Suppose the Earth orbits the Sun in a perfect circle. Does the Sun do any work on the Earth? Explain?

Answer 1

The other people who answered missed the point of your question. The answer is that if the Earth orbited in a perfect circle, no work is done. There are several ways to understand. One is this: work done produces a change in kinetic and/or potential energy. If the Earth stayed the same distance from the sun, its orbital speed is constant. It didn't change its kinetic energy or its gravitational potential energy (with respect to the sun). So, no change in energy = no work done.

Another way to understand it is this: Work done = F d, where F is the force (a vector) and d is the displacement while the force is being applied (also a vector). To evaluate F times d you use the component of d in the direction of the force (the dot product). If the Earth is going in a perfect circle the displacement is at right angles to the Force, so the component of d in the direction of the force is zero.

Finally, remember N's 1st Law? Objects keep travelling at uniform speed if there is no net force. This is equivalent to saying that an object's momentum stays the same in a closed system. It turns out that there is a law of conservation of angular momentum, too. The angular momentum of the Sun-Earth system stays the same. No energy is lost keeping the revolution going.

Answer 2

No work is done. The force of gravity is perpendicular to the direction of travel ( tangent to the orbit) and so no work is done . Work is the dot product of vectors Work=(Force dot Displacement)
or
Work = Change in kinetic energy which is also zero.

Answer 3

If the sun (sun's gravity) didn't do any work, the earth would fly off on a tangent in a straight vector.

Answer 4

It doesn't orbit in a circle.