Increasing interest in asteroid mining and in-situ resource utilization will lead to an increase in asteroid surface operations. The geophysical properties of asteroids are often unknown and play a significant role in the resulting gravitational fields. Surface operations such as mining may significantly alter the asteroid's structure or, in the case of contact binary asteroids, cause the asteroid to split depending on the rotational condition. The coupled problem of estimating unknown parameters of a splitting contact-binary system and controlling a spacecraft's trajectory in the system's vicinity is investigated. An indirect adaptive control scheme is utilized to simultaneously meet both objectives. The results are compared with the traditional 2-body controller and the improvement enabled by the proposed scheme is demonstrated.