A study of the dispersion of a cloud of particles due to a close approach

This paper performs an analytical study of the effects of a close approach between a planet and a cloud of particles. It is assumed that the maneuver is planar and that the particles that form the cloud has a uniform distribution of semi-major axis and eccentricity around a nominal value with a given amplitude (a ± Δa and e ± Δe). The main goal is to study the distribution of those two orbital elements after the close approach, in terms of the amplitude and area (in the plane a-e) of the distribution of the orbital elements. Two solutions are considered for the maneuver, to take into account the possibility of the cloud to pass behind or in front of the planet. For the numerical simulations, the planet Saturn is used.