The proposed work aims to study the orbital motion of a spacecraft orbiting a binary or even a ternary asteroid system. The word full from the full three-body problem is due to the non-spherical bodies that composes the system; in this case, the asteroids. The three-body problem is modeled as the mass of the spacecraft does not influence the motion of the primary bodies, which is the reason for the term "restricted". The problem is complex as the gravitational field is not uniform and it varies over the time due to the non-sphericity of the body and its rotation. The special case where the primary bodies move in circular orbits can lead to some analytical results. For the case where the orbits are not circular, the equations of motion must be solved numerically. The stability of the equilibrium points must be evaluated for each system. The orbits around the asteroids with less perturbation and close to the equilibrium points are close to the Lissajous orbits for a certain period of time. As the non-uniform gravitational potential of the bodies changes over the time, the trajectory deviates and the orbits become unstable. The idea to find less perturbed orbits where the equilibrium points do not exist and search for maneuvers to keep the trajectory with the lowest V possible from the thrusters. Optimal maneuvers with less fuel consumption increase the life-time of space vehicles and increase the mission duration.
News published in Agência FAPESP Newsletter about the scholarship: