Low-latency delivery of satellite imagery is essential for time-critical applications such as disaster response, intelligence, and infrastructure monitoring. However, traditional pipelines rely on downlinking all captured images before analysis, introducing delays of hours to days due to restricted communication bandwidth. To address these bottlenecks, emerging systems perform onboard machine learning to prioritize which images to transmit. However, these solutions typically treat each satellite as an isolated compute node, limiting scalability and efficiency. Redundant inference across satellites and tasks further strains onboard power and compute costs, constraining mission scope and responsiveness. We present EarthSight, a distributed runtime framework that redefines satellite image intelligence as a distributed decision problem between orbit and ground. EarthSight introduces three core innovations: (1) multi-task inference on satellites using shared backbones to amortize computation across multiple vision tasks; (2) a ground-station query scheduler that aggregates user requests, predicts priorities, and assigns compute budgets to incoming imagery; and (3) dynamic filter ordering, which integrates model selectivity, accuracy, and execution cost to reject low-value images early and conserve resources. EarthSight leverages global context from ground stations and resource-aware adaptive decisions in orbit to enable constellations to perform scalable, low-latency image analysis within strict downlink bandwidth and onboard power budgets. Evaluations using a prior established satellite simulator show that EarthSight reduces average compute time per image by 1.9x and lowers 90th percentile end-to-end latency from first contact to delivery from 51 to 21 minutes compared to the state-of-the-art baseline.