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 the planar 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.
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