Regularization of the Hill four-body problem with oblate bodies

TL;DR

This paper studies the Hill four-body problem with oblate bodies, applying regularization techniques to collisions and analyzing how the collision manifold changes with oblateness, revealing a bifurcation at zero oblateness.

Contribution

It introduces a regularization method for collisions in the Hill four-body problem with oblate bodies and analyzes the bifurcation of the collision manifold as oblateness varies.

Findings

Collision manifold undergoes a bifurcation at zero oblateness.

Regularization via McGehee coordinates effectively handles collisions.

The shape of the collision manifold depends on the oblateness coefficient.

Abstract

We consider the Hill four-body problem where three oblate, massive bodies form a relative equilibrium triangular configuration, and the fourth, infinitesimal body orbits in a neighborhood of the smallest of the three massive bodies. We regularize collisions between the infinitesimal body and the smallest massive body, via McGehee coordinate transformation. We describe the corresponding collision manifold and show that it undergoes a bifurcation when the oblateness coefficient of the small massive body passes through the zero value.