Work done on the Earth by the Sun

[nothing123]

Hi,

Homework Statement

I was just wondering, because the Earth follows an elliptical path around the sun and the gravitational force of the sun on the Earth is towards the sun, would the work done on the Earth be considered positive or negative?

Homework Equations

The Attempt at a Solution

Thanks.

 

[Shooting Star]

Because of the ellipticity, the speed of the Earth varies. When the KE of the Earth increases, work done on Earth is positive and vice versa. During a complete orbit however, the total work done is zero.

 

[dynamicsolo]

Quick answer:

The gravitational force is conservative, which implies that the work done by such a force on an object passing from A to B is path-independent. In the model where the Sun alone acts on the Earth, the fact that the Earth completes a closed orbit automatically implies that the net work done on it by the Sun is zero. (Indeed, any closed curve would lead to this conclusion.)

Complicating features:

In reality, the Earth is subject to gravitational interactions with every other massive object in the Solar System (and, to a far lesser extent, the rest of the Cosmos), so its path is in fact not closed. In the long run, the average net work on the Earth (or any of the other bodies) is not zero. There are also dissipative forces at (very slow) work on all the bodies, so the total mechanical energy is not actually conserved.