Orbital maneuvers for a space probe around Titania

For most space missions, it is interesting that the probe remains for a considerable time around the mission target. The longer the lifetime of a mission, the greater are the chances of collecting information about the orbited body. In this work, we present orbital maneuvers that aim to show how to avoid a collision of a space probe with the surface of Titania. Through an expansion of the gravitational potential to the second order, the asymmetry of the gravitational field due to the coefficient $$C_{22}$$ of Titania, the zonal coefficient $$J_2$$ , and the gravitational perturbation of Uranus are considered. Two models of coplanar bi-impulse maneuvers are presented. The first maneuver consists of transferring an initial elliptical orbit to a final circular orbit, and the second has the objective of transferring an initial elliptical orbit to a final orbit that is also elliptical. The lag in the inclination and semi-major axis of the orbits is investigated before performing the maneuvers. To point out the best scenarios for carrying out the maneuvers, a study is presented for different points of an orbit where transfers could be made. In addition, a maneuver strategy is presented to correct the variation of the periapsis argument. The results show that maneuvers performed a few days after integration are more economical than maneuvers performed later, a few days before the collision. The economy of the maneuvers is also demonstrated through an analysis of the ratio of the increase in speed to the lifetime.