Optimal apogee burn time for low thrust spinning satellite in low altitude

In this study, the optimal burn time for low-thrust impulsive propulsion systems is investigated to raise the perigee altitude of a low-Earth orbit. The maneuver is done using spin-stabilized attitude control and impulsive thrusting system for a time interval centered about apogee point. On the one hand, the low value of the thrust level causes more burn time needed to accomplish the transfer. This, in turn, will cause more thrust loss due to the deviation between the thrust axis (spin axis) and the velocity vector of the satellite. On the other hand, for small thrust duration, the transfer needs more revolutions around the Earth and more travel in lower altitudes with dense atmosphere and more drag loss. To transfer the satellite with minimum propellant mass, a compromise between velocity losses due to both drag and thrust deviation angle should be made. An analytical approximate correlation between average thruster burn time and total required propellant mass is formulated in this study and an analytical optimal solution for burn time is found. Nonlinear programming is used to find optimal burn time history. Comparing the analytical and numerical results shows a very good match.