Mass and Distance of Sagittarius A* from Stellar Orbits: A Keplerian Audit

Every physical quantity quoted for the Galactic centre, from the size of the black hole's shadow to the speeds of its fastest stars, descends from two numbers: the mass of Sagittarius A* and the distance to it. This paper audits those numbers with Kepler's third law alone. Combining the published angular semi-major axis of the star S2, 125.058 milliarcseconds, with its period of 16.046 years and a distance of 8,277 parsecs gives a physical semi-major axis of 1035.1 AU and an enclosed mass of 4.307e+06 solar masses, in agreement with the published value of 4.297 million solar masses. The audit also exposes the well-known lever: because the physical orbit size scales with the distance, the inferred mass scales with its cube, so a one per cent distance error becomes a three per cent mass error. The Schwarzschild radius implied by the audited mass subtends 10249.0 microarcseconds and its light-crossing time is 42 seconds. The calculation is a consistency audit of published values, not a new measurement.