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We address the issue of optimal energy allocation and admission control for communications satellites in Earth orbit. Such satellites receive requests for transmission as they orbit the Earth, but may not be able to serve them all, due to energy limitations. The objective is to choose which requests to serve so that the expected total reward is maximized. The special case of a single energy-constrained satellite is considered. Rewards and demands from users for transmission (energy) are random and known only at request time. Using a dynamic programming approach, an optimal policy is derived and is characterized in terms of thresholds. Furthermore, in the special case where demand for energy is unlimited, an optimal policy is obtained in closed form. Although motivated by satellite communications, our approach is general and can be used to solve a variety of resource allocation problems in wireless communications.