Annihilation of Relative Equilibria in the Gravitational Field of Irregular-shaped Minor Celestial Bodies

TL;DR

This paper classifies how relative equilibrium points in irregular minor celestial bodies can annihilate or create as their rotation speeds change, revealing complex behaviors and object-specific classifications.

Contribution

It introduces a detailed classification system for equilibrium point annihilations in irregular-shaped minor celestial bodies, including specific cases for bodies with five, seven, and nine equilibria.

Findings

Most minor bodies have five equilibrium points.

Number of annihilations is twice the number of equilibrium points between one and five.

Different celestial bodies exhibit distinct annihilation classifications.

Abstract

The rotational speeds of irregular shaped minor celestial bodies can be changed by the YORP effect. This variation in speed can make the numbers, positions, stabilities, and topological cases of the minor body s relative equilibrium points vary. The numbers of relative equilibrium points can be reduced through the collision and annihilation of relative equilibrium points, or increase through the creation and separation of relative equilibrium points. Here we develop a classification system of multiple annihilation behaviors of the equilibrium points for irregular shaped minor celestial bodies. Most minor bodies have five equilibrium points; there are twice the number of annihilations per equilibrium point when the number of equilibrium points is between one and five. We present the detailed annihilation classifications for equilibria of objects which have five equilibrium points. Additionally, the annihilation classification for the seven equilibria of Kleopatra shaped objects and the nine equilibria of Bennu shaped objects are also discussed. Equilibria of different objects fall into different annihilation classifications. By letting the rotational speeds vary, we studied the annihilations and creations of relative equilibria in the gravitational field of ten minor bodies.