Fuel-Optimal Transfers Between Coplanar Circular Orbits Using Variable-Specific-Impulse Engines

Minimum fuel circular-to-circular low-thrust orbital transfers with prescribed transfer time and with the thrust always directed parallel to the velocity vector are developed for a variable-specific-impulse system. The changeable specific impulse serves as the control variable. The power input is assumed to be constant, and the resulting thrust magnitude is inversely proportional to the chosen specific impulse. With these engine specifications, and under the assumption that the thrust magnitude always remains small compared to the gravitational forces, it is shown that the optimal specific impulse profile increases linearly with time. The associated optimal thrust magnitude is proportional to the vehicle mass; that is, the thrust per unit of vehicle mass remains constant. The mass fraction obtained with variable specific impulse is shown to be greater than or equal to that obtained with constant specific impulse; the advantage can be significant for orbital transfers with large changes in the semimajor axis.