Multiple repeat cycles for a satellite mission in a Sun-synchronous orbit

Although satellites launched into Sun-synchronous orbits do not necessarily have repeat ground-track characteristics, in space missions where the users demand re-imaging or re-observing the same scene periodically, utilizing a repeat ground-track can satisfy the user requirement. For instance, Radarsat-1 was designed in a Sun-synchronous orbit with a 343/24 repeat cycle that implies after 343 revolutions and 24 nodal days, the satellite shall, within an error due to perturbations, return to the same spot over the Earth. Satellite missions in Sun-synchronous, repeat ground-track orbits require periodic inclination and altitude adjustments to maintain their desired Sun-synchronous and repeat orbit parameters (semi-major axis, inclination, days-to-repeat, revolutions-to-repeat, and Local Time of Ascending Node (LTAN)) due to the perturbing effects of drag, the non-spherical shape of the Earth, and the gravitational attraction of the Sun and Moon. For certain values of the LTAN, the coupled perturbations of the Earth's oblateness and the solar attraction can be exploited to minimize the out-of-plane manoeuvres by changing the repeat cycle of the satellite. This paper proposes an orbit control strategy that periodically decreases the semi-major axis of the satellite to a new set of Sun-synchronous repeat ground-track parameters to reduce the overall ΔV required to maintain the orbital elements during the mission and de-orbit the spacecraft at the end of its life.