Potential Energy

A small body has a certain potential energy relative to a star. It increases with distance. Because the integral ∫1/y²dy has a limit, this energy is limited relative to a star. It would not be limited relative to an infinite set of stars. If the potential energy occupied the same position as the massive objects, stars at the edge of a finite set of stars would be heavier than those further inside. Since energy equals mass, a body in an infinite set of stars would have infinite mass, but it obviously does not have mass if the position of a massive object coincides with the position of its potential energy.
Why is potential energy also mass:
If a comet or planet moves around a star in an elliptical orbit, this object has its lowest velocity at the farthest vertex. Kinetic energy has been converted into potential energy.* The total mass of the system does not change. Thus, potential energy is just as much mass as kinetic energy. If such a body wants to leave the star, its kinetic energy must be greater than its maximum potential energy.**.
Note:
For kinetic energy, the energy mass has already been proven. It is always located in the opposite object from the inertial frame in which an object is at rest. But what about potential energy? The two objects can be at rest relative to each other. In this case, they are in the same inertial frame. But where is the corresponding mass? Is it distributed, can it even be localized, or does it form a kind of "dark" mass?

Ludwig Resch

*In mechanics, potential energy is often understood as the consumed potential energy (Pv). Thus, the difference between kinetic energy and Pv is zero. However, only the remaining potential energy is meant.
**Because the maximum potential energy is not generally known, it is usually set to 0. This gives a negative sign for the calculated potential energy, which is not helpful in this case. Here, potential energy is understood as positive energy with an unknown maximum value.