Multiple Bifurcations in the Periodic Orbit around Eros

TL;DR

This paper analyzes the complex bifurcation structures of periodic orbits around asteroid 433 Eros, revealing multiple types of bifurcations and stable/unstable regions in the orbital dynamics.

Contribution

It identifies and characterizes multiple bifurcation types in periodic orbit families around a highly irregular asteroid, including binary and triple bifurcations, expanding understanding of orbital stability.

Findings

Binary period-doubling bifurcations create nearly circular stable orbits.

Unstable regions separate stable orbital zones around Eros.

Triple bifurcations involve two saddle and one period-doubling bifurcation.

Abstract

We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.