On the Co-orbital Motion of Any Inclination

The co-orbital motion occurs when a celestial body (e.g. an asteroid) shares the same semimajor axis with the perturbing object (e.g. a planet), and thus they are in a 1:1 mean motion resonance. Trojan asteroids in the tadpole orbits around planets in the Solar System are these co-orbital objects. The motion and origin of some Trojan asteroids, particularly those on high-inclination orbits, are still not fully understood. In this paper, a newly developed perturbation function expansion, which is applicable to the 1:1 resonance, is used to investigate the co-orbital motion in three-dimensional space. The position of the resonance center and the resonance width are calculated for different initial orbital elements, and the relationship between the orbital types and the initial orbital elements is analyzed. The results obtained by the analytical method are compared with and verified by the results from numerical simulations. A panorama of the co-orbital motion in the wide orbital elements space is obtained.