Abstract
This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body’s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stability regions in a numerical experiment. Some stability conclusions are obtained. As a typical example, it is shown in detail that near circular 1:2 resonant orbit is always unstable.
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Pravec, P., Harris, A.W.: Fast and slowly rotating asteroids. Icarus 148 12–20 (2000)
Hu, W., Scheeres, D.J.: Numerical determination of stability regions for orbital motion in uniformly rotating second degree and order gravity fields. Planetary and Space Science 52, 685–692 (2004)
Garfinkel, B.: On the motion of a satellite of an oblate planet. The Astronomical Journal 63, 88–96 (1958)
Kozai, Y.: The motion of a close earth satellite. The Astronomical Journal 64, 367–377 (1956)
Brouwer, D., Clemence, G.M.: Methods of Celestial Mechanics. Academic Press, USA (1961)
Kaula, W.M.: Theory of Satellite Geodesy. Blaisdell, Boston (1996)
Gedeon, G.S.: Tesseral resonance effects on satellite orbits. Celestial Mechanics and Dynamical Astronomy 1, 167–189 (1969)
Ely, T.A., Howell, K.C.: Long-term evolution of artificial satellite orbits due to resonant tesseral harmonics. The Journal of the Astronomical Science 44, 167–190 (1996)
Scheeres, D.J.: Dynamics about uniformly rotating triaxial ellipsoids: Applications to asteroids. Icarus 110, 225–238 (1994)
Scheeres, D.J., Ostro, S.J., Hudson, R.S., et al.: Orbits close to asteroid 4769 Castalia. Icarus 121, 67–87 (1996)
Scheeres, D.J., Hu, W.: Secular motion in a 2nd degree and order gravity field with no rotation. Celestial Mechanics and Dynamical Astronomy 79, 183–200 (2001)
Hu, W., Scheeres, D.J.: Spacecraft motion about slowly rotating asteroids. AIAA Journal of Guidance Control and Dynamics 25, 765–775 (2002)
Hu, W.: Orbitalmotion in uniformly rotating second degree and order grivity fields, [Ph.D. Thesis]. The University of Michigan, USA (2002)
Shi, X., Cui, H., Cui, P., et al.: Spacecraft motion analysis about rapid rotating small body. Journal of Harbin Institute of Technology 10, 363–366 (2003)
Danby, J.M.A.: Fundamentals of Celestial Mechanics. (2nd edn.). Willmann-Bell, USA (1992)
Khalil, H.: Nonlinear Systems, (2nd edn). Prentice Hall, USA (1996)
Arnold, V.I.: Dynamical Systems III (Encyclopaedia of Mathematical Sciences). Springer-Verlag, Berlin, Heidelberg (1988)
Hu, W., Scheeres, D.J.: Periodic orbits in rotating second degree and order gravity fields. Chinese Journal of Astronomy and Astrophysics 8, 108–118 (2008) (in Chinese)
Roy, A.E.: Orbital Motion. (3rd edn.). Adam Hilger, Bristol and Philadelphia (1988)
Olsen, Ø: Orbital resonance widths in a uniformly rotating second degree and order gravity field. Astronomy & Astrophysics 449, 821–826 (2006) (in Chinese)
Celletti, A.: Stability and Chaos in Celestial Mechanics. Praxis Publishing, Springer, UK (2010)
Scheeres, D.J.: Orbital mechanics about asteroids and comets. AIAA J. of GCD 35, 987–997 (2012)
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Hu, WD., Scheeres, D.J. Averaging analyses for spacecraft orbital motions around asteroids. Acta Mech Sin 30, 294–300 (2014). https://doi.org/10.1007/s10409-014-0050-9
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DOI: https://doi.org/10.1007/s10409-014-0050-9