the earth travels around the sun in a roughly circular path because the sun's gravity is pulling on the earth. The earth does not fall in to the sun, because it is moving very fast, which gives it...
The moon orbits the Earth, but technically, the moon and Earth orbit each other, around a center of gravity. And due to the moon's size, the moon-earth system is sometimes called a "binary planet"...
A little bit of both. Earth is much more massive than the moon so the moon mostly goes around Earth but the moon does still tug Earth around somewhat.The moon helps with the earth's tide.
Gravity pulls the moon toward the Earth but the moon does not crash into it because it is already moving sideways compared to that gravity. By the time the gravity has pulled the moon down a mile or...