where E is the eccentric anomaly, A* and B* are direction cosines, and E^ and E2 are the eccentric anomaly at which eclipsing begins and ends. Equation 2.4-4 can be approximated by For a geosynchronous orbit, this corresponds to 10.93°. In order to estimate stationkeeping system requirements, perturbations in semimajor axis are related to velocity perturbations. For a circular orbit, velocity is related to semimajor axis byl The stationkeeping system must be sized to correct these perturbations as they occur during eclipse periods. Gravity Perturbation Effect Consider a satellite orbiting a planet with an inverse square law gravity field. The orbit will be an inertially fixed ellipse with the planet center of mass located at one focus. Real gravity fields are predominantly inverse square law but include small perturbations that are not central or inverse square. The effect of the perturbations can be divided into two categories. 1 Battin, R. H., Astronautical Guidance. McGraw-Hill Book Co. (1964).
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