Multiple pass aeroassisted plane change.

Abstract

In the problem of aeroassisted orbital plane change, it has been found that, for a large single-pass aerodynamic plane change, an initial negative lift is used to bring the hypervelocity vehicle to a sufficiently low altitude where most aerodynamic turning is performed before exit and ascent into the final orbit. An alternative to this flight program is to leave the lifting vehicle in the initial elliptic orbit and then perform a small change in the inclination during each perigee passage through the atmosphere. Then the orbit will be gradually contracting while its inclination is slowly increasing. It will take several revolutions for the plane change. The advantage of this flight program is that the heating rate and the deceleration remain low while the vehicle's lifetime is extended. Two illustrative examples have been performed and it is found that for the same energy loss the multiple-pass maneuver produces the same plane change as the single-pass maneuver. The inclination of the osculating plane increases while the elliptic orbit is contracting toward circular. The optimal lift coefficient is oscillating near the value for maximum life-to-drag ratio while the bank angle is nearly periodic varying from $-180\\sp\\circ$ to $+180\\sp\\circ$ with the value of 90$\\sp\\circ$ near the perigee for maximum plane change. Of course, both the altitude and the velocity are oscillating with decreasing magnitude during the circularizing process. Due to the low aerodynamic force, the motion is nearly Keplerian. Hence, an approximate integration of the adjoint equations in the variational formulation can be performed producing an approximate law for the optimal aerodynamic control. It is proposed to use this suboptimal law in the exact equations of motion for the integration. The present numerical integration over several revolutions is long and tedious in the application of the transversality conditions. It is proposed to use the King-Hele method of averaging as applied to the problem of orbit contraction. This will lead to the integration of a reduced set of nonlinear equations using quadratic approximations of nonlinear functions. It results in a mathematical tool for a fast and accurate evaluation of the optimal plane change in the multiple-pass maneuver.