A lower bound of the distance between two elliptic orbits

Denis V. Mikryukov, Roman V. Baluev

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed.

Translated title of the contributionНижняя оценка расстояния между двумя эллиптическими орбитами
Original languageEnglish
Article number28
Pages (from-to)28
Number of pages20
JournalCelestial Mechanics and Dynamical Astronomy
Volume131
Issue number6
DOIs
StatePublished - 12 Jun 2019

Keywords

  • Elliptic orbits
  • MOID
  • Linking coefficient
  • Distance function
  • Catalogs
  • Asteroids and comets
  • Near-Earth asteroids
  • Space debris
  • Close encounters
  • Collisions

Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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keywords = "Elliptic orbits, MOID, Linking coefficient, Distance function, Catalogs, Asteroids and comets, Near-Earth asteroids, Space debris, Close encounters, Collisions",
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A lower bound of the distance between two elliptic orbits. / Mikryukov, Denis V.; Baluev, Roman V.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 131, No. 6, 28, 12.06.2019, p. 28.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Baluev, Roman V.

PY - 2019/6/12

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N2 - We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed.

AB - We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed.

KW - Elliptic orbits

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KW - Linking coefficient

KW - Distance function

KW - Catalogs

KW - Asteroids and comets

KW - Near-Earth asteroids

KW - Space debris

KW - Close encounters

KW - Collisions

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DO - 10.1007/s10569-019-9907-3

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