A new stochastic impressionistic low Earth model of the space debris scenario

Abstract

A new Stochastic IMPressionistic Low Earth (SIMPLE) model of the space debris environment using a stochastic approach is presented in this paper. The present approach and philosophy are similar to that utilized for evolving the international standard or other reference atmospheres. Presently, this model describes the debris scenario up to an altitude of 2000 km and with eccentricity less than 0.2 thus covering about 75% of the large space debris objects catalogued in USSPACECOM two line element (TLE) sets. Two types of models one called ‘gross’ provides insight into the physical process by characterizing the distribution of the number density ‘ n ’, eccentricity ‘ e ’, and the ballistic coefficient ‘ B ’ of objects over the whole of the LEO region for all inclinations put together as also separately. The other called ‘local’ model characterizes the distribution of ‘ e ’ and ‘ B ’ of the debris across suitable local altitude and perigee bins useful for mission analysis and risk assessment for spacecraft designers interested in specific altitude or perigee height bins and inclination bands. The number density ‘ n ’ in all the gross models can be represented in terms of a mixture of Laplace distributions. The SIMPLE model with much less parameters than in ORDEM96 captures closely all the peak fragment densities without loss of accuracy at other altitudes. The distribution of ‘ e ’ and the ‘ B ’ in each and every gross and local model can be represented by suitable lognormal distributions. Qualitatively the parameters of the ‘ n ’ and ‘ e ’ distributions in the gross and the local models exhibit statistically quasi-equilibrium state (though quantitatively the fragment density is varying all over) across the time period from 1999 to 2002 and hence an average is recommended as the model value. Since, the parameters of ‘ B ’ show large variations or trend in their values derived from the TLE data sets, the latest year 2002 value is suggested as a reference in the model. Lastly some application areas of the SIMPLE model are provided along with possible approaches to estimate the spatial density of debris objects and their flux in each altitude bin of interest.