Regularization of the Hill four-body problem with oblate bodies

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.

References in corpus (4)

• Dumb-bell-shaped equilibrium figures for fiducial contact-binary asteroids and EKBOs
• Regularization of the big bang singularity with a time varying equation of state $w>1$
• Surface Gravity of Rotating Dumbbell Shapes
• McGehee regularization of general SO(3)-invariant potentials and applications to stationary and spherically symmetric spacetimes