Searching for orbits around equilibrium points in a binary asteroid system modeled as a mass dipole

Abstract

The objective of the present work is to search for orbits around the equilibrium points L1 and L2 of the restricted three-body synchronous problem (RTBSP). From the equations of motion of a binary system of asteroids, where one of the asteroids is modeled as a rotating mass dipole, it was possible to determine the initial conditions for Lyapunov orbits. The study was carried out by modifying the mass ratio of the system and the size of the dipole mass in rotation. By line-arizing the equations of motion, it is possible to obtain the eigenvectors and eigenvalues, and, with these values, it was possible to determine the initial estimates of periodic orbits around the equilibrium points using Newton's method. Then, a family of orbits was built around the equilibrium points L1 and L2.