Many models of the debris population proposed in the literature usually consider only objects larger than 10 cm as the number of small objects is so large (i.e., 200 million of objects larger than 1 mm) that the cost of simulations would be prohibitive. However, also small objects can be detrimental to operative spacecraft and, in particular, objects between 1 and 10 cm are considered extremely critical because they are too large for current debris shields and too small to be tracked. For this reason, getting a deeper insight on the small fragment population is of priority. SpaceDebECM developed methods to describe the motion of small fragments generated by a collision. The proposed approach do not consider each single fragment; rather, it focuses on the spatial density of the fragments within the generated cloud. Two techniques were analysed, one based on the continuity equation and the solution of the density equation through analytical techniques, the second based on the use of differential algebra to expand a cloud of initial condition and semi-analytical techniques to propagate their orbital dynamics.

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