Free and forced inclinations of orbits perturbed by the central body’s oblateness and an inclined third body

The effect of inclined third-body perturbation on the perturbed body’s inclination evolution has been investigated extensively. However, under various initial orbital elements, the exact effect of the J₂ perturbation and the inclined third-body perturbation on perturbed body’s inclination is still an open problem. In this paper, we use a simplified model for long-term orbital variations to analyze the free and forced inclinations for almost circular orbits with low inclinations. We analyze the influence of the J₂ perturbation on the inclination evolution under various initial orbital elements. The results show that the J₂ perturbation consistently decreases the maximum value of the inclination. Besides, the J₂ perturbation either decreases the amplitude of the inclination’s oscillation, or enables the perturbed body to orbit closer to the equator of the central body. These effects enable the objects with initially low inclinations to maintain their orbits near the equator of the central body for a long time. The results of the study are applied to circum-Jovian orbits and the triple asteroid system 87 Sylvia.