Lunar gravity assists using patched-conics approximation, three and four body problems

Abstract

The gravity assist is a maneuver greatly applied to space missions, with the main goal of giving or removing energy of a spacecraft through a passage near a celestial body. The patched-conics approximation is the first approximation that is usually considered in the mission planning. It gives a good accuracy in the majority of the situations. However, when using the Moon for the close approach, the results have a tendency to diverge from a more complete three body dynamics. This is due to the large mass of the Moon compared to the Earth. In that sense, the goal of the present paper is to study the errors given by the patched-conics approximation in a lunar gravity assist maneuver. To find those errors we compare the results coming from this approximation with the equivalent results obtained from the circular restricted three body problem and the bi-circular restricted four body problem for a same periselenium condition. This comparison is made in the orbital elements before the maneuver and the C3 of the spacecraft after the maneuver under the three models considered. Different values for the initial conditions of the spacecraft are used to obtain general conclusions about the behavior of the errors involved. We conclude that there is a tendency to a better agreement between the patched-conics and the three body problem for retrograde transfer orbits. We also find that the effects of the Sun in the maneuver needs to be included only in more accurate steps of the mission.