Satellite Edge Computing (SEC) enables deploying computational services on Low Earth Orbit (LEO) satellites and transforms LEO constellations into distributed platforms composed of hundreds to thousands of nodes. SEC has the potential to offer a Quality of Service level comparable to mature edge computing solutions, with the advantage of offering global connectivity and low-latency computing in geographical locations not reached by high-speed internet links or 5G networks. The fulfillment of SEC requires computation offloading, resource allocation, and load distribution solutions challenged by scarce computational resources, energy constraints, high-speed motion of computing nodes, communication instability, and fault detection and recovery. This paper focuses on the problem of computation offloading and resource allocation (i.e., task scheduling) by proposing a distributed solution dealing with resource constraints, execution time constraints, satellite motion visibility (sunset), and minimizing the overall average response time. Our solution is based on a system model that captures satellites' orbital motion and removes the classical assumptions made in the literature on the satellite network topology and the maximum number of one-hop connections among satellites. Using DES simulation, we assess the performance of the proposed scheduling algorithms when long-running tasks are executed, i.e., tasks with a service time in the range of sunset time, 25 to 176 seconds. Results show that the proposed solution allows for achieving a very high success rate of the tasks, guaranteeing the execution before sunset; the resource allocation policy permits the completion of a high percentage of tasks within the deadline.