Having the ability to provide seamless coverage and alleviate the frequency scarcity, the cognitive satellite terrestrial network becomes a promising candidate for future communication networks. In the cognitive network, spectrum sensing plays an important role in detecting the channel state for opportunistic utilization, where cooperative spectrum sensing is employed to improve the sensing performance. Additionally, it is critical for battery-powered satellite mobile terminals to diminish energy consumption costs. In this regard, this paper proposes a novel sensing-based cognitive satellite terrestrial network (SCSTN), which integrates the cognitive satellite terrestrial network with the distributed cooperative spectrum sensing network. Specifically, we focus on energy-efficient cooperative sensing in the SCSTN, which maximizes the energy efficiency (EE) of the cognitive satellite network by a tradeoff between the average throughput and the average energy consumption. In the SCSTN, the energy detection threshold of the sensing node and the rule threshold of fusion affect the average throughput and the average energy consumption. Hence, the objective of this paper is to identify the energy detection threshold of the sensing node and the rule threshold of fusion to achieve the maximum EE. We first study the EE formulation of the rule threshold of fusion when the energy detection threshold of the sensing node is given, and transform the ratio-type objective function of EE into a parametric formulation. Subsequently, by exploring the relationship between the two formulations and making use of the monotonicity of the parametric formulation, an algorithm to obtain the optimal rule threshold of fusion for the original problem is developed. Furthermore, we study the optimal formulation of the energy sensing threshold of the sensing node and discuss the effect of the sensing duration and the number of distributed cooperative terminals on the EE. Lastly, the performance of the proposed method is evaluated through numerical simulation results.