Network access via satellites has been identified as a complementary solution to traditional mobile networks. The roll-out of comprehensive 5G networks is often not appropriate in sparsely populated regions. However, satellite networks provide more than a coverage extension for black spots in the coverage map or as backup in disaster scenarios. For the industry, satellite networks gain interest for overload mitigation and to improve the general service quality to their customers for many applications. Consequently, satellite networks aroused research interest in recent years, providing besides network access also the possibility to perform edge computing with integrated processing entities in satellites. This opportunity moves processing capability closer to every global service and opens many new application areas, but also research questions. Therefore, we thoroughly model such a satellite computing network to identify benefits, challenges, and limitations for edge computing in a satellite constellation. We identify the requirement for a migration mechanism to decrease overall system load and we propose a modeling solution to assess system load limitations with our performance model. We derive different application areas and showcase the feasibility and advantages of satellite computing networks. Finally, we verify our modeling results with a comprehensive simulation study for different use cases.