Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.