Minimum Orbital Intersection Distance: Asymptotic Approach. (arXiv:1910.02609v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hedo_J/0/1/0/all/0/1">José Manuel Hedo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Fantino_E/0/1/0/all/0/1">Elena Fantino</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ruiz_M/0/1/0/all/0/1">Manuel Ruíz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pelaez_J/0/1/0/all/0/1">Jesús Pelaez</a>
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.
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.
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