A study of the impact of the initial energy in a close approach of a cloud of particles

摘要

In this paper we perform a study of the effects of a close approach in the three-dimensional space between a planet and a cloud of particles, with the goal of understanding the dispersion of this cloud in terms of the variations of velocity, energy, angular momentum and inclination. It is assumed that the cloud is formed at the periapsis and the particles differ only by the magnitude of the velocity at this point. In this research we use the three-dimensional circular restricted three-body problem as the basic model for this close approach. A numerical algorithm is developed and implemented to study this problem and then it is applied to a cloud of particles, based in an analytical description of the close approach maneuver in the three-dimensional space. Analytical equations based in the patched conics approximation are used to calculate the variation in velocity, angular momentum, energy and inclination of the spacecraft that performs this maneuver.