How Did Stellar Orbits Reveal Sagittarius A*?

What does a fast orbit around an unseen focus let astronomers calculate?

You identified Sgr A* correctly, followed S2 from infrared positions and spectra to an orbital fit, defined every term in the mass relation, and kept the event horizon outside what the orbit directly images.

An artistic reconstruction of bright stars following differently tilted elliptical paths around one unseen focus in the dense centre of the Milky Way. — Vastward artistic reconstruction. The stars and orbit arcs establish the observing idea, but this is not a telescope image, a measured orbit plot, or a view of the black hole itself.

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