Abstract
In this work, sufficient conditions for computing periodic solutions have been obtained in the circular Hill Problem with regard to arbitrary disturbing forces. This problem will be solved by means of using the averaging theory for dynamical systems as the main mathematical tool that has been applied in this work.
Highlights
The three-body problem, as it is known, is a special case of the n−body problem where the motion of three point masses under their mutual gravitational interactions is described
In [2], the authors focused their attention on the case of a perturbed spatial Hill lunar problem using the averaging theory, and in [3], Chavineau and Mignard studied the trajectories of the Hill problem to describe the effect of solar perturbations on the relative motion of a binary asteroid
Our main goal in this study was to find, using the averaging theory, sufficient conditions for the existence of periodic orbits that come from the Lagrangian points of the circular Hill problem with arbitrary disturbing forces
Summary
The three-body problem, as it is known, is a special case of the n−body problem where the motion of three point masses under their mutual gravitational interactions is described. Our main goal in this study was to find, using the averaging theory, sufficient conditions for the existence of periodic orbits that come from the Lagrangian points of the circular Hill problem with arbitrary disturbing forces. We are going to study if and when the parameter ε is sufficiently small, and when the perturbed functions Fi for i ∈ {1, 2, 3} have a period of either pT1 /q or pT2 /q, whether these solutions still exist for the perturbed system (3). Such that, whenever ε → 0, ( x (t, ε), y(t, ε), z(t, ε)) tends to the periodic solution of the unperturbed system q
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