Photon-Orbit Periods and Echo Delays: The Clocks Built Into the Two Shadows

A photon circling a non-rotating black hole at its photon sphere completes an orbit in 2 pi sqrt(27) GM/c^3. For Sagittarius A* that period is 691 seconds, or 11.5 minutes; for M87* it is 290.4 hours, or 12.1 days. A seven-hour track on Sagittarius A* therefore spans 36 photon orbits, while a ten-hour track on M87* spans 0.03 of one. Half-period echo delays, 5.8 minutes and 145.2 hours respectively, set the lag at which a flare's lensed reappearance should be sought in light curves. These periods are the natural clocks of horizon imaging: they fix how fast an image can change for gravitational reasons, how long a flare echo search must run, and why one of the two sources is a movie and the other a portrait. Computed from published masses; simulated, not measured.