Analytical Propagation of Space Debris Density for Collisions near Sun-Synchronous Orbits

The increasing frequency of human launches has led to a dramatic increase in the amount of space debris, especially near sun-synchronous orbits. Most of the fragments are small in size, which may make tracking difficult. Therefore, characterizing the distribution, evolution, and collision risk of small debris has long been a difficult issue. This paper is aimed at investigating the orbital evolution and global dispersion behavior of debris clouds near sun-synchronous orbits. Firstly, the NASA breakup model is used to provide an initial distribution of small fragments after collision events. Secondly, the continuity equation is adopted to propagate the density variation analytically. Furthermore, we introduce some statistical quantities and the entropy of debris clouds to model the randomness and band formation. A theorem concerning the equivalence of the band formation and maximal entropy is presented. The accuracy of the band formation time estimation is also discussed. For noncatastrophic collisions at an altitude of 800 km due to a projectile with a mass of 100 g and a collision velocity of 1 km/s, we compare the analytical and numerical results of space debris density. The results show that the maximal peak error is within 0.17, and the mean square error is about 0.25 at 400 days. Additionally, the entropy of right ascension of the ascending node is 8.5% less than that for debris clouds near an orbit with the same altitude and an inclination of 30 deg. This indicates the concentrating behavior for debris clouds near sun-synchronous orbits.