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Abstract

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]).

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References

  1. Scoville N, Abraham RG, Aussel H et al (2007) COSMOS: hubble space telescope observations. Astrophys J Suppl Ser 172:38–45

    Article  ADS  Google Scholar 

  2. Burlaga LF, Ness NF, Stone EC (2013) Magnetic field observations as voyager 1 entered the heliosheath depletion region. Science 341:147–150

    Article  ADS  Google Scholar 

  3. Akira T, Masayuki U, Takashi M et al (2011) Three-dimensional structure of Hayabusa samples: origin and evolution of Itokawa regolith. Science 333:1125–1128

    Article  Google Scholar 

  4. Cunningham C (1998) Introduction to asteroids: the next frontier, 1st edn. Willmann-Bell, Virginia

    Google Scholar 

  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 2010

    Google Scholar 

  6. Safronov VS (1969) Evolution of the protoplanetary cloud and formation of the earth and planets. Nauka, Moscow

    Google Scholar 

  7. Weidenschilling SJ (2000) Formation of planetesimals and accretion of the terrestrial planets. Space Sci. Rev. 92:295–310

    Article  ADS  Google Scholar 

  8. Bottke Jr WF, Cellino A, Paolicchi P et al (2002) Asteroids III. University of Arizona Press, Tucson

    Google Scholar 

  9. IAU (The International Astronomical Union) Minor Planet Center. Issue 2013. http://www.minorplanetcenter.net/mpc/summary

  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 367–376

    Google Scholar 

  11. Cheng AF, Santo AG, Heeres KJ et al (1997) Near-Earth asteroid rendezvous: mission overview. J. Geophys. Res.: Planets 102:23695–23708

    Article  ADS  Google Scholar 

  12. Hu Z, Xu W (2008) Planetary Science. Science Press, Beijing, pp 334–365

    Google Scholar 

  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 2013

    Google Scholar 

  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 2013

    Google Scholar 

  15. JAXA (Japan Aerospace Exploration Agency). Issue 2010. http://www.isas.jaxa.jp/j/topics/topics/2005.shtml

  16. Tricarico P, Sykes MV (2010) The dynamical environment of dawn at Vesta. Planet. Space Sci. 58:12–38

    Article  Google Scholar 

  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 579–600

    Google Scholar 

  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 601–627

    Google Scholar 

  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. Liu L (2004) Orbital theory of spacecraft. National Defence Industry Press, Beijing

    Google Scholar 

  21. Hobson EW (1965) The theory of spherical and ellipsoidal harmonics. Chelsea, New York

    MATH  Google Scholar 

  22. Chao BF, Rubincam DP (1989) The gravitational field of Phobos. Geoph. Res. Let. 16:859–862

    Article  ADS  Google Scholar 

  23. Barnett CT (1976) Theoretical modeling of the magnetic and gravitational fields of an arbitrary shaped three-dimensional body. Geophysics 41:1353–1364

    Article  ADS  Google Scholar 

  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 2004

    Google Scholar 

  25. Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman, San Francisco

    Google Scholar 

  26. Bierly W (1897) An elementary treatise on fourier’s series and spherical, cylindrical, and ellipsoidal harmonics. Ginnand Company, London

    Google Scholar 

  27. MacMillan WD (1930) The theory of the potential. McGraw-Hill, New York

    MATH  Google Scholar 

  28. Hobson E (1955) The therory of spherical and ellipsoidal harmonics. Chelsea Publishing Company, Vermont

    Google Scholar 

  29. Romain G, Jean-Pierre B (2001) Ellipsoidal harmonic expansions of the gravitational potential: theory and application. Celest. Mech. Dyn. Astron. 19:235–275

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Dobrovolskis AR, Bruns JA (1980) Life near the Roche limit: behavior of ejecta from satellites close to planets. Icarus 42:422–441

    Article  ADS  Google Scholar 

  31. German D, Friedlander AL (1991) A simulation of orbits around asteroids using potential field modelling. Adv. Astron. Sci. Spacefl. Mech. 75:1183–1201

    Google Scholar 

  32. Scheeres DJ (1994) Dynamics about uniformly rotating triaxial ellipsoids: applications to asteroids. Icarus 110:225–238

    Article  ADS  Google Scholar 

  33. Rausenberger O (1888) Lehrbuch der Analytischen Mechanik I.B.G. Teubner: Leipzig

    Google Scholar 

  34. Werner RA (1994) The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celest. Mech. Dyn. Astron. 59:253–278

    Article  ADS  MATH  Google Scholar 

  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. 65:313–344

    Article  ADS  MATH  Google Scholar 

  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 University

    Google Scholar 

  37. Petrović S (1996) Determination of the potential of homogeneous polyhedral bodies using line integrals. J. Geodesy 71:44–52

    Article  ADS  MATH  Google Scholar 

  38. Pohánka V (1988) Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophys Prospect 36:733–751

    Article  ADS  Google Scholar 

  39. Tsoulis D, Petrović S (2001) On the singularities of the gravity field of a homogeneous polyhedral body. Geophysics 66:535–539

