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 ?
When you see a crescent moon, the dark part of the Moon is not the shadow of the earth: it is the “the dark side of the Moon”, i.e. the side of the Moon that is not currently lightened by the Sun.
The inner curve of what you are actually looking is not a circle but an ellipse.
The shadow of Earth in the Moon is what you see in a Lunar eclipse, and it does not match the size of the Moon.