1. ## A Physics Question

Just to keep the old grey matter exercised I am rereading my college textbooks. It is a humbling experience. Did I ever understand this?

So here's my question.

Per the text the gravitational potential energy of an object is;

Since G and M and M are constants,

E = C/r

But if we consider the molecule at the center of the earth it must have infinite energy. Clearly it does not.

Please try to keep to a reasonable level with your debunking of my thought process.

Thanks,
Tom  Reply With Quote

2. I think you need to define a few more symbols/variables for us for the question to make sense. What are G, M, E, C, and r?  Reply With Quote

3. Moderator
Join Date
Apr 2007
Location
New Jersey
Posts
13,053
The potential energy gets bigger with the height right? So wouldnt the /r be a *r?  Reply With Quote

4. The gravitational potential energy of an object is:

mass * g * height

where g is the force of gravity, and height is the height of the object above your chosen zero point.

For most scenarios, the surface of the earth is the chosen zero point, therefore an item resting on the ground has zero gravitational potential energy. As you raise the item above the ground it gains gravitational potential energy.

For your scenario, a molecule at the center of the earth has a height of zero; therefore it has no gravitational potential energy.  Reply With Quote

5. I thought the dinosaurs in the Antarctic caldera caught anything dropped down the hole and sent something up to replace it where the dot products canceled.

I believe the exit point is somewhere in New Jersey.  Reply With Quote

6. Contributor
Join Date
Mar 2018
Location
Orwell, NY
Posts
557
All I know about physics is that if I drop something heavy enough on my foot, it hurts. I admire you for ever having tried to understand things like what you posted, let alone trying to understand it twice.  Reply With Quote

7. Contributor
Join Date
Feb 2003
Location
San Antonio, TX
Posts
406
If you are at the center of the earth you have to take into account the gravitational pull of all the matter pulling from each direction. You can no longer assume the earth is a point mass. If you are in a hollow at the center of mass of the earth the gravitational potential will go to zero because all the mass is surrounding you pulling in opposite directions

A way to think about this is to have two identical earths at some distance apart. If you are on a line between their center of masses, half the distance they are separated, then the gravitational pull of earth 1 is of equal size but opposite direction of that of earth 2. So the gravitational potential goes to zero.

For the case at the center of the earth you have add up all the masses and account for the direction they are pulling on you. Do able if you know the distribution of the masses (and can do a little bit of calculus)

John  Reply With Quote

8. Originally Posted by Jim Matthews I thought the dinosaurs in the Antarctic caldera caught anything dropped down the hole and sent something up to replace it where the dot products canceled.

I believe the exit point is somewhere in New Jersey.
You're thinking of a different kind of portal. https://en.wikipedia.org/wiki/Being_John_Malkovich  Reply With Quote

9. Contributor
Join Date
Feb 2003
Location
San Antonio, TX
Posts
406
F=Gm1m2/r2

F is force due to gravity
G is gravitational constants
the ms are the masses
r is the separation

Dont think about m1 and m2. Being your total mass and the earths total mass, but rather adding up the forces between every pair of individual masses.

At a large distance apart we can approximate that the separation is about the same and can use the difference in the centers of mass and the total masses.  Reply With Quote

10. Moderator
Join Date
Apr 2007
Location
New Jersey
Posts
13,053
Is it that your equation is for gravitational force not potential energy? It makes intuitive sense to me that if the distance between 2 object centers is zero, they are occupying the same space and probably have a darn high attractive force .  Reply With Quote

11. Contributor
Join Date
Sep 2016
Location
Modesto, CA, USA
Posts
5,819
r is the seperation. so if a particle is inside the middle of the earth the seperation is zero. anything times zero is zero. So at the exact center of the earth there is no gravitational force.
Bill D

reading the equation again I see you are dividing by r, not multiplying. dividing by zero gives "undefined" as an answer. So the answer is not zero it is "undefined"
Last edited by Bill Dufour; 03-22-2021 at 11:10 PM.  Reply With Quote

12. Contributor
Join Date
Jun 2012
Location
New Westminster BC
Posts
1,704
I think you need to reread your textbook, don't think the formula is correct. As Steve posted gravitational potential energy is mass x g x height and as John pointed out if the formula is for gravitational force the r should be squared. Now what I find is the tricky part is determining the height. If you have a mass six feet above a four foot high table is h six or ten? Does it matter if the table is strong enough to support the mass when dropped from the six feet? If h is ten feet what if the floor under the table can't support the mass when dropped and the basement floor is eight feet below the main floor? And how about if there is a cave under the basement floor that leads to the center if the earth?  Reply With Quote

13. Originally Posted by Tom Bender Just to keep the old grey matter exercised I am rereading my college textbooks. It is a humbling experience. Did I ever understand this?

So here's my question.

Per the text the gravitational potential energy of an object is;

Since G and M and M are constants,

E = C/r

But if we consider the molecule at the center of the earth it must have infinite energy. Clearly it does not.

Please try to keep to a reasonable level with your debunking of my thought process.

Thanks,
Tom
The bold text is the problem. As other posters have said, once you are inside the Earth "Mearth" (your notation) is no longer a constant, rather, it varies with the cube of r.

Your equation for potential energy is not it's definition. It's definition is the integral of force with distance. (hard to review physics without reviewing calculus too ) The equation you stated is the result of that integration under a particular set of conditions. To calculate the total potential the integral is broken into two parts; one for outside the Earth and the other for inside. The "inside the Earth" integral will converge to a finite value at zero.  Reply With Quote

14. Ok, at first read I ignored Roger's post about defining the terms. On rereading I realized that G is not a constant. As the object approaches the center of the earth, G (the acceleration due to gravity) decreases to zero (John's point) so we have 0/0. This is a reasonable result.

Prashan and Steve,there is a minus sign in the equation so energy does increase with height.

Thanks all for helping me to think this thru.

Tom  Reply With Quote

15. Contributor
Join Date
May 2007
Location
Fort Smith, Arkansas
Posts
1,769
Thank heavens we got that cleared up   Reply With Quote

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•