Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance. Perturbative treatment

TL;DR

This paper analyzes quasi-satellite orbits within the Sun-planet-asteroid three-body problem, using perturbative methods to understand their long-term dynamics and transitions between different orbital regimes.

Contribution

It introduces a perturbative approach with double numerical averaging to model the long-term evolution of quasi-satellite orbits and classifies possible orbital transitions in the 1:1 resonance.

Findings

Long-term evolutionary equations for quasi-satellite orbits derived.

Identification of possible transitions between quasi-satellite and other resonant orbits.

Classification of evolutionary paths for low-eccentricity and low-inclination asteroids.

Abstract

Our investigation is motivated by the recent discovery of asteroids orbiting the Sun and simultaneously staying near one of the Solar System planets for a long time. This regime of motion is usually called the quasi-satellite regime, since even at the times of the closest approaches the distance between the asteroid and the planet is significantly larger than the region of space (the Hill's sphere) in which the planet can hold its satellites. We explore the properties of the quasi-satellite regimes in the context of the spatial restricted circular three-body problem "Sun-planet-asteroid". Via double numerical averaging, we construct evolutionary equations which describe the long-term behaviour of the orbital elements of an asteroid. Special attention is paid to possible transitions between the motion in a quasi-satellite orbit and the one in another type of orbits available in the 1:1 resonance. A rough classification of the corresponding evolutionary paths is given for an asteroid's motion with a sufficiently small eccentricity and inclination.