Analytical Model for the Propagation of Small-Debris-Object Clouds After Fragmentations

Abstract

Current debris evolutionary models usually neglect fragments smaller than 10 cm because of the high computational effort they add to the simulation. However, small debris objects can also be dangerous to operational satellites. This work proposes an analytical approach to describe the evolution of a cloud of small fragments generated by a collision in Low Earth Orbit. The proposed approach considers the cloud globally and derives its evolution analytically, in terms of the change in the spatial density under the effect of atmospheric drag. As a result, the analytical approach allows the representation of small fragments and noticeably reduces the computational time under 10% compared to the numerical propagation of all the fragment trajectories.For altitudes above 800 km the relative error compared to the numerical method is lower than 10%. R E = Earth's radius [km]

Multidimensional extension of the continuity equation method for debris clouds evolution

“…This approach provides an accurate description of the evolution of clouds produced by fragmentation events at altitudes higher than 800 km and for any inclination, with a reduced computational effort with respect to of the numerical propagation (Letizia et al, 2015a). Therefore, it can be applied to study many different scenarios of collisions to understand, for example, which objects, in case of fragmentation, are more likely to have a large impact on the global collision risk for operational satellites (Letizia et al, 2015b).…”

“…The continuity equation can be applied to study a single fragmentation event by using the approach summarised in the block diagram in Figure 2: a brief description of the proposed analytical model for cloud propagation in LEO (cielo, debris Cloud Evolution in Low Earth Orbits) is presented here, whereas an extensive explanation of each block can be found in Letizia et al (2015a). The first block is a breakup model, which generates the fragments and their characteristics (e.g., mass, velocity) given the energy of the fragmentation event.…”

“…• the method can be applied to fragmentation events at 800 km as at lower altitudes the hypothesis of circular orbits in Equation 3 introduces a large error on the evolution of the cloud density (Letizia et al, 2015a).…”

“…In a previous work (Letizia et al, 2015a), this novel approach to debris propagation was validated and applied to study the evolution of debris fragment clouds generated by collisions in LEO. The method, summarised in Section 2, is able to model the evolution of debris clouds including all the small fragments down to 1 mm in size, with a reduced computational effort compared to the propagation of the individual trajectories.…”

Survey of the Current Activities in the Field of Modeling the Space Debris Environment at TU Braunschweig

“…The time history on number of TLE fragments for four different events is shown in Figure 5. These include the Chinese anti-satellite test regarding Fengyun-1C [12], fragments from Cosmos-2251, which was involved in the Cosmos-Iridum collision in 2009 [13] and the explosions of DMSP-F13 [14] and NOOA-16 [15]. Therein, the shaded areas show the time from the last number update until today.…”