The fool that I am, today was the first time I wondered how come the shadow of the earth is almost same in size as the moon. I mean, as I was looking at the crescent moon in the evening, it came upon me that the crescent was like this:
and not like this:
neither do we see as the moon like this:
Of course, this must be because the sizes of moon and earth along with the distance between them. However my question is if this is a mere coincidence, one of the many things that makes planet earth unique or is there a deeper relation between the sizes, masses, distance ? Is there any mathematical equation involving the gravitational constant that describes this fact ?