Fast error-controlling MOID computation for confocal elliptic orbits. (arXiv:1811.06373v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Baluev_R/0/1/0/all/0/1">Roman V. Baluev</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mikryukov_D/0/1/0/all/0/1">Denis V. Mikryukov</a>
We present an algorithm to compute the minimum orbital intersection distance
(MOID), or global minimum of the distance between the points lying on two
Keplerian ellipses. This is achieved by finding all stationary points of the
distance function, based on solving an algebraic polynomial equation of $16$th
degree. The algorithm tracks numerical errors appearing on the way, and treats
carefully nearly degenerate cases, including practical cases with almost
circular and almost coplanar orbits. Benchmarks confirm its high numeric
reliability and accuracy, and that regardless of its error–controlling
overheads, this algorithm pretends to be one of the fastest MOID computation
methods available to date, so it may be useful in processing large catalogs.
We present an algorithm to compute the minimum orbital intersection distance
(MOID), or global minimum of the distance between the points lying on two
Keplerian ellipses. This is achieved by finding all stationary points of the
distance function, based on solving an algebraic polynomial equation of $16$th
degree. The algorithm tracks numerical errors appearing on the way, and treats
carefully nearly degenerate cases, including practical cases with almost
circular and almost coplanar orbits. Benchmarks confirm its high numeric
reliability and accuracy, and that regardless of its error–controlling
overheads, this algorithm pretends to be one of the fastest MOID computation
methods available to date, so it may be useful in processing large catalogs.
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