Simplified Derivation of the Collision Probability of Two Objects in Independent Keplerian Orbits
AffiliationUniv Arizona, Lunar & Planetary Lab
meteorites, meteors, meteoroids
minor planets, asteroids: general
MetadataShow full item record
PublisherIOP PUBLISHING LTD
CitationSimplified Derivation of the Collision Probability of Two Objects in Independent Keplerian Orbits 2017, 153 (5):235 The Astronomical Journal
JournalThe Astronomical Journal
Rights© 2017. The American Astronomical Society. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractMany topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Opik and Wetherill, the collision probability was derived by linearizing the motion near the collision points, and there is now a vast amount of literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Opik-Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.
VersionFinal published version
SponsorsUNAM-DGAPA-PAPIIT [IN107316]; NASA [NNX14AG93G]; NSF [AST-1312498]