Does gravitational potential energy always decrease?

Question

Assuming a system of two particles with no external force acting on it,the two particles would come together due to mutual gravitational forces (ignoring electromagnetic forces). Since gravitational potential energy is considered zero at infinity, is it right to assume that in a closed system, gravitational potential energy always decreases? Assuming it decreases, what does it get converted to?

Answer 1

If you define the gravitational potential energy between two bodies to be zero when the bodies are infinitely far apart, then naturally the gravitational potential is always negative. However, the potential energy can increase in a closed system (while remaining negative).

Consider two bodies that are receding from each other. As they get farther apart, their potential energy increases. This is accompanied by a reduction in their total kinetic energy, i.e. the bodies slow down.

Another example is two bodies orbiting each other, such as a planet orbiting a star in an elliptical orbit. The potential energy increases and decreases periodically: it is minimum when the planet is at its periapsis (closest to the star) and maximum when it is at its apoapsis (farthest from the star).

Answer 2

Definition: The change in gravitational potential energy of the system is defined as the negative of work done by the internal gravitational forces of the system.

In a closed system, the particles attract each due to their mutual gravitational force which does positive work. The positive work done by these forces would definitely lead to decrease in potential energy of the system.

As $W_{ext}=0$ then by Work energy theorem,

$$W_{ext}=\Delta U_{system}+\Delta K_{system}$$

So, $$\Delta U_{system}=-\Delta K_{system}$$

Hence, in a closed system the decrease in potential energy gets converted into kinetic energy of the system.