Evolution of Fragmentation Cloud in Highly Eccentric Earth Orbits Through Continuum Modelling

A considerable number of fragments orbit around the Earth in Highly Eccentric Orbits (HEOs), mainly in the geostationary transfer orbit. These are believed to have originated in part from the 100 plus fragmentations of parent objects in the same orbit. Many of these objects are characterised by a high area-to-mass ratio, and, as such, especially susceptible to forces induced by atmospheric drag and solar radiation pressure. The complicated dynamics make it difficult to model the evolution of a cloud of such objects, as the spreading depends heavily on their area-to-mass ratios which is difficult to assess. Assumptions on the rapid distribution of a HEO fragment cloud into a band limited by its parent orbit inclination were shown to be inaccurate, and thus oversimplify the problem at hand. Moreover, the time to form a uniformly distributed cloud is higher than the time it takes many of the particles to re-enter. This work aims to increase the understanding of these complex dynamics by accurately modelling the evolution of a cloud of fragments in HEO. The fragment cloud is modelled as a continuum, and its phase space density, rather than single objects, is propagated in time using averaged dynamics in Keplerian elements. Such an approach is not only much faster in terms of computational load when compared to the individual propagation of fragments, but it also improves the accuracy of the density estimation. The perturbations considered are atmospheric drag using a model that was specifically developed for highly eccentric orbits, solar radiation pressure, third bodies and a non-spherical central body implemented in the PlanODyn suite.