Hill approximation in a restricted four-body problem

Abstract

We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very small compared with the other two, m1 and m2, and we study the Hamiltonian system describing the motion of the massless particle in a neighborhood of m3. In a similar way to Hill approximation of the lunar problem, we perform a symplectic scaling, sending the two massive bodies to infinity, expanding the potential as a power series in m3, and taking the limit case when m3 tends to cero. We show that the limiting Hamiltonian inherits dynamical features from both the restricted three-body problem and the restricted four-body problem. In particular, it extends the classical lunar Hill problem. We investigate the geometry of the Poincare sections, direct and retrograde periodic orbits about m3, libration points, periodic orbits near libration points, their stable and unstable manifolds, and the corresponding homoclinic intersections. The motivation for this model is the study of the motion of a satellite near a jovian Trojan asteroid.

This work is an improvement of a previous work

References in corpus (3)

• The Puzzling Mutual Orbit of the Binary Trojan Asteroid (624) Hektor
• On the "Blue sky catastrophe termination" in the restricted four-body problem
• The dynamics of the elliptic Hill problem : Periodic orbits and stability regions

Cited by in corpus (5)

• Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
• Families of periodic orbits in the planar Hill four-body problem
• 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