Collision Probability Due to Space Debris Clouds Through a Continuum Approach

Abstract

As the debris population increases, the probability of collisions in space grows. Due to the high level of released energy, even collisions with small objects may produce thousands of fragments. Propagating the trajectories of all the objects produced by a breakup could be computationally expensive. Therefore, in this work debris clouds are modeled as a uid, whose spatial density varies with time under the eect of atmospheric drag. By introducing some simplifying assumptions, such as an exponential model of the atmosphere, an analytical expression for the cloud density evolution in time is derived. The proposed approach enables the analysis of many potential fragmentation scenarios that would be time-limited with current numerical methods that rely on the integration of all the fragments' trajectories. In particular, the proposed analytical method is applied to evaluate the consequences of some recent breakups on a list of target objects. In addition, collision scenarios with dierent initial conditions are simulated to identify which parameters have the largest eect on the resulting collision probability. Finally, the proposed model is used to study the mutual inuence among a set of high risk targets, analyzing how a fragmentation starting from one spacecraft 1 PhD Candidate, Astronautics Research Group, f.letizia@soton.ac.uk 2 Lecturer, PhD, Marie Curie Research fellow at Politecnico di Milano, Italy, AIAA member, c.colombo@soton.ac.uk 3 Senior lecturer, PhD, Astronautics Research Group, h.g.lewis@soton.ac.uk 1 aects the collision probability of the others.

Assessment of breakup severity on operational satellites

“…For non-equatorial orbits β max is set equal to the inclination where the fragmentation occurred i F if i F ≤ π/2 and equal to π −i f otherwise (Letizia et al, 2015c).…”

Multidimensional extension of the continuity equation method for debris clouds evolution

“…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). This was done by applying the proposed method to compute a grid of fictitious breakups, store the scenario evolution, and evaluate their effect on several targets without having to simulate the fragmentations for each target spacecraft.…”

“…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. This enabled to perform an extended analysis on the contribution of small fragments to the collision probability (Letizia et al, 2015b), proving that the method can be useful to evaluate the hazard posed by small fragments to operational spacecraft.…”

Evolution of space debris for spacecraft in the Sun-synchronous orbit

“…Kurihara et al (2015) investigated the impact frequency calculated by the debris environment model and the impact craters on the surface of the exposed instrument of the Tanpopo mission; they suggested that the impact energy is in proportion to the crater volume, and is not related to the projectile materials and relative speed. Letizia et al (2016) modeled the debris clouds as a uid with the density changed under the force caused by the atmospheric drag, they derived the analytical expression for the density evolution of the uid, and the method can be applied for the simulation of several collision scenarios in a short time. Francesconi et al (2015) used the honeycomb sandwich panels to model the structure of the spacecraft and presented an engineering model describing debris clouds.…”