Time-of-Flight Analyses for the Gravitational Capture Maneuver

Abstract

Several aspects of the time of flight involved in the problem of gravitational capture in the regularized, restricted three-body problem are studied. A gravitational capture occurs when a massless particle changes its two-body energy around one celestial body from positive to negative without the use of nongravitational forces. The importance of several parameters involved in a capture in the Earth-moon system is studied. In particular, the time required for the capture is studied under different initial conditions. This information is very important for mission designers for two reasons: 1) the time for gravitational capture has an impact in the duration of any mission that uses this technique; and 2) the gravitational capture is a very sensitive phenomenon and, if the time involved is too large, perturbations from different sources may influence the mission too much. The results show the existence or regions where the time for the capture is reduced by a factor close to 10 with an adequate choice of initial conditions, without the reduction of the energy savings. In addition, the results are used to solve a family of optimization problems, such as the problem of finding trajectories that can perform a gravitational capture in a minimum time with a fixed savings or with maximum savings with an upper time limit.