Part of the Springer Theses book series (Springer Theses)


In the story of mankind, explorations to unknown worlds have never stopped. Eager and curious adventures of every generation, heading for far places and pushing the limits, have empowered the progress of human civilization in history. The evolution of modern technologies spanned the world field of vision: scientists have pointed the Hubble telescope to the far reaches of the universe (Scoville et al. Astrophysical Journal Supplement Series, 172:38–45, 2007, [1]); the interstellar space probe Voyager 1, has flied over the edge of outer Solar System, taking a golden record of human’s information (Burlaga et al. Science, 341:147–150, 2013, [2]); and the Hayahusa spacecraft has successfully returned the regolith samples from the Near-Earth Asteroid 25143 Itokawa (Akira et al. Science, 333:1125–1128, 2011, [3]).


Periodic Orbit Small Body Orbital Dynamic Resonant Orbit Triaxial Ellipsoid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Scoville N, Abraham RG, Aussel H et al (2007) COSMOS: hubble space telescope observations. Astrophys J Suppl Ser 172:38–45ADSCrossRefGoogle Scholar
  2. 2.
    Burlaga LF, Ness NF, Stone EC (2013) Magnetic field observations as voyager 1 entered the heliosheath depletion region. Science 341:147–150ADSCrossRefGoogle Scholar
  3. 3.
    Akira T, Masayuki U, Takashi M et al (2011) Three-dimensional structure of Hayabusa samples: origin and evolution of Itokawa regolith. Science 333:1125–1128CrossRefGoogle Scholar
  4. 4.
    Cunningham C (1998) Introduction to asteroids: the next frontier, 1st edn. Willmann-Bell, VirginiaGoogle Scholar
  5. 5.
    Dankanich JW, Landau D, Martini MC et al (2010) Main belt asteroid sample return mission design. In: Proceedings of the 46th AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit, Nashville, TN, United States, 25–28 July 2010Google Scholar
  6. 6.
    Safronov VS (1969) Evolution of the protoplanetary cloud and formation of the earth and planets. Nauka, MoscowGoogle Scholar
  7. 7.
    Weidenschilling SJ (2000) Formation of planetesimals and accretion of the terrestrial planets. Space Sci. Rev. 92:295–310ADSCrossRefGoogle Scholar
  8. 8.
    Bottke Jr WF, Cellino A, Paolicchi P et al (2002) Asteroids III. University of Arizona Press, TucsonGoogle Scholar
  9. 9.
    IAU (The International Astronomical Union) Minor Planet Center. Issue 2013.
  10. 10.
    Farquhar R, Kawaguchi J, Russell C (2002) Spacecraft exploration of asteroids: the 2001 perspective. In: William F et al (eds) Asteroids III. University of Arizona Press, Tucson, pp 367–376Google Scholar
  11. 11.
    Cheng AF, Santo AG, Heeres KJ et al (1997) Near-Earth asteroid rendezvous: mission overview. J. Geophys. Res.: Planets 102:23695–23708ADSCrossRefGoogle Scholar
  12. 12.
    Hu Z, Xu W (2008) Planetary Science. Science Press, Beijing, pp 334–365Google Scholar
  13. 13.
    Zacny K, Chu P, Craft J et al (2013) Asteroid mining. In: Proceedings of the AIAA SPACE 2013 conference and exposition, CA, San Diego, 10–12 Sept 2013Google Scholar
  14. 14.
    Galimov EM, Pillinger CT, Greenwood RC et al (2013) The Chelyabinsk fireball and meteorite: implications for asteroid hazard assessment. In: Proceedings of the 76th annual meeting of the meteoritical society, Edmonton, Canada, 29 July–7 Aug 2013Google Scholar
  15. 15.
    JAXA (Japan Aerospace Exploration Agency). Issue 2010.
  16. 16.
    Tricarico P, Sykes MV (2010) The dynamical environment of dawn at Vesta. Planet. Space Sci. 58:12–38CrossRefGoogle Scholar
  17. 17.
    Cintala MJ, Head JW, Wilson L (1979) The nature and effects of impact cratering on small bodies. In: Gehrels T (ed) Asteroids. University of Arizona Press, Tucson, pp 579–600Google Scholar
  18. 18.
    Housen KR, Wilikening LL, Chapman CR et al (1979) Regolith development and evolution on asteroids and the Moon. In: Gehrels T (ed) Asteroids II. University of Arizona Press, Tucson, pp 601–627Google Scholar
  19. 19.
