On Satellite Umbra/Penumbra Entry and Exit Positions

Abstract

The problem of computing Earth satellite entry and exit positions through the Earth’s umbra and penumbra, for satellites in elliptical orbits, is solved without the use of a quartic equation. A condition for existence of a solution in the case of a cylindrical shadow is given. This problem is of interest in case one would like to include perturbation force resulting from solar radiation pressure. Most satellites (including geosynchronous) experience periodic eclipses behind the Earth. Of course when the satellite is eclipsed, it’s not exposed to solar radiation pressure. When we need extreme accuracy, we must develop models that turn the solar radiation calculations “on” and “off,” as appropriate, to account for these periods of inactivity.