Repeat ground track orbit design with desired revisit time and optimal tilt

A novel method for designing repeat ground track orbits based on the Number Theory is presented. The desired revisit time, tilt capacity, payload swath width, and side-lap are utilized as mission and payload properties for repeat ground track orbit design. The algorithm is developed in the context of the perturbed two body problem, with the secular J4J4 effect as the only source of perturbation. The concept of the subcycles in the repeat ground track orbits is redefined using the Bezout's theorem and is employed for providing the desired revisit time with the optimal required tilt. This method needs simple calculations and has low computational burden. Therefore, it facilitates the practicing engineers to rapid design of repeat ground track orbits without sophisticated computer programs. The ability of the purposed method is demonstrated by some case studies.