Fast error-controlling MOID computation for confocal elliptic orbits

Research output

1 Citation (Scopus)

Abstract

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 16th 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.

Original languageEnglish
Pages (from-to)11-22
Number of pages12
JournalAstronomy and Computing
Volume27
Early online date27 Feb 2019
DOIs
Publication statusPublished - Apr 2019

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intersections
Orbits
orbits
orbitals
ellipse
ellipses
Polynomials
catalogs
polynomials
Processing
method

Scopus subject areas

  • Astronomy and Astrophysics
  • Computer Science Applications
  • Space and Planetary Science

Cite this

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title = "Fast error-controlling MOID computation for confocal elliptic orbits",
abstract = "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 16th 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.",
keywords = "Catalogs, Close encounters, Computational methods, Near-Earth asteroids, NEOs, DISTANCE FUNCTION, POINTS",
author = "Baluev, {R. V.} and Mikryukov, {D. V.}",
year = "2019",
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T1 - Fast error-controlling MOID computation for confocal elliptic orbits

AU - Baluev, R. V.

AU - Mikryukov, D. V.

PY - 2019/4

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N2 - 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 16th 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.

AB - 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 16th 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.

KW - Catalogs

KW - Close encounters

KW - Computational methods

KW - Near-Earth asteroids

KW - NEOs

KW - DISTANCE FUNCTION

KW - POINTS

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