Orbital determination with Gauss's method

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 a small number of observations. This project focuses on understanding the mathematical and physical foundations of Gauss’s method. Based on this understanding we then develop a fast, user-friendly implementation of Gauss’s method in Python that incorporates modern coding practices and code efficiency.This Python implementation can be used to gain a deeper understanding of Gauss’s method. Running multiple sets of data within a few seconds allows us to easily generate statistics and compare results, providing the opportunity to “dissect” Gauss’s method into its different components to analyze the results. We can look for the solution to more complex questions, such as: When does the method produce the most accurate results? When does it not produce results? How much does the intervalbetween observations affect the results? How does the scale of the measurement error affect the results? This implementation is not only a tool for applying Gauss’s method, but also for studying it in greater depth.