Analytical approximate solutions to ground track adjustment for responsive space

This paper analyzes a civilian or military responsive space mission, in which a specific Earth site needs to be visited in a short time. Approximate analytical solutions for single and dual coplanar impulsive maneuvers to move from initial circular/elliptical orbit to final circular/elliptical orbit whose ground track passes over the Earth site are provided. The problem is solved by computing the semimajor axis of the final orbit by setting the transfer time equal in terms of Kepler's equation and of Greenwich mean sidereal time (GMST). Using an unperturbed Keplerian model, a closed-form solution is obtained by solving a cubic polynomial. Then, by converting mean to osculating orbital elements, the linear J₂ perturbed exact overflight solutions are obtained for impulses and corresponding time instants. Moreover, the exact overflight solutions are extended when using a conical sensor. Several numerical examples with various initial and final orbits are provided to validate this approach.