Analytical Solutions to Aeroassisted Orbital Transfer Problem

In this article, the atmospheric flight of aeroassisted orbit transfer vehicle is investigated analytically. As the flight speed is greater than the first cosmic velocity, the centrifugal force is also larger than gravity. Due to this, the vehicle has to fly with a downward lift and the flight altitude is extremely unstable. To cope with this challenge, the high-precision formulae of altitude and flight-path angle for steady glide are deduced and used to develop the steady glide control technique to stabilize the flight altitude. Upon steady glide, the analytical solutions for 3-D aeroassisted maneuvering trajectory are derived. In the derivation, a reduced-order system with negative lift-to-drag ratio as control variable is obtained by subtly simplifying the nonlinear flight dynamics. To address the complex influence of Coriolis force, the regular perturbation method is used such that the system is further decomposed into two special linear time-varying systems, which can be solved analytically by the spectral-decomposition-based method. Due to the full consideration of the influence of the Earth's curvature and rotation, the analytical solutions can predict the downrange, crossrange, and heading angle of the 3-D trajectory accurately.

I. Introduction

Aeroassisited orbital transfer (AOT) technology is of great significance in constructing the future advanced space transportation system, as it consumes much less fuel than the all-propulsive Hohmann transfer for largely changing orbital plane or decreasing orbital altitude. As shown in Fig. 1, the flight of AOT can be divided into three phases: descending phase (DP), aeroassisted maneuvering phase (AMP), and ascending phase (AP). In the DP, the AOTV leaves the original orbit via a deorbit impulse generated by high-thrust propulsion system. When the vehicle enters the atmosphere, the AMP starts, in which the vehicle performs large-scale lateral maneuvers with the help of aerodynamic forces. Once the vehicle enters the desired orbital plane, the vehicle skips out of the atmosphere. At the targeted orbital altitude, a circularizing impulse is executed to achieve the desired orbit. This article focuses on deriving the high-precision analytical solutions of the aeroassisted maneuvering trajectory, which is the most complicated and critical portion of AOT. With the advantage of extremely high computational efficiency and the capability of revealing how various factors affect the atmospheric flight, the analytical solutions have broad application prospects, such as fast trajectory planning, robust guidance design, rapid prediction of reachable domain, feasibility analysis of missions, and multidisciplinary optimization of AOTV. Fig. 1.

Diagram of aeroassisted noncoplanar orbital transfer.