Gamma guidance of trajectories for coplanar, aeroassisted orbital transfer
Abstract
The optimization and guidance of trajectories for coplaner, aeroassisted orbital transfer (AOT) from high Earth orbit (HEO) to low Earth orbit (LEO) are examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that at most three impulses are employed: one at HEO exit, one at atmospheric exit, and one at LEO entry. It is also assumed that, during the atmospheric pass, the trajectory is controlled via the lift coefficient. The presence of upper and lower bounds on the lift coefficient is considered. First, optimal trajectories are computed by minimizing the total velocity impulse (hence, the propellant consumption) required for AOT transfer. The sequential gradientrestoration algorithm (SGRA) is used for optimal control problems. The optimal trajectory is shown to include two branches: a relatively short descending flight branch (branch 1) and a long ascending flight branch (branch 2). Next, attention is focused on guidance trajectories capable of approximating the optimal trajectories in real time, while retaining the essential characteristics of simplicity, ease of implementation, and reliability. For the atmospheric pass, a feedback control scheme is employed and the lift coefficient is adjusted according to a twostage gamma guidance law. Further improvements are possible via a modified gamma guidance which is more stable with respect to dispersion effects arising from navigation errors, variations of the atmospheric density, and uncertainties in the aerodynamic coefficients than gamma guidance trajectory. A byproduct of the studies on dispersion effects is the following design concept. For coplaner aeroassisted orbital transfer, the liftrangetoweight ratio appears to play a more important role than the lifttodrag ratio. This is because the liftrangetoweight ratio controls mainly the minimum altitude (hence, the peak heating rate) of the guidance trajectory; on the other hand, the lifttodrag ratio controls mainly the duration of the atmospheric pass of the guidance trajectory.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1990
 Bibcode:
 1990STIN...9114365M
 Keywords:

 Aeroassist;
 Aerobraking;
 Atmospheric Entry;
 Orbit Transfer Vehicles;
 Spacecraft Guidance;
 Spacecraft Trajectories;
 Trajectory Optimization;
 Transfer Orbits;
 Aerodynamic Coefficients;
 Aerodynamic Heating;
 Earth Orbits;
 Feedback Control;
 Lift;
 Lift Drag Ratio;
 Optimal Control;
 Trajectory Control;
 Astrodynamics