Gravitational Energy: Infinite Potential & Its Impact on Nature

[pprajwal]

In nature, all forces have a limited value, i.e, their effect is reduced if many objects are influenced by that force. Example, the magnetic force experienced by a single iron nail (in a magnetic field) is greater than that of 2 iron nails in the same field.

Consider gravity,
gravity exerts a force that is related to our mass. Now, on Earth, there are millions of people but everyone experiences the same force even if there are billions or trillions. That means, gravity has infinite potential.
How is this possible?

Thanks for replying

Prajwal

 

[Drakkith]

In nature, all forces have a limited value, i.e, their effect is reduced if many objects are influenced by that force.
Example, the magnetic force experienced by a single iron nail (in a magnetic field) is greater than that of 2 iron nails in the same field.

I'm not sure this is correct. I can see it if you put the nails end to end so that one is further away from the magnet, but not if they are placed at the same distance.

Consider gravity,
gravity exerts a force that is related to our mass. Now, on Earth, there are millions of people but everyone experiences the same force even if there are billions or trillions. That means, gravity has infinite potential.
How is this possible?

Thanks for replying

Prajwal

The electromagnetic force is not the same as gravitation. The EM force has two charges which complicates things. For example, you can "screen" a positively charged particle from the electric field of a negatively charged particle by having another positively charged particle between them. That's why you can have objects which are electrically neutral. This is not possible with gravitation.

In gravitation there is only one "charge" and it is only attractive. It cannot be screened like the EM force can. So adding people onto the Earth will actually ADD to the gravitational force, not reduce it.

In addition, the gravitational potential energy for anyone object is never infinite. You can boost an object from the surface of the Earth to infinity by accelerating it to escape velocity. For the Earth, this velocity is equal to about 25,000 mph.

 

[Dale]

Now, on Earth, there are millions of people but everyone experiences the same force even if there are billions or trillions. That means, gravity has infinite potential.
How is this possible?

The Earth's potential is finite. You only get an infinite potential for a classical point mass, and Earth is not a point mass.

Also, this is the same for electromagnetism. A classical point charge has an infinite potential also, and a non-point charge has a finite potential.

Luckily, classical point sources do not exist.

 

[pprajwal]

The Earth's potential is finite. You only get an infinite potential for a classical point mass, and Earth is not a point mass.

Also, this is the same for electromagnetism. A classical point charge has an infinite potential also, and a non-point charge has a finite potential.

Luckily, classical point sources do not exist.

I do not understand the point of Earth not being a point mass. I mean, how does a point mass and Earth differ in action of gravity (wrt the question).

And, by saying that Earth's potential is finite, do you mean that for every baby born, the gravitational force on me decreases by infinitely small amount?

 

[A.T.]

do you mean that for every baby born, the gravitational force on me decreases by infinitely small amount?

If the babies immediately crawl away from you.

 

[Dale]

I do not understand the point of Earth not being a point mass. I mean, how does a point mass and Earth differ in action of gravity (wrt the question).

The potential energy density of a gravitational field is given by ##u=-\frac{|\mathbf{g}|}{8\pi G}##. If you evaluate that for a uniform spherical ball then you get
$$U=\int u\;dV = -\frac{3GM^2}{5R}$$

Where G is the universal gravitational constant, M is the mass of the ball, and R is the radius of the ball. This number is finite for R>0, and infinite for R=0 (a point mass). Therefore the Earth's gravitational potential energy is finite but the gravitational potential energy of a point mass is not.

And, by saying that Earth's potential is finite, do you mean that for every baby born, the gravitational force on me decreases by infinitely small amount?

Yes. The mass of the Earth goes down and therefore its gravitational potential energy goes down. However, the baby also has a gravitational force and the baby's gravitational potential energy goes up by the same amount that the Earth's potential energy goes down since the baby's mass is the same as the mass removed from the earth. So it really is a complete non-issue.

 

[dauto]

In nature, all forces have a limited value, i.e, their effect is reduced if many objects are influenced by that force.

Right there is your mistake. That's just not true.

 

[Andrew Mason]

And, by saying that Earth's potential is finite, do you mean that for every baby born, the gravitational force on me decreases by infinitely small amount?

For every baby that is born and then taken away by aliens to the distant mothership, gravity decreases. Otherwise a new born baby is just a rearrangement of existing matter.

AM

 

[Andrew Mason]

Right there is your mistake. That's just not true.

I think the OP has in mind a mechanical force. I apply a force F to a mass m, and get acceleration a but if I apply it to 2m I get a/2 for acceleration.

For gravitational and electromagnetic fields, the force is different because the magnitude of the force is proportional not only to the field but to the magnitude of the mass or charge of the bodies in that field: F = mg or F = qE.

AM

 

[dauto]

The OP seems to think that more people being born should reduce Earth's effect on me just like more guests coming in means less soup for me. It doesn't work that way.