    Article  ADS  Google Scholar 

  40. Scheeres DJ, Ostro SJ, Hudson RS et al (1996) Orbits close to asteroid 4769 Castalia. Icarus 121:67–87

    Article  ADS  Google Scholar 

  41. Scheeres DJ, Ostro SJ, Hudson RS et al (1998) Dynamics of orbits close to asteroid 4179 Toutatis. Icarus 132:53–79

    Article  ADS  Google Scholar 

  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. 52:685–692

    Article  ADS  Google Scholar 

  43. Wang Y, Xu S (2013) Gravity gradient torque of spacecraft orbiting asteroids. Aircr. Eng. Aerosp. Technol. 85:72–81

    Article  Google Scholar 

  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 1998

    Google Scholar 

  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, Tucson

    Google Scholar 

  46. Scheeres DJ, Williams BG, Miller JK (2000) Evaluation of the dynamic environment of an asteroid: applications to 433 Eros. J. Guid. Control Dyn. 23:466–475

    Article  ADS  Google Scholar 

  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 21–24

    Google Scholar 

  48. Broschart SB, Scheeres DJ (2005) Control of hovering spacecraft near small bodies: application to asteroid 25143 Itokawa. J. Guid. Control Dyn. 28:343–354

    Article  ADS  Google Scholar 

  49. Antreasian PG, Chesley SR, Miller JK et al (2002) The design and navigation of the NEAR SHOEMAKER landing of EROS. Adv. Astron. Sci. 109:989–1015

    Google Scholar 

  50. Lantoine G, Braun RD (2006) Optimal trajectories for soft landing on asteroids. AE8900 MS Special Problems Report, Space Systems Design Lab

    Google Scholar 

  51. Yano H, Kubota T, Miyamoto H, Okada T et al (2006) Touchdown of the Hayabusa spacecraft at the Muses Sea on Itokawa. Science 312:1350–1353

    Article  ADS  Google Scholar 

  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 2012

    Google Scholar 

  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 2008

    Google Scholar 

  54. Chapman CR, Veverka J, Thomas PC (1995) Discovery and physical properties of Dactyl, a satellite of asteroid 243 Ida. Nature 374:783–785

    Article  ADS  Google Scholar 

  55. Richardson DC, Walsh KJ (2006) Binary minor planets. Annu. Rev. Earth Planet. Sci. 34:47–81

    Article  ADS  Google Scholar 

  56. Scheeres DJ (2002) Stability in the full two-body problem. Celest. Mech. Dynam. Astron. 83:155–169

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. Fahnestock EG, Scheeres DJ (2008) Simulation and analysis of the dynamics of binary near-Earth asteroid (66391) 1999 KW4. Icarus 194:410–435

    Article  ADS  Google Scholar 

  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 2006

    Google Scholar 

  59. Maciejewski AJ (1995) Reduction, relative equilibria and potential in the two rigid bodies problem. Celest. Mech. Dyn. Astron. 63:1–28

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. Scheeres DJ (2002) Stability of binary asteroids. Icarus 159:271–283

    Article  ADS  Google Scholar 

  61. Borderies N (1978) Mutual gravitational potential of N solid bodies. Celest. Mech. 18:295–307

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Braun CV (1991) The gravitational potential of two arbitrary, rotating bodies with applications to the Earth–Moon system. University of Texas at Austin, Texas

    Google Scholar 

  63. Moritz H (1980) Advanced physical geodesy. Abacus Press, Wichmann

    Google Scholar 

  64. Geissler P, Petit JM, Durda DD et al (1996) Erosion and ejecta reaccretion of 243 Ida and its Moon. Icarus 120:140–157

    Article  ADS  Google Scholar 

  65. Ashenberg J (2005) Proposed method for modeling the gravitational interaction between finite bodies. J. Guid. Control Dyn. 28:768–774

    Article  ADS  Google Scholar 

  66. Werner RA, Scheeres DJ (2005) Mutual potential of homogenous polyhedra. Celest. Mech. Dyn. Astron. 91:337–349

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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 2005

    Google Scholar 

  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. 96:317–339

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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 2006

    Google Scholar 

  70. Scheeres DJ, Fahnestock EG, Ostro SJ et al (2006) Dynamical configuration of binary near-Earth asteroid (66391) 1999 KW4. Science 314:1280–1283

    Article  ADS  Google Scholar 

  71. Walsh KJ, Richardson DC, Michel P (2008) Rotational breakup as the origin of small binary asteroids. Nature 454:188–191

    Article  ADS  Google Scholar 

  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, Tucson

    Google Scholar 

  73. Mantz A, Sullivan R, Veverka J (2004) Regolith transport in craters on Eros. Icraus 167:197–203

    Article  Google Scholar 

  74. Thomas PC, Belton MJS, Carcich B et al (1996) The shape of Ida. Icarus 120:20–32

    Article  ADS  Google Scholar 

  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, Tucson

    Google Scholar 

  76. Cheng AF, Barnouin JO, Zuber MT et al (2001) Laser altimetry of small-scale features on 433 Eros from NEAR-Shoemaker. Science 292:488–491

