Abstract
The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill’s equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linearised equations and also of the third-order solution computed by D.L. Richardson and J.W. Mitchell (2003). With the algorithm presented, those orbits can be computed in a fast and efficient way up to a high-order in the in-plane and out-of-plane amplitudes.
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Gómez, G., Marcote, M. High-order Analytical Solutions of Hill’s Equations. Celestial Mech Dyn Astr 94, 197–211 (2006). https://doi.org/10.1007/s10569-005-4821-2
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DOI: https://doi.org/10.1007/s10569-005-4821-2