The goal of this research is to study close approaches between a planet, which is assumed to have an atmosphere, and a cloud of particles. This cloud of particles is formed during the passage of a spacecraft by the atmosphere, due to its explosion. The complete system is formed by two main bodies (the Sun and the planet), that are assumed to stay in circular orbits around their center of mass, and the spacecraft, that is then transformed in a cloud of particles. This spacecraft is moving under the gravitational attractions of the two main bodies when it makes a close approach with the planet in such a position that it passes inside the atmosphere of the planet and then is transformed in a cloud of particles. The motion is assumed to be planar for the spacecraft and all the particles and the dynamics is given by the well-known planar restricted circular three-body problem plus atmospheric drag. For the simulations shown here the planet Jupiter is used as the body for the close approach, but the method works well for any planet. The initial conditions for the spacecraft and the particles of the cloud are specified at the periapsis, because it is assumed that the fragmentation of the spacecraft occurs at this point.
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