Why is gravitational potential energy negative?

[USC 22]

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I'm having a difficult understanding the concept behind PE = -GMm/r.

What does the negative mean? In simple terms, please!!

 

[cheesier]

Because as you get closer to the surface of the body exerting the gravitational force (Earth for instance) you do positive work. When we are at infinity, U = 0. This is just 1 example, but you need a negative sign, so that Uinf - U2 is not a negative value. Because of this, we have -Uinf - (-U2) = 0 - (-U2) = +U2. If we didn't have that negative sign attached to the second term the work would be negative, which is impossible.

 

[USC 22]

Because as you get closer to the surface of the body exerting the gravitational force (Earth for instance) you do positive work. When we are at infinity, U = 0. This is just 1 example, but you need a negative sign, so that Uinf - U2 is not a negative value. Because of this, we have -Uinf - (-U2) = 0 - (-U2) = +U2. If we didn't have that negative sign attached to the second term the work would be negative, which is impossible.

I still don't understand. As two objects increase the distance between them, the potential energy increases, correct? How does that make sense? wouldn't 2 objects 1 billion kilometers apart have very little potential energy?

 

[milski]

You are confusing the force between the two objects with the potential energy. If you started with the objects next to each other and pulled them away you would have to spend a lot of energy to overcome gravity and have them so far apart from each other. If you let them come back together, you're going to get all that energy back - thus it's considered potential energy.

The negative is a convention used for convenience. It allows you to ignore the potential energy due to objects very far away from you. Since when you get closer to them, the potential energy will decrease, it follows that it will become negative.

 

[anon4895]

I'm having a difficult understanding the concept behind PE = -GMm/r.

What does the negative mean? In simple terms, please!!

Gravitational potential energy is the integral of the force with respect to r. Integrate GMm/r^2 with respect to r and you get -GMm/r

You have to have a certain amount of math to understand why integrating that would give you potential energy but I could try to explain it if you want.

 

[anon4895]

I still don't understand. As two objects increase the distance between them, the potential energy increases, correct? How does that make sense? wouldn't 2 objects 1 billion kilometers apart have very little potential energy?

Yes. The energy becomes larger and larger until it disappears at zero. How does that make any sense? Only if the energy is negative. -10 goes to zero by becoming larger.

-5 > -10

 

[MangoPlant]

We know that the integral of force is work/energy.
⌠
| F dr = W
⌡

and we know that F = GMm/r²,

thus,


⌠r
| (GMm)/r² dr = -GMm/r = W
⌡0

 

[MD Odyssey]

I'm having a difficult understanding the concept behind PE = -GMm/r.

What does the negative mean? In simple terms, please!!

First, ignore the other replies - none of them really seemed to be all that helpful.

As you mention, if two objects are very far apart, their gravitational potential energy is very small - in fact, if they are infinitely far apart, the energy of the system is zero.

As two objects get closer together, their energy decreases (i.e., becomes more negative). Think of it in the context of work - the closer two masses are, the more work you would need to do in order to separate them. This is really the reason for potential energy being negative - the work that would need to be done on the system to separate them is positive. Gravitation potential energy is always a negative quantity.

If you understand it for masses (where it is always negative) then you'll also understand it for charges, since the form of the equations are very similar. The difference is that, in the case of charges, the potential energy can be positive, in which case the system does work on its surrounding. That's because the Coulomb force can be either attractive or repulsive depending upon the sign of the charges.

That last paragraph might be a bit complicated, so go back to the gravitation example until it makes sense.

Hope this helps.

 

[solitarius]

The very best explanation I found for this is pretty simple: change in KE = -change in PE. This is the conservation of energy formula.

If a small object gets pulled into a larger object's graviational field, it is obviously accelerating. So velocity and therefore KE is positive and increasing. If mechanical energy is being conserved, then potential energy is decreasing (negative and getting more negative).

As two objects get closer together, their energy decreases (i.e., becomes more negative).

This kinda violates the law of energy conservation, but whatever.

 

[theCLE]

thanks for all the responses. They have been helpful for the most part. I have a follow up question though. The question is....If you triple the distance between two planets, does the gravitational potential energy increase or decrease?

 

[theCLE]

MY QUESTION IS ONE POST UP (yet to be answered)!!! THE ANSWER IS IN THIS POST, BUT I NEED HELP EXPLAINING

I'll just post my thoughts on this. I was going to wait, but...why wait.

Pertaining to the equation, increasing the radius would make U less negative, which means it would "increase" the potential energy. However, BR states that increasing the distance decreases U, which makes sense in theory, since the further objects get, the smaller U gets.

In theory the number would get less negative, which makes it increasing on a time line scale. But I understand it makes sense that if you increase the distance, U should decrease. Can anyone explain this?

***U = gravitational potential energy

 

[mr chievous]

MY QUESTION IS ONE POST UP (yet to be answered)!!! THE ANSWER IS IN THIS POST, BUT I NEED HELP EXPLAINING

I'll just post my thoughts on this. I was going to wait, but...why wait.

Pertaining to the equation, increasing the radius would make U less negative, which means it would "increase" the potential energy. However, BR states that increasing the distance decreases U, which makes sense in theory, since the further objects get, the smaller U gets.

In theory the number would get less negative, which makes it increasing on a time line scale. But I understand it makes sense that if you increase the distance, U should decrease. Can anyone explain this?

***U = gravitational potential energy

I believe gravitational potential energy increases.

