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.