Predicting the visibility of LEO satellites

We present a simple algorithm to determine the visibility-time function of a circular low Earth orbit (LEO) satellite at a terminal on the Earth's surface. The simplicity of the algorithm is based on approximating the ground trace of the satellite (which is not a great circle due to Earth's rotation) during a time interval of the order of in-view period, by a great-circle are. This enables us to use spherical geometry to compute the location and time epoch of the observation of the closest approach of the satellite's ground trace to the terminal. This is also the epoch of the observation of the maximum elevation angle from the terminal to the satellite. Applying a result derived relating the maximum elevation angle to the in-view period, we obtain the visibility-time function of the satellite at the terminal. Numerical results illustrate the accuracy of the algorithm for a wide range of LEO orbit altitudes.