Advances in nanosatellite technology and a declining cost of access to space have fostered an emergence of large constellations of sensor-equipped satellites in low-Earth orbit. Many of these satellite systems operate under a "bent-pipe" architecture, in which ground stations send commands to orbit and satellites reply with raw data. In this work, we observe that a bent-pipe architecture for Earth-observing satellites breaks down as constellation population increases. Communication is limited by the physical configuration and constraints of the system over time, such as ground station location, nanosatellite antenna size, and energy harvested on orbit. We show quantitatively that nanosatellite constellation capabilities are determined by physical system constraints.We propose an Orbital Edge Computing (OEC) architecture to address the limitations of a bent-pipe architecture. OEC supports edge computing at each camera-equipped nanosatellite so that sensed data may be processed locally when downlinking is not possible. In order to address edge processing latencies, OEC systems organize satellite constellations into computational pipelines. These pipelines parallelize both data collection and data processing based on geographic location and without the need for cross-link coordination. OEC satellites explicitly model constraints of the physical environment via a runtime service. This service uses orbit parameters, physical models, and ground station positions to trigger data collection, predict energy availability, and prepare for communication. We show that an OEC architecture can reduce ground infrastructure over 24× compared to a bent-pipe architecture, and we show that pipelines can reduce system edge processing latency over 617×.Computational nanosatellite architects face three key challenges. First, physical constraints on nanosatellite design (e.g.