Astron J 95:925–940

  368. Yeomans DK, Barriot JP, Dunham D, Farquhar R, Giorgini J, Helfrich C, Konopliv A, McAdams J, Miller J, Owen W et al (1997) Estimating the mass of asteroid 253 Mathilde from tracking data during the NEAR flyby. Science 278(5346):2106–2109

  369. Yeomans D, Antreasian P, Barriot JP, Chesley S, Dunham D, Farquhar R, Giorgini J, Helfrich C, Konopliv A, McAdams J et al (2000) Radio science results during the NEAR-Shoemaker spacecraft rendezvous with Eros. Science 289(5487):2085–2088

  370. Yu Y, Richardson DC, Michel P (2017) Structural analysis of rubble-pile asteroids applied to collisional evolution. Astrodynamics 1(1):57–69

  371. Zhang Y, Richardson DC, Barnouin OS, Michel P, Schwartz SR, Ballouz RL (2018) Rotational failure of rubble-pile bodies: influences of shear and cohesive strengths. Astrophys J 857(1):15

  372. Zik O, Levine D, Lipson SG, Shtrikman S, Stavans J (1994) Rotationally induced segregation of granular materials. Phys Rev Lett 73:644

  373. Zuriguel I, Gray JMNT, Peixinho J, Mullin T (2006) Pattern selection by a granular wave in a rotating drum. Phys Rev E 73:061302

Download references

Acknowledgements

This work is a direct result of support by the International Space Science Institute, ISSI Bern, Switzerland, through the hosting and provision of financial support for the international team “Asteroids and Self-Gravitating Bodies as Granular Systems” led by DH. The authors would like to thank the ISSI Institute and staff for their support, and the Paris observatory for financial support. Thanks to MIAPP, Munich Institute for Astro and Particle Physics of the DFG cluster of excellence “Origin and Structure of the Universe” and participants of the the workshop on NEOS for fruitful discussions. EO thanks Prodex (Belspo) and ESA (Topical Team no. 4000103461) for financial support. DCR was supported in part by NASA grant NNX15AH90G awarded by the Solar System Workings program. SRS acknowledges support from the Academies of Excellence: Complex systems and Space, environment, risk, and resilience, part of the IDEX JEDI of the Université Côte d’Azur. SE acknowledges support from the DiRAC Institute in the Department of Astronomy at the University of Washington. The DiRAC Institute is supported through generous gifts from the Charles and Lisa Simonyi Fund for Arts and Sciences, and the Washington Research Foundation. We are grateful to all the other members of the ISSI international team for discussions, exchanges, inputs, and contributions. We are grateful to Brian Warner for kindly providing us an up-to-date ‘spin-rate versus diameter’ figure. This work has made use of Wm R. Johnston archive data http://www.johnstonsarchive.net, and intensive use of NASA’s Astrophysics Data System.

Author information

Correspondence to D. Hestroffer.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Made possible by the International Space Science Institute (ISSI, Bern) support to the international team “Asteroids and Self-Gravitating Bodies as Granular Systems”.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hestroffer, D., Sánchez, P., Staron, L. et al. Small Solar System Bodies as granular media. Astron Astrophys Rev 27, 6 (2019). https://doi.org/10.1007/s00159-019-0117-5

Download citation

Keywords

  • Small bodies of the Solar System SSSB, minor planets, asteroids: general
  • Gravitational aggregates
  • Granular media
  • Methods: numerical, laboratory, observational
  • Planetary formation