An  open Monte Carlo based implementation of Gauss's method for initial orbit determination

José B. Batista-Mendoza; Eduardo Chung; Adam’s Martínez-Soto; Joaquín Fábrega-Polleri; Carlos A. Fernández-Valdés

doi:10.48204/j.tecno.v27n1.a6633

Submitted December 27, 2024

Published 2025-01-03

Artículos

Vol. 27 No. 1 (2025): Tecnociencia

An open Monte Carlo based implementation of Gauss's method for initial orbit determination

José B. Batista-Mendoza ⁺⁻
Eduardo Chung ⁺⁻
Adam’s Martínez-Soto ⁺⁻
Joaquín Fábrega-Polleri ⁺⁻
Carlos A. Fernández-Valdés ⁺⁻

DOI https://doi.org/10.48204/j.tecno.v27n1.a6633

PDF (Español (España))

References

DOI: 10.48204/j.tecno.v27n1.a6633

Published: 2025-01-03

How to Cite

Batista-Mendoza , J. B., Chung , E., Martínez-Soto , A., Fábrega-Polleri , J. and Fernández-Valdés , C. A. (2025) “An open Monte Carlo based implementation of Gauss’s method for initial orbit determination”, Tecnociencia, 27(1), pp. 8–25. doi: 10.48204/j.tecno.v27n1.a6633.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Abstract

Hundreds or thousands of Near-Earth Asteroids (NEAs) are discovered every year, so being able to determine their orbits to follow them successfully in the future is essential to warn of the danger they could present. Numerous methods have been developed to improve the precision and efficiency of calculations used in the Initial Orbit Determination (IOD), with Gauss’s method being the benchmark due to its intuitive formulation, comparable precision, and historical importance. Herein, we present the results of the development of a new

open access tool to simplify the process of IOD of celestial bodies, specifically, NEAs. This tool was based on a modern implementation, using code written in Python to calculate, propagate, and graph the orbits. The results obtained from the test data exhibited significant accuracy, with the maximum discrepancy not exceeding 1.2% compared to the Horizons System tool, and the average being 0.5%. Furthermore, we found that for the Monte Carlo simulations that the code uses, 5,000 iterations were more than enough to achieve the obtained accuracy.

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