Minimum orbital intersection distance: an asymptotic approach

Abstract

The minimum orbital intersection distance (MOID) is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications. The most frequent case is that in which both objects have elliptical osculating orbits. When at least one of the two orbits has low eccentricity, the latter can be used as a small parameter in an asymptotic power series expansion. The resulting approximation can be exploited to speed up the computation with negligible cost in terms of accuracy. This contribution introduces two asymptotic procedures into the SDG-MOID method for the computation of the MOID developed by the Space Dynamics Group (SDG) of the Technical University of Madrid and presented in a previous article, it discusses the results of performance tests and their comparisons with previous findings. The best approximate procedure yields a reduction of 40% in computing speed, without degrading the accuracy of the determinations. This result suggests that some benefits can be obtained in applications involving massive distance computations, such as in the analysis of large databases, in Monte Carlo simulations for impact risk assessment, or in the long-time monitoring of the minimum orbital intersection distance between two objects.