Minimum fuel trajectory transfer in a general gravity field using a finite number of engine firings to cause velocity discontinuities

A method is proposed for computing the strategy of firing a rocket engine so that the rocket is transferred from a given initial trajectory to a specified final trajectory while consuming the minimum amount of fuel. The method involves iterative modification of an approximate firing strategy to improve on the orbital constraints. When the orbital constraints are met, further iterations are made to minimize the amount of consumed fuel. The method allows the use of the rapidly converging Simplex algorithm; both inequality and equality constraints can be handled.