    Shilnikov LP et al (2010) In: Jin C (ed) Methods of qualitative theory in nonlinear dynamics, pt 1, 1st edn. Higher Education Press, Beijing, pp ix–xi (Trans.)Google Scholar
  20. 20.
    Liu L (2004) Orbital theory of spacecraft. National Defence Industry Press, BeijingGoogle Scholar
  21. 21.
    Hobson EW (1965) The theory of spherical and ellipsoidal harmonics. Chelsea, New YorkzbMATHGoogle Scholar
  22. 22.
    Chao BF, Rubincam DP (1989) The gravitational field of Phobos. Geoph. Res. Let. 16:859–862ADSCrossRefGoogle Scholar
  23. 23.
    Barnett CT (1976) Theoretical modeling of the magnetic and gravitational fields of an arbitrary shaped three-dimensional body. Geophysics 41:1353–1364ADSCrossRefGoogle Scholar
  24. 24.
    Jamet O, Thomas EA (2004) Linear algorithm for computing the spherical harmonic coefficients of the gravitational potential from a constant density polyhedron. In: 2nd GOCE user workshop, GOCE, The geoid and oceanography, ESA-ESRIN, Frascati, Italy, 8–10 Mar 2004Google Scholar
  25. 25.
    Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman, San FranciscoGoogle Scholar
  26. 26.
    Bierly W (1897) An elementary treatise on fourier’s series and spherical, cylindrical, and ellipsoidal harmonics. Ginnand Company, LondonGoogle Scholar
  27. 27.
    MacMillan WD (1930) The theory of the potential. McGraw-Hill, New YorkzbMATHGoogle Scholar
  28. 28.
    Hobson E (1955) The therory of spherical and ellipsoidal harmonics. Chelsea Publishing Company, VermontGoogle Scholar
  29. 29.
    Romain G, Jean-Pierre B (2001) Ellipsoidal harmonic expansions of the gravitational potential: theory and application. Celest. Mech. Dyn. Astron. 19:235–275ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Dobrovolskis AR, Bruns JA (1980) Life near the Roche limit: behavior of ejecta from satellites close to planets. Icarus 42:422–441ADSCrossRefGoogle Scholar
  31. 31.
    German D, Friedlander AL (1991) A simulation of orbits around asteroids using potential field modelling. Adv. Astron. Sci. Spacefl. Mech. 75:1183–1201Google Scholar
  32. 32.
    Scheeres DJ (1994) Dynamics about uniformly rotating triaxial ellipsoids: applications to asteroids. Icarus 110:225–238ADSCrossRefGoogle Scholar
  33. 33.
    Rausenberger O (1888) Lehrbuch der Analytischen Mechanik I.B.G. Teubner: LeipzigGoogle Scholar
  34. 34.
    Werner RA (1994) The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celest. Mech. Dyn. Astron. 59:253–278ADSCrossRefzbMATHGoogle Scholar
  35. 35.
    Werner RA, Scheeres DJ (1997) Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 castalia. Celest. Mech. Dyn. Astron. 65:313–344ADSCrossRefzbMATHGoogle Scholar
  36. 36.
    Forsberg RA (1984) Study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report of the Department of Geodetic Science and Surveying, Ohio State UniversityGoogle Scholar
  37. 37.
    Petrović S (1996) Determination of the potential of homogeneous polyhedral bodies using line integrals. J. Geodesy 71:44–52ADSCrossRefzbMATHGoogle Scholar
  38. 38.
    Pohánka V (1988) Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophys Prospect 36:733–751ADSCrossRefGoogle Scholar
  39. 39.
    Tsoulis D, Petrović S (2001) On the singularities of the gravity field of a homogeneous polyhedral body. Geophysics 66:535–539ADSCrossRefGoogle Scholar
  40. 40.
    Scheeres DJ, Ostro SJ, Hudson RS et al (1996) Orbits close to asteroid 4769 Castalia. Icarus 121:67–87ADSCrossRefGoogle Scholar
  41. 41.
    Scheeres DJ, Ostro SJ, Hudson RS et al (1998) Dynamics of orbits close to asteroid 4179 Toutatis. Icarus 132:53–79ADSCrossRefGoogle Scholar
  42. 42.
    Hu W, Scheeres DJ (2004) Numerical determination of stability regions for orbital motion in uniformly rotating second degree and order gravity fields. Planet. Space Sci. 52:685–692ADSCrossRefGoogle Scholar
  43. 43.
    Wang Y, Xu S (2013) Gravity gradient torque of spacecraft orbiting asteroids. Aircr. Eng. Aerosp. Technol. 85:72–81CrossRefGoogle Scholar
  44. 44.
