## 1 Introduction  
Traditional terrestrial networks, like 5G, rely on base stations as their fundamental units of operation. These stations enable the delivery of real-time and rapid services [1]. Nonetheless, terrestrial network deployment faces certain challenges. Primarily, the reach of terrestrial base stations is limited, making it difficult to establish them in regions such as deserts, forests, or mountains. Additionally, terrestrial base stations are susceptible to natural disasters. When events like typhoons, tsunamis, and earthquakes damage these stations, communication systems can fail, and restoring them swiftly is challenging, which leads to severe societal and economic disruptions due to interrupted communications. Consequently, satellite communication systems, especially the low Earth orbit (LEO) satellite networks, offer a flexible deployment option with global coverage, effectively complementing terrestrial networks [2, 3]. In densely populated regions, satellite communication networks can provide substantial support, utilizing their resources for communication, computing, and storage to ease the burden on terrestrial systems. In locales where terrestrial networks are unable to reach, satellite networks can assume the role of transmitting information, thus complementing the terrestrial networks [4]. In the forthcoming era of the Internet of Things (IoT), achieving global connectivity and intelligence will lead to an exponential increase in the number of edge devices and the volume of sensing and communication data. Traditional centralized cloud networks will no longer be able to efficiently process the massive amounts of data generated by the IoT [5; 6]. The advent of augmented reality, enhanced reality, high-definition live streaming, and other novel application scenarios further accentuates this challenge. Limitations in terminal computing power and navigation capabilities may result in suboptimal user experiences, such as the inability to interact in real time. Mobile Edge Computing (MEC), a pivotal technology in fifth-generation mobile communications, addresses these issues by decentralizing resources from central devices to network edge devices. This enables edge devices to possess certain computing capabilities for processing user requests locally, providing users with low-latency, high-bandwidth data processing services. Consequently, MEC alleviates the pressure on core network resources and effectively resolves problems such as data traffic bottlenecks in the core network [7; 8; 9]. In traditional satellite communication systems, satellites usually act as relays for transferring data from user devices. With the emergence of new computing-intensive tasks and delay-sensitive application scenarios, terminal devices need to offload new business computing tasks to the cloud for processing. However, the traditional mode of uploading data to the cloud for processing cannot meet the current computing-intensive business needs in terms of low latency and high bandwidth transmission. Therefore, the integration of satellite communication and edge computing is the development trend of future satellite networks. Moreover, LEO satellite communication systems inherently offer low-latency communication due to their proximity to the Earth's surface and typically orbit at altitudes between 500 and 2000 km [10]. This close proximity significantly reduces the signal propagation delay compared to Geostationary Earth Orbit (GEO) satellites, which orbit at approximately 35,786 km. As a result, LEO satellites can achieve round-trip signal latencies as low as 20-30 ms, making them suitable for real-time and delay-sensitive applications [10; 11]. The deployment of LEO satellite constellations enhances communication reliability through redundant coverage and seamless handover capabilities.