In recent years, Low Earth Orbit (LEO) satellites have witnessed rapid development, with inference based on Deep Neural Network (DNN) models emerging as the prevailing technology for remote sensing satellite image recognition. However, the substantial computation capability and energy demands of DNN models, coupled with the instability of the satellite-ground link, pose significant challenges, burdening satellites with limited power intake and hindering the timely completion of tasks. Existing approaches, such as transmitting all images to the ground for processing or executing DNN models on the satellite, is unable to effectively address this issue. By exploiting the internal hierarchical structure of DNNs and treating each layer as an independent subtask, we propose a satellite-ground collaborative computation partial offloading approach to address this challenge. We formulate the problem of minimizing the inference task execution time and onboard energy consumption through offloading as an integer linear programming (ILP) model. The complexity in solving the problem arises from the combinatorial explosion in the discrete solution space. To address this, we have designed an improved optimization algorithm based on branch and bound. Simulation results illustrate that, compared to the existing approaches, our algorithm improve the performance by 10%-18%