New geometric approach for discontinuous coverage constellations in circular orbits is presented. Satellite constellations for zonal coverage with revisit times more than one-two orbital periods are considered. The method is based on two-dimensional maps of visibility properties. The space dimensions are the right ascension of ascending node (in the inertia! frame) and the time. A new geometric pattern named as a coverage belt is introduced. The coverage belt with saw-tooth boundaries is formed by visibility intervals for a satellite at consecutive revolutions and divided the two-dimensional space into two parts with the revisit time near and more than one orbital period, respectively. The revisit times for the satellite constellations are analytically computed as the sum of two terms: a) the revisit time between straight-line envelopes of adjacent saw-tooth coverage belts and b) relative shifts tooth 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 extensively computer simulation and known solutions. Numerical examples of constellations with 3-4 satellites for discontinuous coverage of a specified latitude band are presented.
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