Question about the sun and the earth

[alias_none]

The sun exerts a force of 4.0 X 10^28 N on the earth, and the Earth travels 9.4 X 10^11 m in its annual orbit around the sun. How much work is done by the sun on the Earth in the course of a year? Explain.

 

[turdferguson]

This is a trick question. The one year length shouold tip you off that displacement is zero, but even if it wasn't, the force is always perpendicular to the displacement by definition. This means that a centripetal force of any kind does no work to displace the rotating object.

 

[Andrew Mason]

This is a trick question. The one year length shouold tip you off that displacement is zero, but even if it wasn't, the force is always perpendicular to the displacement by definition. This means that a centripetal force of any kind does no work to displace the rotating object.

Not quite. The work done is the dot product of force and displacement:

$$dW = \vec{F}\cdot \vec{ds} = Fds\cos\theta$$

Unless the orbit is perfectly circular (the Earth orbit is close to circular but is slightly elliptical) the force is not always perpendicular to velocity or displacement of the Earth (hence $\cos\theta \ne 0$ and $dW \ne 0$). However, over a period of a full year, as you have correctly pointed out, the total work is 0.

AM