    Antreasian PG, Helfrich CL, Miller JK et al (1998) Preliminary considerations for NEAR’s low-altitude passes and landing operations at 433 Eros. In: Proceedings of the AIAA/AAS astrodynamics specialist conference and exhibit, Boston, MA, 10–12 Aug 1998Google Scholar
  45. 45.
    Bottke WF Jr, Vokrouhlický D, Rubincam DP (2002) The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In: William F et al (ed) Asteroids III. University of Arizona Press, TucsonGoogle Scholar
  46. 46.
    Scheeres DJ, Williams BG, Miller JK (2000) Evaluation of the dynamic environment of an asteroid: applications to 433 Eros. J. Guid. Control Dyn. 23:466–475ADSCrossRefGoogle Scholar
  47. 47.
    Scheeres DJ, Gaskell R, Abe S et al (2006) The actual dynamical environment about Itokawa. In: AIAA/AAS astrodynamics specialist conference exhibit, Keystone, Colorado, Aug, pp 21–24Google Scholar
  48. 48.
    Broschart SB, Scheeres DJ (2005) Control of hovering spacecraft near small bodies: application to asteroid 25143 Itokawa. J. Guid. Control Dyn. 28:343–354ADSCrossRefGoogle Scholar
  49. 49.
    Antreasian PG, Chesley SR, Miller JK et al (2002) The design and navigation of the NEAR SHOEMAKER landing of EROS. Adv. Astron. Sci. 109:989–1015Google Scholar
  50. 50.
    Lantoine G, Braun RD (2006) Optimal trajectories for soft landing on asteroids. AE8900 MS Special Problems Report, Space Systems Design LabGoogle Scholar
  51. 51.
    Yano H, Kubota T, Miyamoto H, Okada T et al (2006) Touchdown of the Hayabusa spacecraft at the Muses Sea on Itokawa. Science 312:1350–1353ADSCrossRefGoogle Scholar
  52. 52.
    Hawkins M, Guo Y, Wie B (2012) ZEM/ZEV Feedback guidance application to fuel-efficient orbital maneuvers around an irregular-shaped asteroid. In: Proceedings of the AIAA guidance, navigation, and control conference, Minneapolis, Minnesota, 13–16 Aug 2012Google Scholar
  53. 53.
    Bellerose J, Scheeres DJ (2008) Dynamics and control for surface exploration of small bodies. In: Proceedings of the AIAA/AAS astrodynamics specialist conference and exhibit, Honolulu, Hawaii, 18–21 Aug 2008Google Scholar
  54. 54.
    Chapman CR, Veverka J, Thomas PC (1995) Discovery and physical properties of Dactyl, a satellite of asteroid 243 Ida. Nature 374:783–785ADSCrossRefGoogle Scholar
  55. 55.
    Richardson DC, Walsh KJ (2006) Binary minor planets. Annu. Rev. Earth Planet. Sci. 34:47–81ADSCrossRefGoogle Scholar
  56. 56.
    Scheeres DJ (2002) Stability in the full two-body problem. Celest. Mech. Dynam. Astron. 83:155–169ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Fahnestock EG, Scheeres DJ (2008) Simulation and analysis of the dynamics of binary near-Earth asteroid (66391) 1999 KW4. Icarus 194:410–435ADSCrossRefGoogle Scholar
  58. 58.
    Bellerose J, Scheeres DJ (2006) Periodic orbits in the full two-body problem. In: Proceedings of the AAS/AIAA conference, Tampa, Florida, United States, 22–26 Jan 2006Google Scholar
  59. 59.
    Maciejewski AJ (1995) Reduction, relative equilibria and potential in the two rigid bodies problem. Celest. Mech. Dyn. Astron. 63:1–28ADSMathSciNetCrossRefzbMATHGoogle Scholar
  60. 60.
    Scheeres DJ (2002) Stability of binary asteroids. Icarus 159:271–283ADSCrossRefGoogle Scholar
  61. 61.
    Borderies N (1978) Mutual gravitational potential of N solid bodies. Celest. Mech. 18:295–307ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. 62.
    Braun CV (1991) The gravitational potential of two arbitrary, rotating bodies with applications to the Earth–Moon system. University of Texas at Austin, TexasGoogle Scholar
  63. 63.
    Moritz H (1980) Advanced physical geodesy. Abacus Press, WichmannGoogle Scholar
  64. 64.
    Geissler P, Petit JM, Durda DD et al (1996) Erosion and ejecta reaccretion of 243 Ida and its Moon. Icarus 120:140–157ADSCrossRefGoogle Scholar
  65. 65.
