Spatial density approach for modelling of the space debris population

This article proposes a continuum density approach for space debris modelling. The debris population in Low Earth Orbit (LEO) is represented through its density in semi-major axis, eccentricity and inclination. The time evolution of the density in orbital elements is modelled through the continuity equation. The perturbing effect of aerodynamic drag is included in the divergence term, while the effect of fragmentation can be seen as source term in the equation. The spatial density is then calculated from the orbital element density at each time. The proposed continuum method is used to analyse the evolution of the debris population in LEO; as initial condition the debris 2013 population is used. Then, the effect of a breakup event is superimposed onto the global population of space debris and its effect analysed; the fragment distribution caused by the breakup up of satellite DMSP-F13 is considered as test case scenario.