Abstract by Garret Carver
Study of local behavior at the colinear equilibrium of the restricted 4-body problem
Inspired by the YE5 2017 observation of a binary asteroid pair that had nearly equal masses we conduct a study of the equations of motion that describe a ’restricted’ four body problem. This paper examines the separated collinear equilibrium points and constructs a linear approximation of the position written as a function of the asteroid mass parameters. This provides insight into the local linear behavior of a binary pair of asteroids in their equilibrium positions. We conclude that the position of both asteroids monotonically decreases relative to the first mass parameter and monotonically increases relative to the second mass parameter.