Geometric Analysis and Design Method for Discontinuous Coverage Satellite Constellations

A new geometric approach for discontinuous coverage constellations in circular orbits is presented. Satellite constellations for zonal coverage with revisit times of more than one to two orbital periods are considered. The method is based on two-dimensional maps of visibility properties. The space dimensions are the right ascension of the ascending node (in the Earth-centered inertial frame) and the time. A new geometric pattern named a coverage belt is introduced. The coverage belt with sawtooth boundaries is formed by visibility intervals for a satellite at consecutive revolutions and the two-dimensional space is divided into two parts, with the revisit time near to and more than one orbital period, respectively. The revisit times for the satellite constellations are analytically computed as the sum of two terms: 1) the revisit time between straight-line envelopes of adjacent sawtooth coverage belts, and 2) the relative shift of the teeth in the belts. The last term is more than one and less than two orbital periods. Various types of interfaces between coverage belts are considered. Qualitative aspects of the solutions for well-known Walker-type constellations are discussed. Results are validated using extensive computer simulation and known solutions. Numerical examples of constellations with three to four satellites for discontinuous coverage of a specified latitude band are presented.