Minimum orbital intersection distance: an asymptotic approach

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 MOID between two objects.

Semi-analytical Near-Earth Objects Propagation: The Orbit History of (35107) 1991 VH and (175706) 1996 FG3

“…There are many algorithms available in the literature to compute the MOID (Gronchi 2005;Armellin et al 2010;Wiśniowski & Rickman 2013). In this paper we use the tool derived in Hedo et al (2018Hedo et al ( , 2020 based on an asymptotic approach.…”

Semi-analytical near-Earth objects propagation: the orbit history of (35107) 1991 VH and (175706) 1996 FG3

“…There are many algorithms available in the literature to compute the MOID (Gronchi 2005;Wiśniowski & Rickman 2013;Armellin et al 2010). In this paper we use the tool derived in Hedo et al (2018Hedo et al ( , 2020 based on an asymptotic approach.…”