Analytical Earth-Aerocapture Guidance with Near-Optimal Performance

Abstract

An aerocapture maneuver employs a single atmospheric pass to reduce orbital energy and establish a closed orbit. Modulating the spacecraft’s vertical lift component (via bank control) during atmospheric flight in an optimal fashion will minimize the post-exit propulsive burn required to establish a target orbit. This paper presents a new analytical predictor–corrector guidance algorithm for the Earth-aerocapture problem. Bank control is open loop (lift-up) during the descent phase and closed loop (lift-down) during the ascent phase in order to emulate the bang–bang bank structure of optimal aerocapture. The guidance is developed using analytical functions representing the flight-path angle and the composite effects of atmospheric density, lift and drag coefficients, and vehicle mass along the ascent trajectory. These functions result in a closed-form equation for exit velocity and a method for predicting the switching condition from lift-up to lift-down control. Monte Carlo simulations demonstrate the robustness, accuracy, and near-optimal performance of this new analytical guidance method.