# Bifurcation of equilibrium points in the potential field of asteroid 101955 Bennu

## TL;DR

This study analyzes how variations in density and rotation period affect the number, position, and stability of equilibrium points in Bennu's gravitational potential, revealing bifurcations that complicate its dynamical environment.

## Contribution

It introduces a dimensionless parameter to study the effects of density and rotation on equilibrium points and demonstrates bifurcations in Bennu's potential field due to these variations.

## Key findings

- Nine equilibrium points identified in Bennu's potential field.
- Bifurcations occur as density and rotation period vary.
- Stability of equilibrium points is sensitive to parameter changes.

## Abstract

The stability and topological structure of equilibrium points in the potential field of the asteroid 101955 Bennu have been investigated with a variable density and rotation period. A dimensionless quantity is introduced for the nondimensionalization of the equations of motion, and this quantity can indicate the effect of both the rotation period and bulk density of the asteroid. Using the polyhedral model of the asteroid Bennu, the number and position of the equilibrium points are calculated and illustrated by a contour plot of the gravitational effective potential field. The topological structure and the stability of the equilibrium points are also investigated using the linearized method. The results show that there are nine equilibrium points in the potential field of the asteroid Bennu, eight in the exterior of the body and one in the interior of the body. Moreover, bifurcation will occur with a variation of the density and rotation period. Different equilibrium points will encounter each other and mix together. Thus, the number of equilibrium points will change. The stability and topological structure of the equilibrium points will also change because of the variation of the density and rotation period of the asteroid. When considering the error of the density of Bennu, the range of the dimensionless quantity covers the critical values that will lead to bifurcation. This means that the stability of the equilibrium points is uncertain, making the dynamical environment of Bennu much more complicated. These bifurcations can help better understand the dynamic environment of an irregular-shaped asteroid.