At the Milky Way's center, stars like S2 trace tight ellipses around the compact radio source Sagittarius A*. Decades of tracking these orbits let astronomers apply Kepler's laws to weigh the invisible object they orbit — the result, about 4.3 million solar masses packed into a region smaller than our solar system, is the strongest evidence for a supermassive black hole. Each star sweeps fastest at periapsis (closest approach), exactly as Kepler's second law predicts.
Kepler's third law: T² ∝ a³ / M
Schwarzschild radius: R_s = 2GM / c²
Vis-viva speed: v = sqrt( GM (2/r − 1/a) )
- Black hole mass — heavier central mass shrinks orbital periods and raises orbital speeds for the same orbit size.
- Star count — adds more instanced stars, each on its own randomized elliptical orbit.
- Time speed — fast-forwards the simulated years so multi-year orbits complete within seconds.
- Orbit trails toggle — shows or hides the glowing trace of each star's elliptical path.
This is exactly the method the 2020 Nobel-Prize-winning GRAVITY and Keck/UCLA teams used to confirm Sgr A* as a supermassive black hole.