This paper studies a fully distributed optimal formation flying problem for a multi-satellite system with a chief satellite and some deputy satellites, in order to seek the optimal formation via simple local information exchange. A distributed algorithm is proposed such that the satellites team performance is optimised in finite time while all of the satellites meet the formation constraint. To achieve the optimal flight, the performance functions for each deputy satellite that can describe the satellite's contribution to the task are introduced. Here, the performance functions can be time varying, which generally changes the problem from finding the fixed optimal point to tracking the optimal trajectory. Theoretical studies indicate that the proposed algorithm will optimise the satellites flight and all of the satellites can keep the desired communication distance. Finally, simulation examples are presented to show the validity of the theoretical results.