Equation for Optimal Power-Limited Spacecraft Trajectories
For a power-limited spacecraft the necessary conditions for an optimal (minimum-propellant)
trajectory and the equations of motion can be combined into a single fourth-order
differential equation for the position vector. Every solution to this equation
then represents an optimal trajectory through the specified gravitational
field. By imposing the appropriate boundary conditions on the solution of
this equation, the desired optimal trajectory can be determined. A significant
increase in payload can be attained by an optimal trajectory.