MINIMUM FUEL TRAJECTORIES FOR THRUST LIMITED ROCKETS IN AN ADVERSE SQUARE GRAVITY FIELD.

Minimum fuel trajectories for motion of a rocket in an inverse square gravity field are analyzed. The equations of motion are derived and expressed in terms of non-dimensional parameters making the equations applicable to any inverse square force field. The necessary condition for a minimum fuel path is obtained by using Pontryagins Maximum Principle. Using a trial and error method of solution the optimal control of thrust direction and magnitude is determined and the results are presented as functions of range for three initial thrust to weight ratios. Ranges of 2 to 65 miles on the surface of the moon for initial thrust to weight ratios of approximately 1.6, 1.9, and 2.4 are considered. The solutions obtained are compared with solutions for minimum fuel trajectories in a uniform parallel gravity field. Author