[Jeff]

nmgolfer - you wrote-: "there is no point on a circle that is closer to the center of the circle than any other."

That is correct. Imagine that there a million points on that hypothetical circle's circumference, and imagine that an orbiting object (traveling at a constant finite speed) has to move from from one point on the circumference to the next point on the circumference to the next point on the circumference -- and that it has to complete this process one million times to complete one orbit. In each of those movements (from one point to the next point), the orbiting object needs a tangential force to move it at its constant "finite" speed and a centripetal force to keep it moving on the circular path.

After penning post #265, I have come back to this post to add another comment.

My final statement above was "a centripetal force to keep it moving on a circular path." Keeping an orbiting object traveling in a circle requires a restraining force, a force that prevents the orbiting object from moving off into space (in a straight line direction at right angles to the circumference of the circle). That restraining force, which keeps the orbiting object traveling along a circular path, represents centripetal force, and the constant use of a restraining force (centripetal force) requires the constant expenditure of energy - and that represents work.

Jeff.