Exchange orbits - an interesting case of co-orbital motion

TL;DR

This paper extends the study of exchange orbits, a special co-orbital configuration, to three dimensions and perturbed conditions, demonstrating their stability across various initial parameters.

Contribution

The study introduces three-dimensional and perturbed analyses of exchange orbits, revealing their stability beyond previous two-dimensional models.

Findings

Exchange orbits are stable in three dimensions.

Perturbed exchange orbits maintain stability under various initial conditions.

Both exchange-a and exchange-e configurations persist with stability.

Abstract

In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist -- at least -- theoretically -- two different types: the exchange-a orbits and the exchange-e orbits. The first one is the following: two celestial bodies are in orbit around a central body with almost the same semi-major axes on circular orbits. Because of the relatively small differences in semi-major axes they meet from time to time and exchange their semi-major axes. The inner one then moves outside the other planet and vice versa. The second configuration one is the following: two planets are moving on nearly the same orbit with respect to the semi-major axes, one on a circular orbit and the other one on an eccentric one. During their dynamical evolution they change the characteristics of the orbit, the circular one becomes an elliptic one whereas the elliptic one changes its shape to a circle. This 'game' repeats periodically. In this new study we extend the numerical computations for both of these exchange orbits to the three dimensional case and in another extension treat also the problem when these orbits are perturbed from a fourth body. Our results in form of graphs show quite well that for a large variety of initial conditions both configurations are stable and stay in this exchange orbits.