Date of Award

3-2025

Document Type

Thesis

Degree Name

Master of Science in Astronautical Engineering

Department

Department of Aeronautics and Astronautics

First Advisor

Robert A. Bettinger, PhD

Abstract

This thesis explores a novel approach to approximating three-body trajectories using a knot theory-inspired model for orbit generation and determination. Traditional methods for solving the Circular Restricted Three-Body Problem (CR3BP) rely on numerical integration and correction schemes to generate trajectories, often requiring iterative refinements. This research investigates the application of knot theory principles—such as torus knots, Alexander polynomials, and Reidemeister moves—to categorize and model complex orbital trajectories in the CR3BP. By leveraging these mathematical tools, the study aims to enhance trajectory prediction, orbit determination, and mission planning for spacecraft operating in the cislunar environment. The results demonstrate that knot theory can provide a structured framework for classifying and generating three-body orbits, offering potential benefits for space situational awareness and deep-space navigation.

AFIT Designator

AFIT-ENY-MS-25-M-146

DTIC Accession Number

AD1356400

Comments

An embargo was observed for posting this thesis.

Distribution A: Approved for Public Release, Distribution Unlimited.

PA clearance case 88ABW-2025-0560

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