A study of the close approach between a planet and a cloud of particles

Abstract

In the present paper we study the close approach between a celestial body and a cloud of particles. This is the situation that occurs when a fragmented comet crosses the orbit of a planet like Jupiter, Saturn, etc. It is assumed that the dynamical system is formed by two main bodies that are in circular orbits around their center of mass and a cloud of particles that is moving under the gravitational attraction of the two primaries. 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 goal is to study the change of the orbit of this cloud of particles after the close approach with the planet. 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 planet. It is desired to known those values after the close approach. In particular, we will study the effects of the periapsis distance in this maneuver.