An Intuitive Approach to Orbital Deprojection: Analyzing the Orbit of S2 in the Sagittarius A* Cluster

The orbit of the star S2 around the supermassive black hole Sgr A* at the center of the Milky Way provides one of the most compelling observational laboratories for testing gravitational dynamics. This project develops an intuitive and educationally accessible yet physically rigorous framework for modeling the orbit of S2 using publicly available astrometric and spectroscopic data, specifically the dataset compiled by Gillessen et al. (2017) from observations with the ESO Very Large Telescope. The methodology enables students—from secondary school to undergraduate levels—to derive the six classical orbital elements describing S2’s motion and to estimate the mass of Sgr A* using Keplerian dynamics. Additionally, radial velocity data are used to validate the orbital solution and estimate the distance to the Galactic Center. Beyond the technical objectives, the project aims to foster intuitive understanding and scientific curiosity by bridging modern observational data with classical celestial mechanics. The framework is implemented in both a slider-based Desmos interface for introductory engagement and an Excel-based workflow for more advanced analysis. This project thus serves not only as a pedagogical tool but also as a case study in democratizing access to high-precision astrophysical datasets and methods.