| This research presents the phased development of an algorithm to plan impulsive orbital maneuvers based on the relative motion between multiple satellites and multiple ground locations. The algorithm leverages the state transition matrix derived from the equations of motion and the equations of variation for the non-spherical Earth and air drag effects. The algorithm determines the impulsive maneuver to achieve the user-defined terminal conditions. The first phase solves for the first burn of an orbital transfer between user-defined altitudes. The optimum trajectory is determined and compared to the first burn in a Hohmann Transfer. The results are expanded to include varying the inclination and eccentricity of the initial orbit. The second phase solves for the minimum time trajectory resulting from a fixed fuel maneuver to transfer a satellite between user-defined altitudes. The results include the transfer time and transfer angle for the minimum time trajectory. The third phase places a satellite within a sphere, of user-defined radius, centered on a non-maneuvering satellite within a constrained time. The results are presented for prograde orbits. An empirical method to determine the optimum DeltaV is provided. The fourth phase places a satellite within the overlapping spheres, of user-defined radii, centered on multiple non-maneuvering satellites, within a constrained time. Empirical methods are presented to determine the separation distance and optimum DeltaV. The final phase culminates by delivering a satellite within the overlapping spheres, centered on multiple non-maneuvering satellites and ground locations, constrained by range and elevation angle, within a constrained time. An empirical model to calculate the optimum DeltaV is shown. All results illustrate mission design trade-offs including ballistic coefficient, orbit inclinations, eccentricity and orbit sizes. |
