Oscillatory orbits in the restricted elliptic planar three body problem

TL;DR

This paper proves the existence of oscillatory trajectories in the restricted elliptic planar three body problem for nearly circular primary orbits, demonstrating complex long-term behaviors in celestial mechanics.

Contribution

It establishes the existence of oscillatory orbits in the restricted elliptic three body problem for nearly circular primary orbits, extending understanding of dynamical complexity.

Findings

Existence of oscillatory trajectories proven

Applicable for primaries in nearly circular orbits

Advances understanding of long-term celestial dynamics

Abstract

The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if it leaves every bounded region but returns infinitely often to some fixed bounded region. We prove the existence of such type of trajectories for any values for the masses of the primaries provided they make almost circular orbits.