Families of periodic orbits in the planar Hill four-body problem

Abstract

In this work we perform a numerical exploration of the families of planar periodic orbits in the Hill's approximation in the restricted four body problem, that is, after a symplectic scaling, two massive bodies are sent to infinity, by mean of expanding the potential as a power series in m3^1/3, (the mass of the third small primary) and taking the limit case when m3 tends to zero. The limiting Hamiltonian depends on a parameter mu (the mass of the second primary) and possesses some dynamical features from both the classical restricted three- body problem and the restricted four-body problem. We explore the families of periodic orbits of the infinitesimal particle for some values of the mass pa- rameter, these explorations show interesting properties regarding the periodic orbits for this problem, in particular for the Sun-Jupiter-asteroid case. We also offer details on the horizontal and vertical stability of each family.

Preprint

References in corpus (3)

• Periodic orbits in the restricted four-body problem with two equal masses
• On the "Blue sky catastrophe termination" in the restricted four-body problem
• Hill approximation in a restricted four-body problem

Cited by in corpus (4)

• Regularization of the Hill four-body problem with oblate bodies
• Critical homoclinics in a restricted four body problem: numerical continuation and center manifold computations
• Homoclinic dynamics in a spatial restricted four body problem blue skies into Smale horseshoes for vertical Lyapunov families
• The spatial Hill four-body problem I -- An exploration of basic invariant sets