Orbital Periods Near Sagittarius A*: From the Innermost Stable Orbit to the Timed Flare Loops

In 2018 the GRAVITY interferometer watched bright features in the flaring emission of Sagittarius A* move on the sky in loops with periods of tens of minutes, at radii of a few gravitational radii. This paper supplies the timing ruler those observations are read against. For a mass of 4.297 million solar masses, one gravitational radius corresponds to 21.2 seconds of light-travel time, and the Keplerian period at the innermost stable circular orbit of a non-rotating hole, six gravitational radii, is 32.6 minutes. Inverting the relation, periods of 45 and 90 minutes correspond to orbital radii of 7.4 and 11.8 gravitational radii for non-rotating geometry, bracketing the radii the flare astrometry reported. A maximally rotating hole shortens the innermost period to 4.4 minutes, so the timing of future, better-resolved loops carries spin information. The table of periods from one to twenty gravitational radii is computed from the audited mass; it is a ruler, not a new observation.