Gravitational Potential Energy with reference point at infinity?

In summary, the gravitational potential energy of a mass "X" from the sun is 100 joules. However, when measured from the reference point of infinity, the potential energy is -100 joules. This is due to the negative symbol, and the value of the mass remains the same. The different values of "R" and "r" are used to calculate the potential energy from a specific reference point, such as the surface of a planet. The formula for potential energy, "-Gmm/r", is derived from the work needed to move an object from an extremely large distance to a specific point in space. GMm/R is used to calculate the potential energy at a specific distance from the center of the planet.
  • #1
Tommy1995
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0
So, the gravitational potential energy of a mass "X" from the sun is, let's say, 100joules.

Why is it that when we take the gravitational potential energy of the mass from the reference point of infinity that the gravitational potential energy is -100joules?

I understand the negative symbol but it amazes me that the mass would still have the exact same value of 100.

Please help me! :P
 
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  • #2
It's not. You are misunderstanding something. If it's -100J from reference at infinity, it doesn't mean it's 100J with reference at the surface. At the surface, you have -MmG/R from infinity. So if you are distance r away, the energy with reference to surface is MmG/R-MmG/r.
 
  • #3
Aaaahh I see K^2, thanks!

But you see how u said, "So if you are distance r away, the energy with reference to surface is MmG/R-MmG/r." What would be the different values of "R" and "r"? I'd like help to know how you can calculate the values of Potential energy from a reference point such as the surface of a planet.

I made up my own thought experiment, finding the potential energy of a 10kg ball at distance 100m from the Earth's surface and found the Gravitational potential energy to be 1000J using the formula W=FS. It was totally different to the Ep found using the formula "-Gmm/r" to find the Ep from infinity... So I have another question, how did they derive "Ep=-Gmm/r" ? It seems I don't quite understand how it calculates the work needed to move an object from an extremely large distance to a point X in space :/

Thanks again for helping me clear up my misunderstandings!
 
  • #4
Tommy1995 said:
But you see how u said, "So if you are distance r away, the energy with reference to surface is MmG/R-MmG/r." What would be the different values of "R" and "r"? I'd like help to know how you can calculate the values of Potential energy from a reference point such as the surface of a planet.
That's what these are for. R is radius of the planet. r is position at which you want potential energy, also from center of the planet. M is mass of the planet, and m is mass of the body whose potential you want.
 
  • #5
Thanks again K^2! :D

Btw what is GMm/R finding?
 

FAQ: Gravitational Potential Energy with reference point at infinity?

What is gravitational potential energy with reference point at infinity?

Gravitational potential energy with reference point at infinity is the energy possessed by an object due to its position relative to an infinite distance away from a gravitational source. This type of potential energy is often used in calculations involving celestial bodies, where the reference point is typically taken to be at infinity.

2. How is gravitational potential energy with reference point at infinity different from other types of potential energy?

Unlike other types of potential energy, gravitational potential energy with reference point at infinity is not dependent on the height of an object, but rather on its distance from the gravitational source. This makes it useful for calculating the potential energy of objects in space, where height is not always a relevant factor.

3. What is the formula for calculating gravitational potential energy with reference point at infinity?

The formula for calculating gravitational potential energy with reference point at infinity is PE = -GMm/r, where G is the gravitational constant, M is the mass of the larger object, m is the mass of the smaller object, and r is the distance between the two objects.

4. How does the reference point at infinity affect the value of gravitational potential energy?

The reference point at infinity affects the value of gravitational potential energy by setting a baseline value for the potential energy of an object at an infinite distance away from the gravitational source. This allows for a more convenient and consistent way of calculating potential energy in systems involving celestial bodies.

5. What is the significance of gravitational potential energy with reference point at infinity?

Gravitational potential energy with reference point at infinity is significant because it allows for the calculation of potential energy in systems involving celestial bodies, where the distance between objects is often very large. It also helps to simplify calculations by providing a consistent reference point for potential energy. Additionally, it is a key concept in understanding the behavior and interactions of objects in space.

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