Why is Gravitational Potential Energy Negative? (Gravity, Physics)

The Gravitational Potential Energy of a system of 2 masses is always negative. Why is that? According to Newton’s universal law of gravitation, when two masses are infinitely distant, the gravitational force / interaction is zero, thus the potential energy is zero. To bring them closer, the work on the system must be negative. The work being a transfer of energy, the potential energy can thus only be negative.

In a second part of the video, I also prove that by deriving the formula for gravitational potential energy: a minus sign appears while all the variables involved are positive in nature.

Finally, the last part of the video widens our understanding with a generalisation: The sign of potential energy is negative when the interaction is attractive, and positive when it is repulsive.

#gravity #physics #potentialenergy

0:00 – Why is gravitational potential energy always negative (Introduction)
0:37 – Reminder that work is a transfer of energy (notion needed for the proofs that follow)
1:33 – Explains why gravitational Potential energy is always negative
4:02 – Deriving the formula for gravitational potential energy (based on Newton’s Universal Law of Gravitation)
7:10 – Sign of potential energy (general rule)
10:31 – Conclusion and card links to useful videos:

For a deeper dive into the basics of Gravity, here is a fantastic course on the subject:

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This video is produced and presented by Edouard Reny, Ph.D. in solid state chemistry and private tutor in Physical Sciences.

For access to great resources that will help you with your studies of high school Physics, visit and subscribe to the "Physics Made Easy" website:

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Footage credit (Space background at end of video):
Traverse galaxy, F. Summers, G. Bacon (STScI). Simulation: C Hummels, P. Hopkins (CalTech) and A. Wetzel (UC Davis)

Credit for Thumbnail image: AllenMcC. / CC BY-SA

[johnyfausman]

This was the best explanation I have seen for this. Thanks, we need more people like you.

[a_vi]

This channel is a great resource for physics enthusiasts as your explanations are very intuitive.
Keep up the great work!

[rajkumars]

Amazingly lucid ! The conclusion with atrractive and repulsive forces was stunning. Thank you Sir. Please continue your good work. It is so rare to find a teacher who gives conceptual clarity.

[ndwani]

I see this YouTube is really a fantastic social media which is giving us the golden opportunity to get our clarifications of every aspects but only drawback is we find these golden videos and golden creators rare and finding them is very hard. After watching 10 videos 2/10 are found fantastic videos.

[raindrops]

youtube is a blessing, so is this man

[thegoldenllama]

I have genuinely spent the entire day looking for a good explanation of GPE and your video has made it all crystal clear - subscribed!

[Brainiac]

Hello
At time 5:24 you mention work also has to be done if you want to bring a mass m closer to mass M, in this case is the work done negative as the potential energy is decreasing and so is the distance between the two masses ?

[shrishirol]

Brilliant Explanation Professor. Thank you. This is the Best Demonstration of Good Teaching and Conceptual Clarity.

[Ii-fopq]

Please never stop posting videos.. I've been searching this kind of video for months now I finally understood why negative energy particle falls into the black hole and positive energy particle escapes.. you're a great teacher I must say👏👏

[syedmuhammadfaheem]

after all, my confusion gets clear.
thank you very much sir.
so clear and calculus based explanation.

[alohahoward]

The negative sign has always bothered me, now it make sense. When I took physics in school I found it difficult but fascinating. I think the problem I had was that the concepts were not adequately explained. I could work the problems because I memorized the formulas but I still was often confused. Thanks for the great explanations.

[amritrajdash]

It's a shame this channel isn't more popular. Loved the explanation!

[Tzaounis]

The best explanation I have watched so far. With mathematical and logical clarity.

[The_Green_Man_OAP]

2:53 The energy that was _transmitted to_ the moon _increased_ the _gravitational potential energy level_, which _decreased_ the _gravitational potential binding energy_ for the moon/planet system at that distance from it's _barycenter._

For a conservative applied forces, potential gradient exist such that the work done on masses can be calculated for displacements over equipotential lines instead of using along the exact trajectories.

The work done is then path independent.

[gamertothecore-borngamer]

What is this a coincidence? I got this doubt now on 18th October 2021, and you uploaded this on 17th October, 2020. Haha, nice helping me on the first anniversary of this video! Amazing explanation btw :)

[ello-isa]

I would like to say, thank you. This video really helped me a lot to understand the concepts

[The_Green_Man_OAP]

3:14 The problem with that is that the best estimate for the size of the Universe is at about 93 billion light years, which is a far cry from infinity, therefore we need a better definition of potential that doesn't invoke infinities. 


Btw, another way to get zero gravitational potential is at Lagrange points of reference, where gravitational fields cancel out.


So, instead of invoking infinities, it may be better to map Lagrange points out throughout the galaxy and estimate them throughout the Universe.

[sweetumms]

This was reeaallyy helpful! Thank you so much❤

[AdhamMGhaly]

A brilliant explanation.

Glad to see Phil Collins explaining physics :)

[lexanris]

Thanks for making this amazing video. Explanations very concise!
But i still have 1 query:

What I you understood is that Since GPE = -W by gravitational force to bring from infinity to r & W done by gravitational force in this case must >0 as the displacement is in same direction as force, GPE must be <0

But if you do this:
GPE = -W done by gravitational force to bring from infinity to r = - integral F dr … = GMm/r which is wrong

Why is it wrong only when i evaluate the integral?

I was just wondering abt this, hope it’s clear enough. Thanks in advance!