Photon-Sphere and Critical-Curve Scales for the Two Imaged Black Holes and the Mass Ladder Between Them

For a non-rotating black hole the photon sphere sits at three gravitational radii and the critical impact parameter that outlines the shadow sits at sqrt(27) gravitational radii. Evaluated for the two imaged sources, the photon-sphere radius is 28.8 trillion metres for M87*, whose gravitational radius is 9.60 trillion metres, and 19.0 billion metres for Sagittarius A*, whose gravitational radius is 6.35 billion metres in the units used in the deposited table. The mass ratio of the two sources is 1.51e+03, and every linear scale in the problem follows that ratio exactly, while the angular scales do not, because the distances differ by a much larger factor. The photon sphere subtends a diameter of 22.9 microarcseconds in M87* and 30.7 microarcseconds in Sagittarius A*, and light crosses the M87* photon sphere in 26.7 hours against 63.5 seconds for Sagittarius A*. The ladder between stellar-mass and billion-solar-mass holes is tabulated so that any future target can be placed on it by mass alone. Computed, not measured.