# Potential energy definition in terms of work done

It's true the source might not be the most reliable of all, however it states that:

The potential energy $U$ is equal to the work you must do to move an object from the $U=0$ reference point to the position $r$. The reference point at which you assign the value $U=0$ is arbitrary, so may be chosen for convenience, like choosing the origin of a coordinate system.

It's true if we look at, for example, the gravitational potential energy formula for small distances from the earth: $U=mgh$. On the ground level, the potential energy is zero. To move the object up to a certain height, we need to perform work on that object and it is equal to the potential energy of that body after we're done.

However, the general formula for gravitational potential energy choses the point at infinity to be the reference point with zero potential energy. So, moving an object from infinity towards the earth requires no work, and thus the above statement is not valid anymore in this case.

What they probably forgot to add is the assumption that the object should be moved at a constant speed (or not to move at all before we started moving it and after we've finished) - or more generally, the kinetic energy after the process should be the same as before we started. Correct? Is there anything else that should be added?

I can see where the usually reliable Hyperphysics site is confusing or incomplete here. A better definition is: "Potential energy is the negative of the internal work done by a conservative force during a change in the configuration of a system" $$\Delta U = -W_\mathrm{internal}$$