"A note on the full two-body problem and related restricted full three-" by Xiyun Hou and Xiaosheng Xin

Article Title

A note on the full two-body problem and related restricted full three- body problem

Authors

Xiyun Hou, School of Astronomy and Space Science, Nanjing University, Nanjing 210023, China Institute of Astrodynamics and Space Environment, Nanjing University, Nanjing 210093, China
Xiaosheng Xin, School of Astronomy and Space Science, Nanjing University, Nanjing 210023, China Institute of Astrodynamics and Space Environment, Nanjing University, Nanjing 210093, China

Keywords

full two-body problem (F2BP), restricted full three-body, problem (RF3BP), binary asteroid, collinear libration point

Abstract

Truncating at the second order of the mutual potential between two rigid bodies, time-explicit first order solutions to the rotations and the orbital motion of the two bodies in theplanar full two-body problem (F2BP) are constructed. Based on this analytical solution,equations of motion (EOMs) for the related restricted full three-body problem are given.In the case of the synchronous or double synchronous states for the full two-body problem,EOMs for the related restricted full three-body problem (RF3BP) are also given. At last,one example—the “collinear libration point” in the binary asteroid system—is given.