Date of Award

3-2025

Document Type

Thesis

Degree Name

Master of Science in Aeronautical Engineering

Department

Department of Aeronautics and Astronautics

First Advisor

Robert A. Bettinger, PhD

Abstract

Multi-body dynamical models are a valuable tool used to examine certain aspects of spacecraft orbital mechanics by applying assumptions to restrict the problem. The Circular Restricted Three-Body Problem (CR3BP), one of these dynamical models, has been examined extensively in the last few decades; however, this model is not sufficient in the case of more than two massive celestial bodies gravitationally affecting a spacecraft. A novel model called the Circular Restricted N-Body Problem (CRNBP) is studied in this research as an alternative to the traditional CR3BP where necessary. A variety of systems are examined in this thesis, including the Jovian, Saturnian, Uranian, and Plutonian systems, as well as several Sun-centric cases. The effect of initial system configurations based on the location of each celestial body in the system is outlined, uncovering a potential application of the CRNBP to initial mission planning as the model can be used to determine which configuration yields more or less perturbed results. Additionally, equilibrium conditions are investigated under the influence of a greater number of system bodies. These equilibrium points take the form of dynamical substitutes as opposed to the traditional Lagrange or libration points. The level of perturbation demonstrated at these stable points is used to characterize which celestial bodies are necessary within the CRNBP dynamical model for multiple planetary systems. Finally, Poincaré mapping techniques are implemented to understand the broader behavior of the CRNBP by testing multiple initial configurations, Jacobi constants, and secondary system bodies. Quasi-periodic trajectories are extracted from the Poincaré maps and compared to the corresponding CR3BP trajectories. In summary, this thesis presents a detailed view of multiple novel aspects of the CRNBP dynamical model, supporting the usage of the CRNBP in initial mission planning and as an intermediate model when transitioning to higher-fidelity, dynamically comprehensive models.

AFIT Designator

AFIT-ENY-MS-25-M-143

DTIC Accession Number

AD1356371

Comments

An embargo was observed for posting this thesis.

Distribution A: Approved for Public Release, Distribution Unlimited.

PA clearance case 88ABW-2025-0475

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