    Article  ADS  Google Scholar 

  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, Tucson

    Google Scholar 

  78. Hamilton DP, Burns JA (1991) Orbital stability zones about asteroids. Icarus 92:118–131

    Article  ADS  Google Scholar 

  79. Hamilton DP, Burns JA (1991) Orbital stability zones about asteroids. II. The destabilizing effects of eccentric orbits and of solar radiation. Icarus 96:43–64

    Article  ADS  Google Scholar 

  80. Chauvineau B, Mignard F (1990) Dynamics of binary asteroids. I. Hill’s Case. Icarus 83:360–381

    Article  ADS  MATH  Google Scholar 

  81. Richter K, Keller HU (1995) On the stability of dust particle orbits around cometary nuclei. Icarus 114:355–371

    Article  ADS  Google Scholar 

  82. Hamilton DP, Krivov AV (1997) Dynamics of distant moons of asteroids. Icarus 128:241–249

    Article  ADS  Google Scholar 

  83. Chauvineau B, Farinella P, Mignard F (1993) Planar orbits about a triaxial body: applications to asteroidal satellites. Icarus 105:370–384

    Article  ADS  Google Scholar 

  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 413:394–396

    Article  ADS  Google Scholar 

  85. Korycansky DG, Asphaug E (2004) Simulations of impact ejecta and regolith accumulation on asteroid Eros. Icarus 171:110–119

    Article  ADS  Google Scholar 

  86. Chapman C (2004) Space weathering of asteroid surfaces. Ann. Rev. Earth Planet. Sci. 32:539–567

    Article  ADS  Google Scholar 

  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. 47:1087–1097

    Article  ADS  Google Scholar 

  88. Bottke WF Jr, Melosh HJ (1996) Binary asteroids and the formation of doublet craters. Icarus 124:372–391

    Article  ADS  Google Scholar 

  89. Miljković K, Collins GS, Mannick S, Bland PA (2013) Morphology and population of binary asteroid impact craters. Earth Planet. Sci. Lett. 363:121–132

    Article  ADS  Google Scholar 

  90. Halamek P (1988) Motion in the potential of a thin bar. University of Texas at Austin, Texas

    Google Scholar 

  91. Arnold VI (2010) Mathematical methods of classical mechanics. Springer, New York

    Google Scholar 

  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. 81:235–248

    Article  ADS  MathSciNet  MATH  Google Scholar 

  93. Riaguas A, Elipe A, Lara M (1999) Periodic orbits around a massive straight segment. Celest. Mech. Dyn. Astron. 73:169–178

    Article  ADS  MathSciNet  MATH  Google Scholar 

  94. Liu X, Baoyin H, Ma X (2011) Periodic orbits in the gravity field of a fixed homogeneous cube. Astrophys. Space Sci. 334:357–364

    Article  ADS  MATH  Google Scholar 

  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. 333:409–418

    Article  ADS  MATH  Google Scholar 

  96. Liu X, Baoyin H, Ma X (2013) Dynamics of surface motion on a rotating massive homogeneous body. Sci. China Phys. Mech. Astron. 56:818–829

    Article  ADS  Google Scholar 

  97. Ostro SJ, Hudson RS, Benner LAM (2002) Asteroid radar astronomy. In: William F et al (ed) Asteroids III. University of Arizona Press, Tucson

    Google Scholar 

  98. Kammeyer PC (1978) Periodic orbits around a rotating ellipsoid. Celest. Mech. 17:37–48

    Article  ADS  MathSciNet  MATH  Google Scholar 

  99. Yu Y, Baoyin H (2012) Orbital dynamics in the vicinity of asteroid 216 Kleopatra. Astron. J. 143:62–71

    Article  ADS  Google Scholar 

  100. Yu Y, Baoyin H (2013) Resonant orbits in the vicinity of asteroid 216 Kleopatra. Astrophys. Space Sci. 343:75–82

    Article  ADS  Google Scholar 

  101. Yu Y, Baoyin H (2012) Generating families of 3D periodic orbits about asteroids. Mon. Not. Royal Astron. Soc. 427:872–881

    Article  ADS  Google Scholar 

  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. 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 25:137–148

    Google Scholar 

  104. Jiang Y, Baoyin H, Li J, Li H (2014) Orbits and manifolds near the equilibrium points around a rotating asteroid. Astrophys. Space Sci. 349:83–106

    Article  ADS  Google Scholar 

  105. Maruskin JM, Scheeres DJ, Bloch AM (2009) Dynamics of symplectic subvolumes. Siam J. Appl. Dyn. Syst. 8:180–201

    Article  ADS  MathSciNet  MATH  Google Scholar 

  106. Tsuda Y, Scheeres DJ (2009) Computation and applications of an orbital dynamics symplectic state transition matrix. J. Guid. Control Dyn. 32:1111–1123

    Article  ADS  Google Scholar 

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Yu, Y. (2016). Introduction. In: Orbital Dynamics in the Gravitational Field of Small Bodies. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52693-4_1

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