Is the moon the most full only for one moment
Or does if stay the same full for a longer period of time (maybe because, the sun is grater then it, and light spreads out)
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$\begingroup$ It seems to be, because from the Moon, the earth takes up a fair bit more sky space than the sun does, we never get a truly entirely round full moon. You can get it full in one axis but not both. But I think your argument is largely correct. The sun takes up 1/2 degree of the sky, so there should be a 1/2 degree of space where the Moon would appear completely illuminated as it crosses the far side of Earth. It's the Moon's orbit around the earth that matters so 1/720 x 28 days = 56 minutes, (I would think), but that's only across it's equator. it's still not full pole to pole. $\endgroup$ – userLTK Aug 2 '15 at 22:32
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$\begingroup$ As your second link correctly points out, the moon is never truly full, since the Sun-Earth-Moon angle is only a perfect 180 degrees during a lunar eclipse. $\endgroup$ – barrycarter Aug 6 '15 at 14:23
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$\begingroup$ @barrycarter I understand that, that is why I used the words "most full" and "same full" $\endgroup$ – hazoriz Aug 6 '15 at 14:25
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tl;dr: Perfectly full moon lasts, never more than, approximately 2 minutes.
Estimating an answer from the point of view of Plain Geometry:
If we approximate, that the sun is at an infinite distance, then exactly half of the moon is illuminated.
Next, how much of the Moon do I see when I look at it from Earth? (This has nothing to do with illumination of the Moon.) Estimate: Radius of moon (Rm), 1740km. Distance to the moon (Dm), 384,000km. Doodle this into a diagram that is VERY much not to scale...
arctan(Rm / Dm) gives us 0.260 degrees. So as long as the observer is within that angle from the Moon-Sun-centerline, the portion of the Moon which is visible, would be a circular disc fully illuminated.
Here, I suspect that the variation in the Moon's distance is the biggest thing I've estimated away.
The question now is: combining the Moon's motion of revolution (aka orbit about the Earth) with the Earth's rotation, how long does it take an observer to perceive the moon moving half a degree (1/4 degree either side of the Moon-Sun-centerline)? Rotation of the Earth gives 15 degrees-per-hour, minus the Moon's 1/2 degree per hour... 14.5 degrees per hour apparent motion.
I get approximately 2 minutes duration when the Moon's shifting of apparent position would only hide/show illuminated portions of it's disc.
But the lunar orbit is inclined
So it's only 2 minutes if the Moon is very close to the plane of the Equator. As the Moon's orbit carries it out of the plane, the time would be reduced. Beyond half a degree out of the plane, you would actually never (pure geometry) seen a fully illuminated disc.
So I think the best answer is probably, "Never more than 2 minutes."
