Optimal aeroassisted orbital transfer involving elliptical orbits

Minimum-fuel orbital transfer between elliptical orbits is studied by first analyzing separately the three phases of aeroassisted orbital transfer (deorbit, atmospheric fly-through and post atmospheric maneuvers). For the atmospheric fly-through of a ballistic vehicle, second-order analytical solutions for the altitude and flight path angle are obtained using Poincare's method of small parameters. Expressions for the speed, time of flight, longitudinal deceleration, and critical entry angle are also derived. For a vehicle whose coefficient of drag can be modulated between a maximum and a minimum value, an explicit self-correcting guidance law is derived to achieve the targeted exit speed with small flight path angle. For a vehicle with lifting capability, a near optimal control with constant normalized lift coefficient and explicit bank modulation is obtained to maximize the atmospheric plane change. The influence of maximum lift-to-drag ratio on the atmospheric plane change is also assessed. Regions of optimality for deorbit to a prescribed entry angle are obtained and the post atmospheric maneuvers necessary to achieve the target final orbit are derived. The problem of transfer between coplanar elliptic orbits is studied. The two impulse transfer is obtained by solving three equations for three unknowns.