Quasi-frozen orbits around a slowly rotating asteroid
The purpose of this study is to identify orbits with quasi-constant orbital elements around a slowly rotating asteroid. To this end, a recurrence approach has been developed to formulate the high-order averaged disturbing potential. The order of the model can be determined based on the irregularity of the asteroid and the required accuracy. The proposed approach presents significant advantages in studying long-term behaviors around asteroids where the second degree and order gravity model fails or does not work well. The averaged model has been applied to an ellipsoid-shaped asteroid, and families of nearly circular orbits with constant inclination and longitude of the ascending node in the body-fixed frame have been determined, as functions of semimajor axis, inclination, and rotation period of the asteroid. Finally, by transforming the mean elements into the corresponding osculating elements, the obtained frozen solutions have been propagated in the full model, where they become quasi-frozen.