Gravitational Capture Using a Four-Body Model

Abstract: A spacecraft (or any particle with negligible mass) suffers a gravitational capture when its orbit changes from hyperbolic (small positive energy) around a celestial body into elliptic (small negative energy) using only gravitational forces. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third and the fourth bodies involved in the dynamics. Those forces are equivalent of a zero cost control applied to the spacecraft, equivalent to a continuous thrust. One of the most important applications of this property is the construction of trajectories to the Moon. The concept of gravitational capture is combines with the principles of the gravity-assisted maneuver and the bi-elliptic transfer orbit, to generate a trajectory that requires a fuel consumption smaller than the one required by the Hohmann transfer. The present paper study the energy required for the ballistic gravitational capture in a dynamical model that has the presence of four bodies. Those bodies are assumed to follow the assumptions of the bi-circular model. In particular, the Earth-Moon-Sun-Spacecraft system is considered