I am an engineering researcher at the University of California-Santa Barbara. Thank you for your question “Does gravity prevent Earth from flying away from the Sun OR flying into the Sun?”

The answer to your question is that gravity does prevent the Earth from flying away from the sun. The Earth travels through space at a very, very fast speed. Several hundred years ago, a very famous scientist named Sir Isaac Newton taught us that an object moving at a certain speed will continue at that speed in a straight line unless some other force acts on the object. So this means that, if there was no gravity between the earth and the sun, and the Earth was traveling at its current speed, then the Earth would shoot off into space in a straight line. But since there is always gravity, the earth is kept in a nice stable orbit around the sun. The situation is the same as if you take a string with a small weight attached to the end of the string, and then you swing string over your head in a circle like a helicopter. In this case, you would be the sun, the weight would be the earth, and the string would be “gravity.” If, while you were swinging the weight, you suddenly let go of the rope, then the weight would fly off away from you into space. This concept is illustrated in the link to an image I have included below.

However, if the Earth were not moving at a very fast velocity through space, and instead was just standing still, then the sun’s gravity would pull the Earth toward the sun, and the whole Earth would be burned up by the sun (oh no!). But thankfully, Earth is traveling very fast, and the sun’s gravitational force directly balances Earths velocity through space and keeps our planet in a nice stable orbit.

I hope this helps with your question!