Method of graphoanalytical finding borders space-time areas of reachability service spacecraft man-made space objects in geostationary orbit

At the present time at various stages of creation and development there are several projects of service spacecraft. One of the tasks of which is to service orbital objects as soon as possible. During the planning maintenance is needed to perform a large amount of calculations associated with the choice of a rational flight scheme. To reduce the amount of computation, an approach is needed that provides a search for the set of realized flight paths. One of such approaches is the method for determining the boundaries of the spatiotemporal reachability regions, which allows one to evaluate the a priori capabilities of service spacecraft for servicing orbital objects located in circular orbits. To construct spatiotemporal reachable regions, the mathematical apparatus of the hodograph theory is used, which allows, sequentially, based on the analytical solution of the optimization problem of a two-pulse flight, to determine the minimum and maximum duration of the spacecraft’s movement, which is understood as the time required for the flight from the point of maneuvering to the meeting point with the serviced an orbital object under the condition of the application of one velocity impulse. A graphical comparison of the trajectories of the serviced orbital objects and spatiotemporal reachable areas of the service spacecraft makes it possible to determine the potential for service, as well as the time intervals and phase angles at which such service is possible. The proposed methodological apparatus can be used to find a solution providing an initial approximation for the subsequent accurate calculation of the trajectory of motion by numerical methods, as constructing a control program for the spacecraft.