Why does the earth orbit the sun rather than be pulled into it?
Answers
That's a great question! You're correct that the Sun exerts roughly twice as much gravitational force on the Moon as does the Earth. You can calculate that from Newton's Law of Universal Gravitation by comparing M/R2 to m/r2, where R is the distance from the Sun, r is the distance from the Earth to the Moon, M is the Sun's mass, and m is the Earth's mass. As it turns out, however, that force comparison is meaningless in this context.
Imagine the Earth-Moon system exists in a completely uniform gravitational field. The motion of the Moon around the Earth would continue as it does now, with the field doing nothing to change their relative positions. In fact, the Moon would orbit the Earth in precisely the same way that it would if there were no background uniform gravitational field at all. It follows that what matters is not the average field that the sun exerts on the Earth-Moon system, but how much that field changes from place to place. It's these changes that cause the bodies to accelerate differently, and thus affect how the Moo