The evolution of the Line of Variations at close encounters: an analytic approach

TL;DR

This paper presents an analytical approach to understanding how close encounters affect the evolution of the Line of Variations, providing insights into orbit changes and velocity vectors, validated by numerical simulations.

Contribution

It introduces an analytical framework for analyzing the post-encounter evolution of the Line of Variations, enhancing understanding of close encounter dynamics.

Findings

Analytical expressions for the evolution of the LoV after close encounters.

Comparison shows good agreement between analytical results and numerical simulations.

Insights into how encounters influence the minimum distance and velocity vectors.

Abstract

We study the post-encounter evolution of fictitious small bodies belonging to the so-called Line of Variations (LoV) in the framework of the analytic theory of close encounters. We show the consequences of the encounter on the local minimum of the distance between the orbit of the planet and that of the small body, and get a global picture of the way in which the planetocentric velocity vector is affected by the encounter. The analytical results are compared with those of numerical integrations of the restricted 3-body problem.