A lower bound of the distance between two elliptic orbits

Research outputpeer-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.

Original languageEnglish
Article number28
Pages (from-to)28
Number of pages20
JournalCelestial Mechanics and Dynamical Astronomy
Volume131
Issue number6
DOIs
Publication statusPublished - 12 Jun 2019

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asteroid
Orbits
Orbit
Lower bound
orbits
Asteroids
orbital elements
circular orbits
asteroids
catalogs
Elementary Functions
Distance Function
Intersect
Vanish
Processing
Benchmark
If and only if
speed

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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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

KW - MOID

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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