Giusy Falcone, Zachary R. Putnam

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationASTRODYNAMICS 2020
EditorsRoby S. Wilson, Jinjun Shan, Kathleen C. Howell, Felix R. Hoots
PublisherUnivelt Inc.
Number of pages16
ISBN (Print)9780877036753
StatePublished - 2021
EventAAS/AIAA Astrodynamics Specialist Conference, 2020 - Virtual, Online
Duration: Aug 9 2020Aug 12 2020

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


ConferenceAAS/AIAA Astrodynamics Specialist Conference, 2020
CityVirtual, Online

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science


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