Symmetric periodic solutions generated by stationary equilibrium states of the average Hill problem with allowance for the planet's oblateness

Astronomy and Astrophysics – Astronomy

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Scientific paper

This paper continues the study of the periodic solutions of double-averaged Hill problem with allowance for the central planet's oblateness. These solutions are generated by the steady-state solutions, stable in the linear approximation. The method of numerical continuation of periodic solutions from a small vicinity of the equilibrium position is used to construct the families of symmetric solutions for the model Sun-Uranus-Satellite system. The evolution of these symmetric solutions as a function of the average perturbing function - the parameter representing the first integral of the problem - is studied and the cases in which the types of solutions change are revealed. The results are illustrated by the projections of symmetric periodic solutions onto the pericenter argument-eccentricity plane and onto the nodal longitude-inclination plane.

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