I would appreciate it if you'd remove that section from the Wiki because it is a misrepresentation of what astronomy texts say. They may say 100%, and my point is that 99.7% is certainly close enough to 100% that you would stop quibbling over it. 99.7% is not the MAXIMUM illumination. I clearly stated that was the MINIMUM. And I actually said it goes to 100%.
One might suggest that since Inkitham's good artwork is apparently more correct than dozens of astronomy websites on the internet that were created by astonomers and educators, many which define a full moon as 100% illumination and say that a full moon happens every month, then perhaps it is Inkitham's artwork that should stay up and it is those website that should be changed.
You said that it goes to 100% on rare events, but you did not show it. You did a good job showing the 99.7, and I will give you good credit for that. Lets try to do it for the closest the moon could get to the earth's umbra.
From earlier:
Angular Size of the Sun from the Moon
Average distance between earth and moon = 238900 miles (Source: Google)
Distance from Moon to Sun if Moon is directly behind earth
93,000,000 + 238900 = 93,238,900
2(Arctan (865000 / (93238900 x 2))) in degrees = 0.5315 degrees
Angular Size of the Earth from the Moon
Dist from Earth to Moon = 238,900
Diameter of Earth = 7917.5
2(Arctan (7917.5 / (238900 x 2))) in degrees = 1.899 degrees
Assume that the moon sees 100% of the sun's body sitting right on top of the earth. To get the angular distance from the center of the sun to the center of the earth we can do the following:
0.5315 / 2 = 0.2656
1.899 / 2 = 0.9495
Distance from center of sun to center of earth = 1.2151 degrees. I estimate that this should be the closest the moon can get to the earth and be fully illuminated.
Plop that into your calculations in place of the 5.x degrees and see what you get.
I haven't bothered to double-check your numbers. I just did as you asked and plugged it into my formula. For an observer standing on a direct line between Earth and moon (at 1.2151 latitude), the moon's illumination would be 99.989%. Farther away from the equator, that number INCREASES. As I pointed out already, that's well below the tolerance of my simple photo analysis method to determine any difference between that and 100%. To the nearest 1/10th of 1 percent, That's actually 100.0%.
Re-reading the wiki, I'll agree that the words there aren't technically
wrong. But they are very misleading. The diagram is correct, and it actually DOES show that the moon is illuminated by 100% in the extreme case. That would be the case I was alluding to where the observer is well above the equator. It is the wording that is misleading. The wording seems to suggest that RET predicts we'd never see a full moon. What RET predicts is that the full moon almost always has a tiny little sliver of darkness on it that you'd need a telescope to notice. But if you break out a telescope, you can see it.
As far as the websites that say 100%. They are correct unless they say 100.0%. And as the diagram on the wiki shows, even perfect illumination
is technically possible - just not everywhere on Earth, and not every month.
The wiki article currently says, "However, in order to see a full moon with 100% totality under a you would need to be looking at the moon's daylight side face-on. But according to the geometry of RET we would never see the daylight side face-on, otherwise the earth would get in the way of the sunlight. There should always be a portion of the moon that is unlit. 100% totality should be impossible, no matter how much mental gymnastics are done with the scale. If we are not looking at the daylight side face on, complete totality is impossible."
Since I insist that is not Tom's intention to deliberately mislead anyone, and we've all agreed that RET predicts the typical full moon to range from 99.7% to 99.99%, perhaps that is worth noting on there. We could just add a single sentence like so:
"However, in order to see a full moon with 100% totality under a you would need to be looking at the moon's daylight side face-on. But according to the geometry of RET we would never see the daylight side face-on, otherwise the earth would get in the way of the sunlight. There should always be a portion of the moon that is unlit. 100% totality should be impossible, no matter how much mental gymnastics are done with the scale. If we are not looking at the daylight side face on, complete totality is impossible. RET predicts full moons that range from 99.7% to 99.99% illuminated when there isn't an eclipse."
What do you say to that?
Bobby's link to the Space.com article is a really good one. Very concise and clear. Not mathy at all. Good read.