Does the sun do any work on earth, when earth revolves around the sun in a perfectly circular orbit?

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Solution

No, because the motion of the Earth is always at right angles to the force from the sun.
Work done is force x (distance moved in the direction of the force). In vector notation, work is force .
distance but the dot-product of two vectors at right angles is zero. That’s the more elegant vectorish way
of saying the same thing.
Given that the orbit is actually slightly elliptical, the Sun’s gravitational field does do some work on the Earth,
just a little, causing us to speed up at the close-in part of the ellipse. And we slow down again as we move around to the more distant end (just now we’re at the close-in end of the ellipse).

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