I've been talking about the reflectance of the moon in recent posts, and the issue came up of why the appearance of the Moon is so out of whack with what should be called for by the theory of diffuse reflection. The classic Lambertian reflector has the singular property that it looks just as bright whatever your viewing angle: but this property does not extend to the angle of illumination! In other words, it most certainly does not look just as bright no matter what angle you illuminate it from. So why does the moon look uniformly bright all the way across its disk? Why does it look like a flat cut-out?
It occurs to me to ask the question: what if the moon were made of golf-balls? Each golf-ball would be a mini-moon: when the moon was at half-phase, each of the little golf-balls would look like half moons to us here on earth. Except they'd be too small to see. So we'd just see the average of all of them, and the local average would be the same wherever we looked. So maybe the moon would look uniformly bright everywhere.
Except the golf-balls low on the horizon would also be partly in the shadow of other golf-balls, so the fringes should still look darker. In other words, I'm not completely buying my own explanation. But it's a thought.
Meanwhile, I tried to apply some calculus to this question, and I'm not too sure of my technique, but I got an answer and I wonder if anyone out there would like to double-check it. I compared the real moon...that is, the ideal, bright-white Lambertian "real" moon...to a flat cut-out sheet of drywall. According to my calculation, if you compare these two models at midnight on a full moon, the flat drywall cut-out provides 50% more night-time illumination than my "ideal/real" Lambertian moon. I'm not going to try and repeat my calcuations here, but I'm just wondering if anyone out there wants to see if they get the same answer as me.