Review and Assessment of the Steep Lifting Entry Closed-Form Trajectory Solution

Abstract

The complete, historical closed-form steep lifting entry trajectory solution is documented and developed from first principles. The efficacy and accuracy of the solution is assessed for application to aeroassist missions of interest, including aerocapture and entry. Specifically, analytical assessment of the primary assumptions in the solution shows the solution is applicable across a wide range of initial states for vehicles with nonzero lift-to-drag ratios. Solution accuracy is assessed relative to the planar equations of motion; accuracy improves for steeper trajectories and larger lift-to-drag ratios. The steep lifting entry estimate of peak acceleration is shown to be accurate to within 10% for initial flightpath angles steeper than approximately -10 deg across a variety of vehicles, missions, and planetary destinations. Overall, the steep lifting entry solution provides a simple, rapid first-order trajectory solution capability for lifting aeroassist vehicles with relatively steep initial flight-path angles.