While thousands of satellites photograph Earth every day, most of that data never makes it to the ground because downlink bandwidth simply cannot keep up. Processing data in the Low Earth Orbit (LEO) zone offers promising capabilities to overcome this limitation. We propose SpaceCoMP, a MapReduce-inspired processing model for LEO satellite mesh networks. Ground stations submit queries over an area of interest; satellites collect sensor data, process it cooperatively at light-speed using inter-satellite laser links, and return only the results. Our compute model leverages space physics to accelerate computations on LEO megaconstellations. Our distance-aware routing protocol exploits orbital geometry. In addition, our bipartite match scheduling strategy places map and reduce tasks within orbital regions while minimizing aggregation costs. We have simulated constellations of 1,000-10,000 satellites showcasing 61-79% improvement in map placement efficiency over baselines, 18-28% over greedy allocation, and 67-72% reduction in aggregation cost. SpaceCoMP demonstrates that the orbital mesh is not merely useful as a communication relay, as seen today, but can provide the foundations for faster data processing above the skies.