    Ashenberg J (2005) Proposed method for modeling the gravitational interaction between finite bodies. J. Guid. Control Dyn. 28:768–774ADSCrossRefGoogle Scholar
  66. 66.
    Werner RA, Scheeres DJ (2005) Mutual potential of homogenous polyhedra. Celest. Mech. Dyn. Astron. 91:337–349ADSMathSciNetCrossRefzbMATHGoogle Scholar
  67. 67.
    Fahnestock EG, Scheeres DJ, McClamroch NH et al (2005) Simulation and analysis of binary asteroid dynamics using mutual potential and potential derivatives formulation. In: Proceedings of the AAS/AIAA astrodynamics specialist conference, Lake Tahoe, CA, United States, 7–11 Aug 2005Google Scholar
  68. 68.
    Fahnestock EG, Scheeres DJ (2006) Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach. Celest. Mech. Dyn. Astron. 96:317–339ADSMathSciNetCrossRefzbMATHGoogle Scholar
  69. 69.
    Fahnestock EG, Lee T, Leok M et al (2006) Polyhedral potential and variational integrator computation of the full two body problem. In: Proceedings of the AIAA/AAS astrodynamics specialist conference, Keystone, Colorado, United States, 21–24 Aug 2006Google Scholar
  70. 70.
    Scheeres DJ, Fahnestock EG, Ostro SJ et al (2006) Dynamical configuration of binary near-Earth asteroid (66391) 1999 KW4. Science 314:1280–1283ADSCrossRefGoogle Scholar
  71. 71.
    Walsh KJ, Richardson DC, Michel P (2008) Rotational breakup as the origin of small binary asteroids. Nature 454:188–191ADSCrossRefGoogle Scholar
  72. 72.
    Holsapple K, Giblin I, Housen K (2002) Asteroid impacts: laboratory experiments and scaling laws. In: William F et al (ed) Asteroids III. University of Arizona Press, TucsonGoogle Scholar
  73. 73.
    Mantz A, Sullivan R, Veverka J (2004) Regolith transport in craters on Eros. Icraus 167:197–203CrossRefGoogle Scholar
  74. 74.
    Thomas PC, Belton MJS, Carcich B et al (1996) The shape of Ida. Icarus 120:20–32ADSCrossRefGoogle Scholar
  75. 75.
    Scheeres DJ, Durda DD, Geissler PE (2002) The Fate of Asteroid Ejecta. In: William F, et al (ed) Asteroids III. University of Arizona Press, TucsonGoogle Scholar
  76. 76.
    Cheng AF, Barnouin JO, Zuber MT et al (2001) Laser altimetry of small-scale features on 433 Eros from NEAR-Shoemaker. Science 292:488–491ADSCrossRefGoogle Scholar
  77. 77.
    Weidenschilling SJ, Paolicchi P, Zappalá V (1989) Do asteroids have satellites? In: Binzel R P et al (ed) Asteroids II. University of Arizona Press, TucsonGoogle Scholar
  78. 78.
    Hamilton DP, Burns JA (1991) Orbital stability zones about asteroids. Icarus 92:118–131ADSCrossRefGoogle Scholar
  79. 79.
    Hamilton DP, Burns JA (1991) Orbital stability zones about asteroids. II. The destabilizing effects of eccentric orbits and of solar radiation. Icarus 96:43–64ADSCrossRefGoogle Scholar
  80. 80.
    Chauvineau B, Mignard F (1990) Dynamics of binary asteroids. I. Hill’s Case. Icarus 83:360–381ADSCrossRefzbMATHGoogle Scholar
  81. 81.
    Richter K, Keller HU (1995) On the stability of dust particle orbits around cometary nuclei. Icarus 114:355–371ADSCrossRefGoogle Scholar
  82. 82.
    Hamilton DP, Krivov AV (1997) Dynamics of distant moons of asteroids. Icarus 128:241–249ADSCrossRefGoogle Scholar
  83. 83.
    Chauvineau B, Farinella P, Mignard F (1993) Planar orbits about a triaxial body: applications to asteroidal satellites. Icarus 105:370–384ADSCrossRefGoogle Scholar
  84. 84.
    Thomas PC, Veverka J, Robinson M, Murchie S (2001) Shoemaker crater as the source of most ejecta blocks on the asteroid 433 Eros. Nature 413:394–396ADSCrossRefGoogle Scholar
  85. 85.
    Korycansky DG, Asphaug E (2004) Simulations of impact ejecta and regolith accumulation on asteroid Eros. Icarus 171:110–119ADSCrossRefGoogle Scholar
  86. 86.
