Generation of initial debris cloud distributions for breakup events based on CARDC-SBM

Abstract

With the dramatic increase in the number of resident space objects, the risk of collision between space objects and debris is growing. To protect spacecraft from such collisions, it is crucial to determine the generation patterns of space debris and analyze the evolution of debris clouds. In this paper, a continuous distribution formula is derived for each parameter of the breakup debris based on the China Aerodynamics Research and Development Center spacecraft breakup model (CARDC-SBM). Using CARDC-SBM, we theoretically establish a normal distribution for the separation velocity of the breakup debris in relation to the breakup mass center. Based on this foundation, the mean and standard deviation of the debris separation velocity distribution are empirically modeled using polynomial and exponential functions. Consequently, an empirical formula with a broad range of applicability is derived, which significantly reduces the computation time of debris cloud simulations. The initial velocity distribution given by this empirical formula is employed as the initial condition for the evolution of debris clouds from the perspective of a boundary value problem. Simulations using CARDC-SBM and subsequent analysis of the debris cloud evolution resulting from a breakup event reveal that the distribution of each parameter is determined solely by the relative collision velocity and the spacecraft's nominal density in the impact breakup scenario. Our results show that the empirical formula for the debris cloud distribution provides good agreement with Monte Carlo simulations.