Improvements to time of closest approach calculation

Space debris constitutes a major and growing threat to space missions. To assess the probability of collision, the time of closest approach between the spacecraft and the debris must first be calculated. This paper presents three new methods for the calculation of the time of closest approach. The first is a surrogate-based optimization algorithm, using the Alfano-Negron Close Approach Software as the model, allowing a compromise between calculation speed and accuracy. The second is a generalization of this software, treating a cloud of debris as a continuous object and searching for the time of closest approach over initial conditions as well as time. The third uses Alfano-Negron Close Approach Software generalization as a model for surrogate-based optimization. Using the third method, a strategy for safe operation of a spacecraft cluster in a debris-rich environment is proposed. All methods are demonstrated and compared. It is shown that Alfano-Negron Close Approach Software and the generalization thereof are very fast in estimating the time of closest approach, and that the surrogate-based optimization algorithms are somewhat slower, but are highly accurate.