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Space Computing Power Network (Space-CPN) is a promising solution for deploying remote sensing applications which require real-time processing of high-resolution data by providing onboard computing and extensive coverage capabilities. However, the limited computational resources on satellites, along with the dynamic and heterogeneous nature of the satellite networks, present significant challenges for effective deployment of these applications. To solve this problem, we decompose monolithic remote sensing applications into independent microservices, enabling flexible allocation of computational tasks across heterogeneous satellite resources and improving system scalability. To allocate microservices, this paper proposes a framework that leverages Large Language Models (LLMs) to optimize their deployment in Low Earth Orbit (LEO) satellite networks. The deployment problem is formulated as an NP-hard optimization problem that aims to minimize the overall application latency by optimizing the placement of microservices across satellites, while considering computation delay, transmission delay, and the time-varying latencies of inter-satellite links (ISLs). Experimental results show that our framework effectively automates the modeling and solving of the optimization problem, surpassing traditional deployment strategies in efficiency and achieving results close to the theoretical optimum.