Close Approaches for a Cloud of Particles with the Moon

摘要

The goal of this research is to study close approaches between the Moon and a cloud of particles. The system is formed by two main bodies (the Earth and the Moon) and it is assumed that they are in circular orbits. The cloud of particles is moving under their gravitational attraction. The motion is assumed to be planar for all the particles and the dynamics given by the "patched-conic" approximation is used, which means that a series of two-body problems are used to generate analytical equations that describe the problem. The main obejctive is to understand the change of the orbit of this cloud of particles after the close approach with the Moon. It is assumed that all the particles that belong to the cloud have semi-major axis a ± da and eccentricity e ± de before the close approach with the Moon, such that the particles are inside a circle (in the semi-major axis-eccentricity plane) with center in the center of mass of the cloud. It is desired to known those values after the close approach.