Analytical low-thrust satellite maneuvers for rapid ground target revisit

This paper presents an analytical solution for a low-thrust maneuver to reduce the flyover time of a given terrestrial target. The work extends the general solution previously developed by the authors for a 3-phase spiral transfer that results in a change in the relative right ascension of the ascending node and argument of latitude of satellites in a constellation, by varying the orbital period and the J2 effect experienced by each satellite. This work improves the accuracy of the existing method by including the periodic effects of J2 in the analytical solution. Using these improved equations, a calculation of the flyover time of a given latitude can be determined, and the passes for which the target longitude is in view identified. Validation against a numerical orbit propagator shows the analytical method to accurately predict the sub-satellite point of the satellite to within ±1° of longitude after 15 days. A case study is performed showing that the method can successfully be used to reduce the time of flyover of Los Angeles from 14 days to just 1.97 days, with a change of velocity (ΔV) of 63m/s. The full exploration of the solution space shows the problem to be highly complex, such that an increase in the ΔV used for a maneuver will not necessarily reduce the time of flyover, potentially making optimization using a numerical solution challenging. It also shows that very similar flyover times can be achieved with very different ΔV usage. As such, an overview of the solution space is extremely valuable in allowing an informed trade-off between the time of flyover and maneuver ΔV.