How can the overall potential energy be the same in these two examples?

In summary: As long as the object does not leave the gravitational field of the larger body, it will always have some potential energy relative to the larger body. And as long as the object has kinetic energy, it can be converted into potential energy by moving it farther away from the larger body. But it will always have some potential energy as long as it is within the gravitational field.
  • #1
J. Richter
9
0
Imagine a universe A, containing only two identical heavy planets situated at an almost infinite distance from each other.

Imagine another universe B, containing only two identical lighter planets situated at an almost infinite distance from each other.

In both cases the gravitational potential energy between the planets are said to be almost zero.

How can that be?

I think there must be a bigger overall potential in universe A.
Don’t you?

Two bigger planets “falling together” trough billions of years, must lead to a bigger fireworks, than two lighter planets “falling together” trough billions of years.

How do we describe this actual difference in the overall potential between universe A and B?
 
Physics news on Phys.org
  • #2
almost zero? who says that? what does 'almost' mean?
 
  • #3
Well...one is bigger. You just approximate both as zero.

Example one potential could be 0.000000000000001 J/kg
and the other could be 0.0.0000000000000000001 J/kg.

Yes both are approx. zero yet one is bigger than the other.
 
  • #4
Yes. And as times goes by this small little difference grows, and turns into a huge difference.

If I were a salesman of universes, I would take different prices for universes with different overall energies.

How do I sell universe A and B, what do I tell my customers?

“Well universe A is more expensive, because after billions of years the collision of the heavier planets will lead into much bigger fireworks.
I know the declaration on the package says, that there is only a very small little difference in potential energy between universe A and B. A difference that is 0,0000000000000000001 J/kg compared to 0,000000000000001 J/kg. But for some reason the factory decided, that people should calculate this overall potential themselves, by using the law of potential energy.”

That seems strange to me to give that kind of an explanation, because collisions between masses in universes must be a very common thing. So there must be a better and more simple way of describing the final difference in energy between universe A and B.

How do I declare the packages in a better way;-)
 
  • #5
I think you are missing something here: gravitational potential energy increases with distance.

For a small object a huge distance from earth, the GPE will approach a maximum of 61,605,000 j/kg.

Regardless, even if you were right about it being "almost zero", the other guys are right: "almost" isn't good enough. If there is a difference, there's a difference and you can't simply ignore it. Just in case you run into small numbers somwhere else and decide you want to make them equal...
 
Last edited:
  • #6
J. Richter said:
Imagine a universe A, containing only two identical heavy planets situated at an almost infinite distance from each other.

Imagine another universe B, containing only two identical lighter planets situated at an almost infinite distance from each other.

In both cases the gravitational potential energy between the planets are said to be almost zero.

How can that be?

I think there must be a bigger overall potential in universe A.
Don’t you?

Two bigger planets “falling together” trough billions of years, must lead to a bigger fireworks, than two lighter planets “falling together” trough billions of years.

How do we describe this actual difference in the overall potential between universe A and B?
First, I agree with the other comments about "almost equal" is not "equal" etc. Basically [tex]\lim_{x\to \infty } \, a(x)=\lim_{x\to \infty } \, b(x)[/tex] does not imply [tex]\lim_{x\to \infty } \, (a(x)=b(x))[/tex]

In addition, using zero for the potential at infinity is just a matter of convenience. The universes don't care where you set your zeros and you are actually free to set your zero point wherever you want. That is because potentials are physically meaningless, only the differences in potentials are physically meaningful.

J. Richter said:
If I were a salesman of universes, I would take different prices for universes with different overall energies.

How do I sell universe A and B, what do I tell my customers?
:smile: In your brochure you don't talk about potentials, you talk about energy. You can especially talk about KE at collision. That also allows you to mark up the price on universes with the identical masses but more dense planets or universes with initial velocities. If a competitor uses potentials in their literature you educate the customer and make your competitor look like they are trying to manipulate the customer.
 
  • #7
russ_watters said:
"almost" isn't good enough. If there is a difference, thee's a difference and you can't simply ignore it. Just in case you run into small numbers somwhere else and decide you want to make them equal...

I understand that, and will take note on that. What I meant was that the difference is negligible small.

russ_watters said:
For a small object a huge distance from earth, the GPE will approach a maximum of 61,605,000 j/kg.

What happens to these 61,605,000 j/kg if this small object annihilates with another small object of antimatter, and their masses converts into electromagnetic radiation?

Gone with the annihilation? No mass, no potential?

Even if a spaceship did work on bringing the small object to this huge distance from Earth?
 
  • #8
It goes into reducing the gravitational redshift of the radiation.
 
  • #9
J. Richter said:
I understand that, and will take note on that. What I meant was that the difference is negligible small.
Well it's not. In the example you gave, one is ten thousand times bigger than the other. That's a huge difference, not a negligible difference. If you don't see that, you're not going to be a very good universe salesman. However, if you have a universe to sell that you think is worth $10,000, I'll certainly be willing to buy it from you for $1!
What happens to these 61,605,000 j/kg if this small object annihilates with another small object of antimatter, and their masses converts into electromagnetic radiation?

Gone with the annihilation? No mass, no potential?
The energy released by such a collision is vast and the pre-collision potential energy of the objects isn't lost, but it is truly insignificant compared to the energy released in the annihilation.
Even if a spaceship did work on bringing the small object to this huge distance from Earth?
I don't see what that has to do with anything.
 
  • #10
J. Richter said:
...What happens to these 61,605,000 j/kg if this small object annihilates with another small object of antimatter, and their masses converts into electromagnetic radiation?

Gone with the annihilation? No mass, no potential?
Not gone at all. Remember E=mc^2, energy and mass are equivalent; more importantly here they are both subject to space time curvature caused by gravitational fields, as famously shown by the deflection of light passing near the Sun. http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury
 

1. How is potential energy defined?

Potential energy is the stored energy an object possesses due to its position or state. It is the energy that an object has the potential to convert into other forms of energy, such as kinetic energy.

2. What is the overall potential energy?

The overall potential energy is the sum of all the potential energy an object possesses, including gravitational potential energy, elastic potential energy, and chemical potential energy.

3. How can the overall potential energy be the same in two different examples?

The overall potential energy can be the same in two different examples if the objects have the same mass and are at the same height or position, resulting in the same gravitational potential energy. It can also be the same if the objects have the same spring constant and displacement, resulting in the same elastic potential energy.

4. What factors affect the overall potential energy in an object?

The overall potential energy in an object is affected by its mass, height or position, spring constant, and displacement. Additionally, the type of potential energy (gravitational, elastic, chemical) also plays a role.

5. How is potential energy related to other forms of energy?

Potential energy can be converted into other forms of energy, such as kinetic energy, thermal energy, or electrical energy. For example, when a ball is dropped from a height, its potential energy is converted into kinetic energy as it falls. Similarly, when a spring is released, its potential energy is converted into kinetic energy as the spring moves back to its resting position.

Similar threads

  • Mechanics
Replies
7
Views
1K
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
985
  • Introductory Physics Homework Help
Replies
7
Views
1K
Replies
2
Views
700
  • Introductory Physics Homework Help
Replies
23
Views
286
  • Classical Physics
Replies
6
Views
767
  • Introductory Physics Homework Help
2
Replies
55
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
827
  • Classical Physics
Replies
6
Views
592
Back
Top