English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Many topics in planetary studies demand an estimate of the collisionprobability of two objects moving on nearly Keplerian orbits. In the classicworks of \"Opik (1951) and Wetherill (1967), the collision probability wasderived by linearizing the motion near the collision points, and there is now avast literature using their method. We present here a simpler and morephysically motivated derivation for non-tangential collisions in Keplerianorbits, as well as for tangential collisions that were not previouslyconsidered. Our formulas have the added advantage of being manifestly symmetricin the parameters of the two colliding bodies. In common with the\"Opik-Wetherill treatments, we linearize the motion of the bodies in thevicinity of the point of orbit intersection (or near the points of minimumdistance between the two orbits) and assume a uniform distribution of impactparameter within the collision radius. We point out that the linearapproximation leads to singular results for the case of tangential encounters.We regularize this singularity by use of a parabolic approximation of themotion in the vicinity of a tangential encounter.

Simplified derivation of the collision probability of two objects in independent Keplerian orbits