Orbital edge computing reduces the data transmission needs of Earth observation satellites by processing sensor data on-board, allowing near-real-time insights while minimizing downlink costs. However, current orbital edge computing architectures are inflexible, requiring custom mission planning and high upfront development costs. In this paper, we propose a novel approach: shared Earth observation satellites that are operated by a central provider but used by multiple tenants. Each tenant can execute their own logic on-board the satellite to filter, prioritize, and analyze sensor data. We introduce Trabant, a serverless architecture for shared satellite platforms, leveraging the Function-as-a-Service (FaaS) paradigm and time-shifted computing. This architecture abstracts operational complexities, enabling dynamic scheduling under satellite resource constraints, reducing deployment overhead, and aligning event-driven satellite observations with intermittent computation. We present the design of Trabant, demonstrate its capabilities with a proof-of-concept prototype, and evaluate it using real satellite computing telemetry data. Our findings suggest that Trabant can significantly reduce mission planning overheads, offering a scalable and efficient platform for diverse Earth observation missions.