Solar and lunar eclipses -- how rare I was fortunate enough to see the solar eclipse in southern Illinois last year. The clouds were not friendly, but we did have one spectacular moment of perfect eclipse. It is an eerie sensation, and I cannot imagine how utterly terrifying it must have been for our ancient ancestors to see the moon eating the Sun.

However, it got me wondering. A solar eclipse can occur in the spectacular fashion it does because the angular dimension on the moon and the Sun are almost exactly the same -- this despite the fact that they are dramatically different in actual dimension. This seems a remarkable coincidence to me -- the ratio of the distances being almost exactly the same as the ratio of their diameters. 

I was wondering if there are any other known examples of such a phenomenon occurring anywhere else in the universe? Can we make any estimate of how often something like that might occur in a galaxy?
TOTAL solar eclipses and TOTAL lunar eclipses are actually not that common in places outside of the solar system. For these TOTAL eclipses to occur, and I'm emphasizing total bc partial eclipses happen all the time, there needs to be the perfect distance so that an object perfectly covers the Sun.

In other words, you are correct - it is such a remarkable coincidence that this occurs in our Solar System. I'm not entirely sure about how many exoplanetary systems also experience this phenomenon, but I assume that it won't be a lot. I do know that it DOES HAPPEN in other places, but it just isn't common.

Just for a fun fact - the Moon is actually moving away from us, meaning that in a few million years, total solar eclipses won't be possible anymore - and we'll only see partial eclipses.

Hope that helps! :)