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Satellite power systems can be understood as islanded dc microgrids supplied by specialized and coordinated solar cell arrays augmented by electrochemical battery systems to handle high-power loads and periods of eclipse. The periodic availability of power, the limited capacity of batteries, and the dependence of all mission service on power consumption create a unique situation in which temporal power and energy scarcity exist. A multi-period model of an orbital satellite power system’s performance over a mission’s duration can be constructed. A modular power system architecture is used to characterize the system’s constraints. Using mathematical programming, an optimization problem can be posed such that the optimal power and energy ratings for the power system are determined for any load schedule imposed by a given mission’s requirements. The optimal energy trajectory of the electrical power system over a mission’s duration is also determined when the mathematical programming problem is solved. A generic set of mission requirements is identified to test this approach, but the objective function of the resulting optimization problem can be modified to return different results. These results can provide a clear illustration of the trade-offs that designers of such power systems consider in the design process.