Autonomous farm vehicles (AFVs) encounter significant challenges in large-scale networking and massive data transmission. The rapid development of global low Earth orbit (LEO) satellite networks provides reliable support for AFVs. However, the time-varying characteristics of the satellite-terrestrial channel and large-scale collaborative scheduling among AFVs pose challenges for joint computation offloading between satellites and AFVs. This paper proposes a satellite and autonomous farm vehicle integrated network (SAFVIN) architecture. We formulate the joint satellite and AFVs computation offloading problem as a Markov decision process (MDP). We propose a deep rein forcement computation offloading (DRCO) method that adapts to satellite networks. Unlike traditional computation offloading methods, the proposed DRCO takes into account the time varying satellite network channel states. The DRCO can rapidly converge to high-quality decisions in satellite network with strong randomness, thereby adapting to dynamic environments more quickly and achieving superior performance. We compare the proposed DRCO with the heuristic coordinate descent (CD), and with deep Q-network (DQN) and deep deterministic policy gradient (DDPG) algorithms. The DRCO achieves a 2% lower latency loss while only incurring 21% of the time overhead required by the CD. Furthermore, unlike DQN and DDPG algorithms, which rely on continuous time frame input and output for network updates, the proposed DRCO can directly leverage past experience to adapt to dynamic satellite network. Compared with other deep reinforcement learning algorithms including DQN and DDPG, the DRCO achieves an average energy consumption reduction of approximately 10%.