Generating Symmetric Periodic Orbits and Their Optimal Maintenance in a Binary Asteroid System

Abstract

In this paper, generating symmetric periodic orbits around a binary asteroid and optimal maintenance of spacecraft on these periodic orbits are investigated. Due to the irregular shape of asteroids, numerical methods are needed to generate periodic orbits. In this regard, the 32 families of symmetric periodic orbits were calculated by grid search and shooting methods utilizing the restricted three-body problem as a basic model. The irregularity of the shape of asteroids and solar radiation pressure are considered perturbations. These perturbations should be compensated by a thruster with a continuous thrust through the continuous control strategy, i.e., the linear quadratic regulator (LQR) method. The effect of different matrix coefficients in the performance of the LQR method is examined. The results show that the LQR method could appropriate control spacecraft on periodic orbits with specular shapes. Also, the practical feasibility of a continuous thrust control strategy is discussed.