I think the 50% thought is quite intuitive but incorrect because we do not observe from a point but rather the surface of a <relatively> large object and so have varying views of the moon.
But that is not the majority of the reason anyway- most of the increase beyond 50% is due to libration, of which there are three kinds: libration in latitude, libration in longitude and diurnal libration.
There is a pretty good explanation along with a video of how it works here:
http://www.wwu.edu/skywise/lunar_libration.htmlWhen doing celestial navigation by hand, via a sextant and sight reduction tables, there is an error correcting calculation needed because the Earth does not rotate neatly but rather wobbles slightly and unless compensated for can cause, if memory serves, up to an eight minute error, which would be eight nautical miles at the equator- not an insignificant error.
Hey, this is not my world, I just happen to live here and so have to compensate all the time for lots' of stuff.
Brian
I'm surprised by this. I always thought it would be 50% or maybe 50.009%. I didn't think the angle difference between a moon rise and moon set and north pole and south pole would be enough to see another 9% of the surface. But after calculating ( cos(7,000/240,000) I used 7,000 since the diameter of the moon is ~1,000 miles and earth is ~8,000 miles ) there is almost 1 degree difference in observation angle.