Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

The present paper has the goal of studying close approaches between a planet and a group of particles. The mathematical model includes the presence of the atmosphere of the planet. This cloud is assumed to be created by the passage of the spacecraft in the atmosphere of the planet, which can cause the explosion of the spacecraft. The system is assumed to be formed by the Sun, the planet, and the spacecraft that explodes and becomes a cloud of particles. The Sun and the planet are assumed to be in circular orbits and the motion is planar. The equations of motion are the ones given by the circular planar restricted three-body problem combined with the forces given by the atmospheric drag. In the numerical simulations, the planet Jupiter is the celestial body used for the close approaches. The initial positions and velocities of the spacecraft and the particles are specified at the periapsis, because it is assumed that this is the point where the explosion occurs.