Regarding the moon you can use classical mechanics. If the orbit was circular:
F = ma
work = F * (distance traveled in the direction of F).
There's acceleration because of the curved orbit, so there's a force F. However that force is always perpendicular to the direction of motion, so the 2nd equation says no work is done.
Correct me if I am wrong but my understanding of the work function is that it is an engineering device given by the following equation: W = F d, where W is the work done, F is the force used and d is the distance over which the work is carried out. Great for calculating the amount of coal needed to take your train from A to B.
The W F does not necessarily assess the amount of energy expended in a given operation.
Picture a situation in which a horse is being used to try to move an enormously heavy object. If the attempt is successful the work function can be applied to it, but suppose the horse is unable to move the object. The distance then becomes zero, so F in the second half of the work function equation must be multiplied by 0. Obviously, any quantity multiplied by zero must equal nothing, so the equation becomes W = 0. No work has been done; therefore no energy has been expended, notwithstanding the possibility that the horse might be totally exhausted by its attempts to move the object. An owner who then argued that his horse had done no work, and therefore needed no food, would soon find he had a seriously undernourished horse.
You will probably point out that in order to apply the work function to an orbiting situation you have to add the term “cosθ”, but does that improve things? The equation then becomes W = F d cosθ. The angle “Θ” represents the angle between the direction in which the object is pushed, or pulled, and the direction in which it actually moves.
In the case of an orbiting object the direction of movement lies at 90 degrees to the direction of pull, so cosθ becomes zero, thus F d must be multiplied by zero. No work, no energy expenditure! Try swinging a heavy weight on a rope for a while and see if you agree that you are doing no work and using no energy.
