Analytical model for the propagation of small debris objects after a fragmentation event

Current debris evolutionary models usually neglect fragments smaller than 10 cm in their predictions because of the high computational effort they add to the simulation. However, also small fragments can be dangerous to operational satellites. This work proposes an analytical approach to describe the evolution of a cloud of small fragments generated by a collision in Low Earth Orbit. The proposed approach considers the cloud globally and derives analytically its evolution in terms of density, under the effect of drag. As a result, the analytical approach allows the representation of small fragments and noticeably reduces the computational time.