Space debris cloud evolution in Low Earth Orbit

Abstract

The Earth is surrounded by inoperative objects generated from past and current space missions. Because of the high orbital speed, even the impact with small fragments is a hazard to operational spacecraft as it could lead to the partial or complete loss of the mission. Therefore, it is important to assess the collision risk due to space debris considering small fragments, which are usually not included in space debris modelling because their large number would make simulations extremely complex. In this work, an analytical approach is developed to describe the evolution of debris clouds created by fragmentations in Low Earth Orbit. In contrast to traditional approaches, which follow the trajectory of individual fragments, with the proposed method the cloud behaviour is studied globally, so that the presence of small fragments can be modelled. This give a deeper insight into the dynamics of debris clouds and reduces the computational effort needed to estimate the consequences of a collision. A standard breakup model is used to describe the dispersion of the fragments in terms of characteristic length, area-to mass ratio and velocity. From the velocity distribution, the fragment spatial dispersion is derived. The cloud density is expressed by a continuous function that depends on the altitude and that is set as initial condition for the orbit propagation. Based on an analytical approach proposed in the literature for interplanetary dust and spacecraft swarms, the fragment cloud evolution in time is derived through the continuity equation, which is used to describe the variation of debris density considering the effect of atmospheric drag. The approach has been extended to express the cloud density as a function of multiple orbital parameters and to model additional perturbations such as the Earth’s oblateness. The method has been validated through the comparison with the traditional numerical propagation and then applied to study many breakup scenarios. The proposed approach proves to be flexible and able to study the collision risk coming from several breakup events and to evaluate the vulnerability of different targets. It is also applied to derive an index of the environmental criticality of spacecraft.

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ORCID for C. Colombo: orcid.org/0000-0001-9636-9360

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