Duality

so I was listening to this song and a thought occurred to me: Earth's sun and moon look almost exactly the same size in the sky, but there is no natural reason for this, it's just an incredible coincidence which I think is so cool. Apparently the sun is 400 times as wide as the moon AND 400 times as far away. This is very unlikely and very satisfying

but as I was typing all this another thought occurred to me: IS it a coincidence? Since there is a such a thing as a "habitable zone," i.e. a planet can only support life if it is a certain distance from its star, it's reasonable to think that on any hypothetical life-supporting planet, one's star looks approximately the same size in the sky as the sun does to us. But what about the moon? Is there a correlation between a celestial object becoming a moon to a planet and this moon's mass/distance from its planet (i.e. its size in the sky)? Maybe not but that got me curious about how big various moons in our solar system look in their respective planets' skies. And someone made a thing about that which was really cool to see: http://umich.edu/~lowbrows/reflections/2008/jmaguran.1.html

That link has some really fascinating information I thought, especially in the table at the bottom. For the moons in the table, I calculated the correlation between their distance from their planet and their diameter. The correlation coefficient was just -.17, which is pretty weak with a sample size of 23 observations. So it does seem to be just a coincidence that our moon looks like a very similar size to our sun

interesting stuff idk i should probably be asleep or doing something productive