Date

12-17-2025

Document Type

Thesis

Abstract

Accurately predicting the orbital trajectory of celestial objects is essential for precise spacecraft navigation, planning planetary missions, avoiding potential collisions with space debris, and studying the long-term stability of planetary systems. Gauss’s method for orbital determination provides a way to predict the path of a celestial body accurately using only a small number of observations. In this project, we create an implementation that is not just a tool for executing Gauss’s method, but also an opportunity to study the formulation of the method itself. It allows for a practical and detailed examination of how different inputs, assumptions, and numerical choices affect the results. This project enables a clear and systematic exploration of Gauss’s method both theoretically and computationally, providing an in-depth understanding of the mathematical and physical foundations behind it. Building on this foundation, we then develop a fast and up-to-date implementation of Gauss’s method in Python that incorporates modern coding practices, numerical clarity, and code efficiency. This Python implementation can be used to gain a deeper, more intuitive understanding of Gauss’s method. Running multiple sets of observational data within a few seconds allows us to efficiently generate results for large datasets and seamlessly compare those results across different scenarios. This provides the opportunity to essentially “dissect” Gauss’s method into its different components and examine how each part contributes to the final orbital solution. As a result, this project becomes a practical tool for investigating several important questions about the properties and behavior of Gauss’s method, such as when does the method produce the most accurate results, when does it fail to produce any results, and what causes this behavior? How much does the time interval between observations influence the quality of the final solution? How does the scale of measurement error affect the method’s performance and its ability to converge?

Department

Computer Science, Physics

Thesis Committee

Dr. Jennifer Winters, Thesis Advisor
Dr. Laura K. Gross, Thesis Advisor
Dr. Jamie Kern, Committee Member
Dr. John F. Santore, Committee Member

Copyright and Permissions

Original document was submitted as an Honors Program requirement. Copyright is held by the author.

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