You could only estimate the diameter if you knew the material and the rough pointing of the reflector. That's a lot of assumptions.

True.

What if the observer is near or on the same longitude as the satellite, and takes magnitude estimates over a period of hours? If you observe a consistent brightest magnitude, could one

*assume* that the main dish is face-on to the observer at the time of maximum brightness? It's still calculations based on an assumption of the satellite's attitude with respect to the observer, but it could at least provide a lower limit on dish diameter?

Has anyone in the amateur astronomer/satellite observer community ever tried to determine the reflective albedos of likely dish surface materials?

Could magnitude observations of commercial geosynchronous communications satellites with large, deployed dishes of known diameter and orientation with respect to the observer, then be reliably extrapolated to estimate the diameter of an unknown, presumably larger dish?

Another, more exotic idea: Observe a stellar occultation. Determining the occultation chord length would place a lower bound on the dish diameter.

Well, just some thinking aloud, thinking like an observational astronomer. I wonder if anyone has ever tried anything like this.