Advances in space exploration have led to an explosion of tasks. Conventionally, these tasks are offloaded to ground servers for enhanced computing capability, or to adjacent low-earth-orbit satellites for reduced transmission delay. However, the overall delay is determined by both computation and transmission costs. The existing offloading schemes, while being highly-optimized for either costs, can be abysmal for the overall performance. The computation-transmission cost dilemma is yet to be solved. In this paper, we propose an adaptive offloading scheme to reduce the overall delay. The core idea is to jointly model and optimize the transmission-computation process over the entire network. Specifically, to represent the computation state migrations, we generalize graph nodes with multiple states. In this way, the joint optimization problem is transformed into a shortest path problem over the state graph. We further provide an extended Dijkstra's algorithm for efficient path finding. Simulation results show that the proposed scheme outperforms the ground and one-hop offloading schemes by up to 37.56% and 39.35% respectively on SpaceCube v2.0.