Fitting an Ellipse to the Orbit of a Star near the Galactic Center

This Demonstration shows how the equation for the best-fitting ellipse can be determined for several predefined points in the Cartesian plane. The points are the locations of a star known as S2 near the center of our galaxy.

In order to achieve the most suitable formula for an ellipse, the method of least squares is used, which minimizes the sum of the distances () between the data points and the curve.

Use the controls to find the best-fit ellipse by attempting to minimize the sigma () value. Axial lengths of the ellipse are fit automatically and the resulting equation parameters are displayed on the right.

The data points used in this Demonstration are the coordinates representing the position of star S2 orbiting around Sagittarius A*. They have been collected by the Very Large Telescope, Keck, and NTT since 1992.

Sagittarius A* is the strong radio source considered to be the center of our Milky Way galaxy and where a supermassive black hole might be situated. Since star S2 is drifting around an elliptic path, according to Kepler’s laws of planetary motion, the mass of an object at the foci of the ellipse can be determined.

Reference

[1] S. Gillessen, F. Eisenhauer, T. K. Fritz, H. Bartko, K. Dodds-Eden, O. Pfuhl, T. Ott, and R. Genzel, "The Orbit of the Star S2 around Sgr A* from VLT and Keck Data," The Astrophysical Journal, 707, 2009 pp. L114–L117.