The Massive Black Hole
By following the motions of individual stars we have measured the mass associated with the radio source Sgr A* – we see stars on Keplerian ellipses surrounding an object of four million times the mass of the Sun. The physics at play is extremely simple: it is Newton's law of gravity. The precision of these measurements is stunning – see the orbit of the star S2 (Gillessen et al 2009, Gillessen et al 2017, GRAVITY Collaboration 2018, 2019, 2020, 2021).
S2 is the best example of the orbits, and constraints the mass most. Overall, we can measure the mass with a precision of well below 1% (Gillessen et al 2019). Furthermore, we can locate the mass and show that its position agrees to better than 1 milliarcseond with the location of the radio source Sgr A* (Plewa et al. 2015). This measurement uses a few SiO maser stars, which are visible both in the infrared and at radio wavelengths.
Since we can determine both the proper motion of S2 on the sky as well as its radial velocity along the line of sight, our measurements allow us to calculate both the mass of the black hole as well as the distance R0 to the Galactic Center. The GRAVITY instrument has allowed us to measure these two quantities with unprecedented precision and accuracy. By combining the precise astrometry from GRAVITY with the spectral measurements of SINFONI, we found out that the distance to the Galactic Center is 8,249 parsecs ±9 stat ±45 sys (Gillessen et al 2019). The statistical error is dominated by the uncertainty in measuring the radial velocity, while the systematic error stems from the GRAVITY instrument.