We propose a novel covert communication system in which a ground user, Alice, transmits unauthorized message fragments to Bob, a low-Earth orbit satellite (LEO), and an unmanned aerial vehicle (UAV) warden (Willie) attempts to detect these transmissions. The key contribution is modeling a scenario where Alice and Willie are unaware of each other's exact locations and move randomly within a specific area. Alice utilizes environmental obstructions to avoid detection and only transmits when the satellite is directly overhead. LEO satellite technology allows users to avoid transmitting messages near a base station. We introduce two key performance metrics: catch probability (Willie detects and locates Alice during a message chunk transmission) and overall catch probability over multiple message chunks. We analyze how two parameters impact these metrics: 1) the size of the detection window and 2) the number of message chunks. The paper proposes two algorithms to optimize these parameters. The simulation results show that the algorithms effectively reduce the detection risks. This work advances the understanding of covert communication under mobility and uncertainty in satellite-aided systems.