    Chapman C (2004) Space weathering of asteroid surfaces. Ann. Rev. Earth Planet. Sci. 32:539–567ADSCrossRefGoogle Scholar
  87. 87.
    Durda DD, Charpman CR, Merline WJ et al (2012) Detecting crater ejecta-blanket boundaries and constraining source crater regions for boulder tracks and elongated secondary craters on Eros. Meteorit. Planet. Sci. 47:1087–1097ADSCrossRefGoogle Scholar
  88. 88.
    Bottke WF Jr, Melosh HJ (1996) Binary asteroids and the formation of doublet craters. Icarus 124:372–391ADSCrossRefGoogle Scholar
  89. 89.
    Miljković K, Collins GS, Mannick S, Bland PA (2013) Morphology and population of binary asteroid impact craters. Earth Planet. Sci. Lett. 363:121–132ADSCrossRefGoogle Scholar
  90. 90.
    Halamek P (1988) Motion in the potential of a thin bar. University of Texas at Austin, TexasGoogle Scholar
  91. 91.
    Arnold VI (2010) Mathematical methods of classical mechanics. Springer, New YorkGoogle Scholar
  92. 92.
    Riaguas A, Elipe A, López-Moratalla T (2001) Non-linear stability of the equilibria in the gravity field of a finite straight segment. Celest. Mech. Dyn. Astron. 81:235–248ADSMathSciNetCrossRefzbMATHGoogle Scholar
  93. 93.
    Riaguas A, Elipe A, Lara M (1999) Periodic orbits around a massive straight segment. Celest. Mech. Dyn. Astron. 73:169–178ADSMathSciNetCrossRefzbMATHGoogle Scholar
  94. 94.
    Liu X, Baoyin H, Ma X (2011) Periodic orbits in the gravity field of a fixed homogeneous cube. Astrophys. Space Sci. 334:357–364ADSCrossRefzbMATHGoogle Scholar
  95. 95.
    Liu X, Baoyin H, Ma X (2011) Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube. Astrophys. Space Sci. 333:409–418ADSCrossRefzbMATHGoogle Scholar
  96. 96.
    Liu X, Baoyin H, Ma X (2013) Dynamics of surface motion on a rotating massive homogeneous body. Sci. China Phys. Mech. Astron. 56:818–829ADSCrossRefGoogle Scholar
  97. 97.
    Ostro SJ, Hudson RS, Benner LAM (2002) Asteroid radar astronomy. In: William F et al (ed) Asteroids III. University of Arizona Press, TucsonGoogle Scholar
  98. 98.
    Kammeyer PC (1978) Periodic orbits around a rotating ellipsoid. Celest. Mech. 17:37–48ADSMathSciNetCrossRefzbMATHGoogle Scholar
  99. 99.
    Yu Y, Baoyin H (2012) Orbital dynamics in the vicinity of asteroid 216 Kleopatra. Astron. J. 143:62–71ADSCrossRefGoogle Scholar
  100. 100.
    Yu Y, Baoyin H (2013) Resonant orbits in the vicinity of asteroid 216 Kleopatra. Astrophys. Space Sci. 343:75–82ADSCrossRefGoogle Scholar
  101. 101.
    Yu Y, Baoyin H (2012) Generating families of 3D periodic orbits about asteroids. Mon. Not. Royal Astron. Soc. 427:872–881ADSCrossRefGoogle Scholar
  102. 102.
    Arnold VI (2006) In: Qi M (ed) Mathematical methods of classical mechanics, 4th edn. Higher Education Press, Beijing, pp iii–v (Trans.)Google Scholar
  103. 103.
    Gutiérrez-Romero S, Palacían JF, Yanguas P (2004) The invariant manifolds of a finite straight segment. Monografas de la Real Academia de Ciencias de. Zaragoza 25:137–148Google Scholar
  104. 104.
    Jiang Y, Baoyin H, Li J, Li H (2014) Orbits and manifolds near the equilibrium points around a rotating asteroid. Astrophys. Space Sci. 349:83–106ADSCrossRefGoogle Scholar
  105. 105.
    Maruskin JM, Scheeres DJ, Bloch AM (2009) Dynamics of symplectic subvolumes. Siam J. Appl. Dyn. Syst. 8:180–201ADSMathSciNetCrossRefzbMATHGoogle Scholar
  106. 106.
    Tsuda Y, Scheeres DJ (2009) Computation and applications of an orbital dynamics symplectic state transition matrix. J. Guid. Control Dyn. 32:1111–1123ADSCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Beihang UniversityBeijingChina

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