On mean visibility time of non-repeating satellite orbits

Depending on orbit altitude and orbit inclination a non-geostationary satellite offers different visibility times to fixed ground terminals. The moving sub-satellite point defines a ground track crossing a small circle around a fixed ground station which is defined by the minimum elevation angle of the ground terminal. In this work we are interested in the mean visibility time of a non-geostationary satellite with non-repeating ground track as seen by a fixed ground station and we provide an approximation and a mathematical analysis for the calculation of this visibility. The calculations show a good match with simulation results at all latitudes and the underlying mathematical approach is foreseen to be useful for analyzing and designing complete satellite constellations.