Study of collision probability considering a non-uniform cloud of space debris

The present paper aims to study the cumulative collision probability of a target that crosses a cloud of particles that has the orbital parameters of each individual element modified by a close approach with the Earth. Clouds of this type are formed when natural or man-made bodies explode for some reason. After an explosion like that, the individual particles have different trajectories. The clouds are specified by a non-uniform distribution of semi-major axis and eccentricity of their particles which are assumed to pass close to the Earth, making a close approach that modifies the trajectory of every single particle that belongs to the cloud. This study makes simulations considering separately two different clouds based on the patched conics model to obtain the new trajectories of each particle and to analyze the density of the whole cloud. Then it is possible to map the new distribution of the orbital elements of the fragments that constituted the cloud, using the distribution as initial conditions. After calculating the spatial density for the whole cloud, it is possible to obtain the cumulative collision probability for one space vehicle that crosses the cloud. These pieces of information are important when planning satellite missions where a spacecraft passes close to a cloud of this type, because we can determine values to study the risks of collision and the possible maneuvers that need to be made to avoid them.