Analytical model for the propagation of small-debris-object clouds after fragmentations

Current debris evolutionary models usually neglect fragments smaller than 10 cm because of the high computational effort they add to the simulation. However, small-debris objects can also be dangerous to operational satellites. This work proposes ananalytical 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 its evolution analytically, in terms of the change in the spatial density under the effect of atmospheric drag. As a result, the analytical approach allows the representation of small fragments and noticeably reduces the computational time under 10% compared to the numerical propagation of all the fragment trajectories. For altitudes above 800 km, the relative error compared to the numerical method is lower than 10%.