Collision risk against space debris in Earth orbits

Öpik's formulae for the probability of collision are applied to the analysis of the collision risk against space debris in Low-Earth Orbit (LEO) and Medium Earth Orbit. The simple analytical formulation of Öpik's theory makes it applicable to complex dynamical systems, such as the interaction of the ISS with the whole debris population in LEO The effect of a fragmentation within a multiplane constellation can also be addressed. The analysis of the evolution of the collision risk in Earth orbit shows the need of effective mitigation measures to limit the growth of the collision risk and of the fragmentation debris in the next century.