Circular revisit orbits design for responsive mission over a single target

The responsive orbits play a key role in addressing the mission of Operationally Responsive Space (ORS) because of their capabilities. These capabilities are usually focused on supporting specific targets as opposed to providing global coverage. One subtype of responsive orbits is repeat coverage orbit which is nearly circular in most remote sensing applications. This paper deals with a special kind of repeating ground track orbit, referred to as circular revisit orbit. Different from traditional repeat coverage orbits, a satellite on circular revisit orbit can visit a target site at both the ascending and descending stages in one revisit cycle. This typology of trajectory allows a halving of the traditional revisit time and does a favor to get useful information for responsive applications. However the previous reported numerical methods in some references often cost lots of computation or fail to obtain such orbits. To overcome this difficulty, an analytical method to determine the existence conditions of the solutions to revisit orbits is presented in this paper. To this end, the mathematical model of circular revisit orbit is established under the central gravity model and the J2 perturbation. A constraint function of the circular revisit orbit is introduced, and the monotonicity of that function has been studied. The existent conditions and the number of such orbits are naturally worked out. Taking the launch cost into consideration, optimal design model of circular revisit orbit is established to achieve a best orbit which visits a target twice a day in the morning and in the afternoon respectively for several days. The result shows that it is effective to apply circular revisit orbits in responsive application such as reconnoiter of natural disaster.