On the dynamics of a probe in the vicinity of a binary asteroid

• Analysis of the long-term dynamics in a hierarchical triple system • Investigation of the indirect effect of the oblateness • Application to the Didymos-Dimorphos system and comparison with the non-averaged dynamics This paper investigates the dynamics of a probe orbiting an oblate celestial body (primary) and affected by a perturbing body that is positioned on the equatorial plane of the primary. The perturbing body describes an orbit around the primary that is inner with respect to that of the probe, as often occurs in proximity to a binary asteroid. Accordingly, in the present study, the mathematics is applied to a probe moving in the vicinity of two celestial bodies having the same characteristics as the Binary Asteroid (65803), composed of Didymos and Dimorphos (secondary asteroid). In such a dynamical model, the inner disturbing potential related to the secondary asteroid is approximated up to the hexadecapole order and double-averaged to obtain the long-term equations for the motion of the probe. Then, the difference between the long-term dynamics and the non-averaged dynamics of the probe is evaluated, considering the influence coming from the oblateness of the primary asteroid on both the probe and the secondary.