Analysis of the Potential Field of Asteroids with Arbitrary Mass Distribution Using Polyhedral Approach

Abstract

The paper develops a new method to calculate the potential field of the asteroids with arbitrary mass distribution. The accuracy of this method is based on both the resolution of the polyhedron and the truncation error of the Legendre series. Here we compare the potential fields get by both our method and the traditional method using homogeneous polyhedral model to indicate the feasibility of our method. We also show the differences in the potential fields and the corresponding equilibrium points between the homogeneous model and the heterogeneous model to emphasize the great importance of the heterogeneous model in the researches about the dynamical environment of asteroids.

Keywords

polyhedral model / heterogeneous asteroids / potential field

References

[1] 崔平远, 乔栋. 小天体附近轨道动力学与控制研究现状与展望[J]. 力学进展, 2013, 43(5): 526-539. Cui P Y,Qiao D.Research progress and prospect of orbital dynamics and control near small bodies[J].Advances in Mechanics,2013, 43(5): 526-539.
[2] Werner R A. The gravitational potential of a homogeneous polyhedron or don't cut corners[J]. Celestial Mechanics and Dynamical Astronomy, 1994, 59(3): 253-278.
[3] Miller J K, Konopliv A S, Antreasian P G, et al. Determination of shape, gravity, and rotational state of asteroid 433 Eros[J]. Icarus, 2002, 155(1): 3-17.
[4] Scheeres D J, Broschart S, Ostro S J, et al. The dynamical environment about Asteroid 25143 Itokawa: target of the Hayabusa Mission[C]//AIAA/AAS Astrodynamics Specialist Conference and Exhibit. [S. l]: AIAA, 2004: 16-19.
[5] Wang X, Jiang Y, Gong S. Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies[J]. Astrophysics and Space Science, 2014, 353(1): 105-121.
[6] Fahnestock E G, Scheeres D J. Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach[J]. Celestial Mechanics and Dynamical Astronomy, 2006, 96(3-4): 317-339.
[7] 张振江, 崔祜涛, 任高峰. 不规则形状小行星引力环境建模及球谐系数求取方法[J]. 航天器环境工程, 2012 (3): 383-388. Zhang Z J,Cui H T,Ren G F.Modeling for the gravitation potential environment of anirregular-shaped asteroid and the spherical harmonic coefficient estimation[J].Spacecraft Environment Engineering,2010(3): 383-388.
[8] Scheeres D J, Khushalani B, Werner R A. Estimating asteroid density distributions from shape and gravity information[J]. Planetary and Space Science, 2000, 48(10): 965-971.
[9] Werner R A, Scheeres D J. Mutual potential of homogeneous polyhedra[J]. Celestial Mechanics and Dynamical Astronomy, 2005, 91(3-4): 337-349.