Is Work Done by the Sun in a Circular Earth Orbit?

[Saraharris38]

Okay, this is not a homework question, but a conceptual question already answered in the book.

Problem: Suppose the Earth's orbit around the sun is perfectly circular. What is the work done by the gravitational force of the sun on the Earth through a small displacement over a small time interval?

Answer: No work is done

My problem:

I understand that the centripetal portion of the force does not do any work on the Earth through a small displacement because it is perpendicular and thus the cos factor is zero. However, doesn't the tangential portion of the force act (for very small displacements) essentially parallel to the displacement, and thus do a bit of work?

Thanks!

 

[Doc Al]

However, doesn't the tangential portion of the force act (for very small displacements) essentially parallel to the displacement, and thus do a bit of work?

But there's no tangential component of the force--you are assuming a perfectly circular orbit.