Optimal Injection into Near Synchronous Orbit by Three Apogee Motor Burns Accounting for Operational Constraints and Execution Errors

Abstract

The method of injecting TV-SAT, the german broadcasting satellite to be launched in 1986 from an elliptical transfer orbit into a near-synchronous orbit by a liquid fuel apogee boost motor, is presented. The apogee manoeuver is split into three, in order to satisfy solar constraints, to reduce long arc burning losses and to minimize the fuel required to compensate for the thrust errors in magnitude and direction. The optimal thrust direction and firing parameters are computed taking into consideration the finite burning times and various mission constraints. Included are the limitation of the total time for injection, the minimum time required between two successive manoeuvers for orbit determination and thruster calibration, visibility to ground stations and the location of spacecraft in the orbit with respect to the Sun, when the manoeuvers are executed. The final orbit, resulting from the execution of three manoeuvers, even with execution errors in thrust magnitude and direction, must lie in the optimal acquisition range, defined by a combination of deviations of satellite longitude with respect to its geostationary position, apogee height and perigee height, which require minimum fuel for the station acquisition manoeuvers. The problem is formulated as a non-linear optimization problem with equality and inequality constraints, and is solved by a nonlinear parameter optimization algorithm. Approximate initial guesses for the parameters to be optimized are generated by solving the problem assuming two-body motion, impulsive thrusts and accounting for the most essential constraints. The procedure is translated into a computer software and some simulation studies are carried out to check its capability. Injection strategies from nominal and some nonnominal transfer orbits are investigated and the results are presented. The software will be used during the TV-SAT mission operations by the German Space Operations Center.