Eclipse design limits for circular orbits.

By means of simple geometric construction compact expressions for the maximum and minimum eclipse durations of a circular orbit, whose semimajor axis and inclination are specified, can be obtained. The method outlined in this note provides the designer with the necessary envelope of eclipse durations that a spacecraft will experience throughout its lifetime, and, therefore, provides a quick method of estimating necessary thermal constraints. Moreover, the closed form method presented eliminates the need for extensive machine time expenditure previously required for this type of analysis. Some numerical data to aid in the design of the spacecraft is provided.