What work is done to rotate the earth around the sun?

Answer 1

In order for work to be done, a force must be applied over a distance, as illustrated by the formula W = Fd. One of the forces acting upon the Earth is the gravitational force between it and the sun. This is a centripetal force since it pulls the Earth to the center of a (more or less) circular orbit. But it does not do any work since the Earth is not gaining kinetic energy or potential energy. It is simply a force that keeps our planet orbiting, like a rope attached to a spinning metal ball (for some kind of Track and Field sport I just made up). One of the important concepts to understand is that the Earth has inertia and would fly out of the solar system on a tangential path if the sun suddenly disappeared (neglecting the gravitational forces of neighboring planets). So what keeps the Earth 'going' is its own momentum. All the sun does is change its direction so that it does not fly out of orbit. We can illustrate this concept with the following formula for centripetal acceleration: ac = v2/r where v is velocity and r is the radius of a circular path. The gravitational force exerted on our planet by the sun can be divided by the mass of the Earth to give us this acceleration (remember F = ma) that is precisely equal to the speed of the earth squared and divided by our separation distance from the sun. If we move any faster, we fly out of our orbit and into a larger one. Any slower, and we swirl into a smaller orbit closer to the sun. Not to worry, though; our planet does not seem to be slowing down and dropping into the sun.