On the periodically evolving orbits in the singly averaged Hill problem

Details On the periodically evolving orbits in the singly averaged Hill problem On the periodically evolving orbits in the singly averaged Hill problem

Apr 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008astl...34..280v&link_type=abstract

Astronomy Letters, Volume 34, Issue 4, pp.280-288

Astronomy and Astrophysics

Astronomy

1

Scientific paper

We continue to analyze the periodic solutions of the singly averaged Hill problem. We have numerically constructed the families of solutions that correspond to periodically evolving satellite orbits for arbitrary initial values of their eccentricities and inclinations to the plane of motion of the perturbing body. The solutions obtained are compared with the numerical solutions of the rigorous (nonaveraged) equations of the restricted circular three-body problem. In particular, we have constructed a periodically evolving orbit for which the well-known Lidov-Kozai mechanism manifests itself, just as in the doubly averaged problem.

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