Minimum Orbital Intersection Distance: Asymptotic Approach

TL;DR

This paper introduces asymptotic methods to efficiently compute the minimum orbital intersection distance, significantly speeding up calculations with minimal accuracy loss, beneficial for large-scale astronomical analyses.

Contribution

It presents two novel asymptotic procedures integrated into the SDG-MOID method, improving computational speed while maintaining accuracy.

Findings

40% reduction in computation time

Negligible accuracy degradation

Effective for large database analysis

Abstract

The minimum orbital intersection distance 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 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 remarkable result suggests that large 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.