All objects exert attractive forces on each other. Let's talk about the Earth and the Sun. If the Earth is 5 km away and has PE of 100 J and KE of 100 J, and if you take the Earth away from the sun and lets say put it 8 km away, you would expect the PE to be 150 J and KE to be 50 J. I'm not sure if this is correct, but this is how two oppositely charged point charges work so I figured it would be the same.

 

[theCLE]

I believe gravitational potential energy increases.

All objects exert attractive forces on each other. Let's talk about the Earth and the Sun. If the Earth is 5 km away and has PE of 100 J and KE of 100 J, and if you take the Earth away from the sun and lets say put it 8 km away, you would expect the PE to be 150 J and KE to be 50 J. I'm not sure if this is correct, but this is how two oppositely charged point charges work so I figured it would be the same.

I like this comparison, thank you. It correctly corresponds to the idea that as two planets are further away, gravitational potential energy increases from a negative number to zero. Can anyone explain why Berkeley Review Physics Chapter 2 (passage 1 Question 2 from 2011 version BR phys) says that moving two planets away decreases the GPE (U)?😕

 

[HardWork1]

MY QUESTION IS ONE POST UP (yet to be answered)!!! THE ANSWER IS IN THIS POST, BUT I NEED HELP EXPLAINING

I'll just post my thoughts on this. I was going to wait, but...why wait.

Pertaining to the equation, increasing the radius would make U less negative, which means it would "increase" the potential energy. However, BR states that increasing the distance decreases U, which makes sense in theory, since the further objects get, the smaller U gets.

In theory the number would get less negative, which makes it increasing on a time line scale. But I understand it makes sense that if you increase the distance, U should decrease. Can anyone explain this?

***U = gravitational potential energy

U = -GMm/r.

Let's suppose you have a total value of 10 on the numerator, and a distance of 1 in the denominator. U would be -10.
U = -10/1 = -10.

Now if you increase the distance from 1 to 5. U would be -2.
U = -10/5 = -2

Therefore increasing the distance from 1 to 5 increased U from -10 to -2. Remember -2>-10. As you increase the distance between two objects the gravitational potential energy increases, but if you keep on increasing the distance, U would just end up at 0.

 

[theCLE]

U = -GMm/r.

Let's suppose you have a total value of 10 on the numerator, and a distance of 1 in the denominator. U would be -10.
U = -10/1 = -10.

Now if you increase the distance from 1 to 5. U would be -2.
U = -10/5 = -2

Therefore increasing the distance from 1 to 5 increased U from -10 to -2. Remember -2>-10. As you increase the distance between two objects the gravitational potential energy increases, but if you keep on increasing the distance, U would just end up at 0.

right, but why does BR say it's decreasing? is it a mistake?

 

[mr chievous]

If TBR said PE decreases as planets move away, then my guess is that it is a mistake

 

[Yorick]

right, but why does BR say it's decreasing? is it a mistake?

Does BR say the MAGNITUDE decreases? Then that would be correct.

 

[Plotinus]

Answering Question 1,"What does the negative mean?" :

Answer from me: The negative means nothing. We do not care what the negative means because the sign of U has no bearing on our calculations. Can there even be a positive U?

The devil is in the definition of U. Remember, alot of understanding science is about definitions.

Now to answer Why is "U" negative:
From Wikipedia: From "Potential Energy"-->gravitational potential energy-->General Formula
"Choosing the convention that K=0 makes calculations simpler, albeit at the cost of making U negative; for why this is physically reasonable, see below." So, we wanted a constant to be 0, but to do this U had to be negative. It is an artifact of convienience.

"Potential Energy"-->gravitational potential energy-->Why choose a convention where the gravitational energy is negative?
"Since physicists abhor infinities in their calculations, and r is always non-zero in practice, the choice of U=0 at [ r= ] infinity is by far the more preferable choice, even if the idea of negative energy in a gravity well appears to be peculiar at first."

My translation "U is negative because physicists are lazy. They want calculations to be as simple as possible. So, U is negative because calculations would be more time consuming if it were positive."


The wikipedia link: http://en.wikipedia.org/wiki/Potential_energy
and if you love wikipedia visit their donation page. I won't link it because then this would look scammy. If you think Wikipedia Works then tell them when you donate 🙂.


Good questions tho. These are good to ask. I majored in physics and I couldn't answer right away.Great review. I reccomend reading that wikipage.

If you have any more questions I'll be happy to try and answer for you.

 

[theCLE]

Does BR say the MAGNITUDE decreases? Then that would be correct.

here is the exact answer from BR. Please excuse me if this is copywrite infringement- just delete the post.

"Choice D is the best answer. The gravitational potential energy is given by Equation 2:
u =-GMm.
r
From that relationship, we know that U« 1. So, if r is tripled, then the magnitude of Umust be decreased by afactor of 3.
ChoiceD is therefore the best answer. Choices A and B definitely cannot be correct, because the potential energy decreases
as the distance increases. As a point of interest, the gravitational potential energy is a negative number! If the distance
between the two masses is tripled, the gravitational potential energy becomes a less negative number. The best answer is
choice D."


so, yes, it does say magnitude. This is why BR is correct, but in a sense we are also correct. BR doesn't take into consideration direction. This is what makes the question confusing though! I wouldn't know whether the test makers want us to include direction or not!!!!!!!!!!!Thank you "thefool" for figuring out what BR was saying.