TY - GEN

T1 - CLOSED-FORM TRAJECTORY SOLUTION FOR SHALLOW, HIGH-ALTITUDE ATMOSPHERIC FLIGHT

AU - Falcone, Giusy

AU - Putnam, Zachary R.

N1 - Publisher Copyright:
© 2021, Univelt Inc. All rights reserved.

PY - 2021

Y1 - 2021

N2 - A closed-form approximate solution for shallow, high-altitude atmospheric flight, consistent with aerobraking passes is proposed. The solution includes expressions for velocity, flight-path angle, and altitude for lifting, high-speed atmospheric flight, which can be used to quickly evaluate trajectories. The complete derivation of the solution is presented. The solution is based on the assumptions of small flight-path angles and altitude rate changing linearly with respect to time. Results show a good match between the proposed approximate solution and numerical integration of the full equations of motion for a variety of trajectory parameters, including vacuum periapsis altitudes, initial flight-path angles and velocities, and vehicle aerodynamic coefficients. Larger, but bounded errors are present in predicted atmospheric exit velocities. Generally, results show that the predicted final velocity has a maximum error of approximately 0.6% in nominal conditions where the assumptions hold. Exit velocity errors are lower for trajectories that dissipate less energy during atmospheric flight. Finally, a Monte Carlo simulation is used to show how errors in altitude, flight-path angle, and velocity remain bounded in the presence of perturbations. Overall, results indicate that the proposed approximate solution can be used for first-order fast trajectory design for aerobraking and other grazing atmospheric trajectories.

AB - A closed-form approximate solution for shallow, high-altitude atmospheric flight, consistent with aerobraking passes is proposed. The solution includes expressions for velocity, flight-path angle, and altitude for lifting, high-speed atmospheric flight, which can be used to quickly evaluate trajectories. The complete derivation of the solution is presented. The solution is based on the assumptions of small flight-path angles and altitude rate changing linearly with respect to time. Results show a good match between the proposed approximate solution and numerical integration of the full equations of motion for a variety of trajectory parameters, including vacuum periapsis altitudes, initial flight-path angles and velocities, and vehicle aerodynamic coefficients. Larger, but bounded errors are present in predicted atmospheric exit velocities. Generally, results show that the predicted final velocity has a maximum error of approximately 0.6% in nominal conditions where the assumptions hold. Exit velocity errors are lower for trajectories that dissipate less energy during atmospheric flight. Finally, a Monte Carlo simulation is used to show how errors in altitude, flight-path angle, and velocity remain bounded in the presence of perturbations. Overall, results indicate that the proposed approximate solution can be used for first-order fast trajectory design for aerobraking and other grazing atmospheric trajectories.

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M3 - Conference contribution

AN - SCOPUS:85126233203

SN - 9780877036753

T3 - Advances in the Astronautical Sciences

SP - 2121

EP - 2136

BT - ASTRODYNAMICS 2020

A2 - Wilson, Roby S.

A2 - Shan, Jinjun

A2 - Howell, Kathleen C.

A2 - Hoots, Felix R.

PB - Univelt Inc.

T2 - AAS/AIAA Astrodynamics Specialist Conference, 2020

Y2 - 9 August 2020 through 12 August 2020

ER -