Series Expansions for EncounterType Solutions of Hill's Problem
Abstract
Hill's problem is defined as the limiting case of the planar threebody problem when two of the masses are very small. This paper describes analytic developments for encountertype solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem.
 Publication:

Celestial Mechanics
 Pub Date:
 January 1986
 DOI:
 10.1007/BF01234287
 Bibcode:
 1986CeMec..38...67H
 Keywords:

 Hill Method;
 Orbital Rendezvous;
 Rendezvous Trajectories;
 Three Body Problem;
 Circular Orbits;
 Eccentric Orbits;
 Equations Of Motion;
 Numerical Integration;
 Astrophysics