# Is the Gravitational potential energy work done by Gravitational force or not?

The definition of potential energy is:- "The gravitational potential energy at a point in the gravitational field is defined as the work done to bring a particle from infinity to that point in the gravitational field. The work done referred here (the one I highlighted) is done by gravitational force or some other force?? I think it is done by gravitational force because in the calculations above we took force F = gravitational force. Kindly clarify.

• Hello! It is preferable to type out screenshots or images of text; for formulae, one can use MathJax. Thanks! Commented Dec 16, 2021 at 18:45
• Okay, I will do it next time.
– Xyz
Commented Dec 17, 2021 at 3:25

Potential energy is calculated only for conservative forces. In this case the conservative force is the gravitational force.

Potential energy of a system is defined as negative of the work done by the internal conservative forces acting in that system.

$$dU = -dW_{c}$$ $$dU = -\vec{F}_{c}.d\vec{x}$$

Now there is an another way to calculate potential energy of a system. Consider an external force (not necessarily conservative) equal to the internal conservative force but opposite in direction of it. Under action of these forces, object is moved such that equilibrium is maintained at every point thus there is no change in kinetic energy of the system.
Then, from Work Energy Theorem: $$W_{ext} + W_{con} = \Delta KE$$ Since, $$\Delta KE = 0$$ therefore, $$W_{ext} = -W_{con}$$ and $$-W_{con} = \Delta U$$ therefore,

$$W_{ext} = \Delta U$$

You can calculate gravitation potential energy from any of the two methods, but generally in textbooks the second one is mentioned.

Hope this helps

• Thanks for answering does that mean the kinetic energy is the same at each point when an object travels from infinity to a point
– Xyz
Commented Dec 18, 2021 at 16:40
• @YajyaDwivedi Yes but it is completely theoretical. We consider no change in kinetic energy since we don't want to disturb the calculation of potential energy of the system i.e. its pure potential energy. When equal and opposite forces act on a body it does not move thus $\Delta KE =0$ ,but here object is moving so slowly that we can say previous statement for this case also thus at each and every point kinetic energy remains same and only potential energy changes. Commented Dec 18, 2021 at 19:02
• Okay 👍.........
– Xyz
Commented Dec 19, 2021 at 4:33

As your first equation indicates, the potential energy is equal to the work done to bring a particle from infinity to a point within the gravitational field. This work is accomplished by the gravitational field, not the force.