In summary, taking a reference point other than the center of the Earth for calculating the gravitational potential energy is not a good idea because the GPE is indeterminate for r=0.
  • #1
Pratik Saha
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Can someone please show that calculation of gravitational potential energy at a point R+h from the centre of the Earth by choosing the centre of the Earth to be at zero potential. Here R is the radius of the Earth and h is not very small wrt to R
 
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  • #2
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Pratik Saha said:
by choosing the centre of the Earth to be at zero potential
That's a very bad place to take your reference from because the GPE is proportional to 1/r and it is indeterminate (aka -Infinity) for r=0. The normal reference for GPE in general is Infinity (for which the GPE reference is 0 (1/∞) or Mean Sea Level when you are doing calculations on Earth.
If you are going below that level then the GPE would be negative but no problem.
Google Gravitational Potential and all the common formulae (mgh etc.) can be found along with interesting reading.
 
  • #3
sophiecentaur said:
That's a very bad place to take your reference from because the GPE is proportional to 1/r and it is indeterminate (aka -Infinity) for r=0.
That is correct for an idealized Earth with all of its mass concentrated in the center (and maybe a thin shell we can stand on at 6000 km radius).

For a realistic Earth, using a zero point at the center is still a poor choice because we have no highly accurate way of measuring potential difference between here and there. By contrast, we do have accurate measurements for the potential difference between here and infinity.
 
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  • #4
jbriggs444 said:
By contrast, we do have accurate measurements for the potential difference between here and infinity.
Yes but how would we calibrate our Earthbound measuring machines without still referring to some 'standard' measurement point on Earth? Most space navigation problems get away with a reference at infinity but most Earthbound problems are solved by assuming a spherical Earth and then applying some correction to the value of g if necessary. Where is your 'here'? :smile:
Both approaches have their place, I think.
 
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  • #5
sophiecentaur said:
Yes but how would we calibrate our Earthbound measuring machines without still referring to some 'standard' measurement point on Earth?
I am not a metrologist. I suspect that your point is entirely correct and that "the geoid" is used as the operational standard rather than "infinity" for many purposes.
 
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  • #6
sophiecentaur said:
Hello and welcome to PF

That's a very bad place to take your reference from because the GPE is proportional to 1/r and it is indeterminate (aka -Infinity) for r=0. The normal reference for GPE in general is Infinity (for which the GPE reference is 0 (1/∞) or Mean Sea Level when you are doing calculations on Earth.
If you are going below that level then the GPE would be negative but no problem.
Google Gravitational Potential and all the common formulae (mgh etc.) can be found along with interesting reading.
Thanks a lot! I was thinking the same bc the answer would come same btw 2 points in however reference I take it, but not to mention that calculation would be a bit hectic to formulate coz the visualization of such case is indeed unusual...
 
  • #7
Thanks a lot to everyone for sharing their opinion on this topic! :)
 

1. What is a gravitational potential reference point?

A gravitational potential reference point is a location in space where the gravitational potential energy is defined as zero. It is a theoretical point used to measure the potential energy of an object in a gravitational field.

2. How is a gravitational potential reference point determined?

A gravitational potential reference point is determined by considering the gravitational forces acting on an object and finding the point where the potential energy is zero. This point can vary depending on the objects and their positions in the gravitational field.

3. What is the significance of a gravitational potential reference point?

The gravitational potential reference point is significant because it provides a standard for measuring gravitational potential energy. It allows scientists to compare the potential energy of objects in different locations and understand how they interact with each other in a gravitational field.

4. Can the gravitational potential reference point change?

Yes, the gravitational potential reference point can change depending on the objects and their positions in the gravitational field. For example, the reference point on Earth's surface will be different from the reference point in space.

5. How is the gravitational potential reference point related to the concept of escape velocity?

The gravitational potential reference point is directly related to the concept of escape velocity. The escape velocity is the minimum speed an object needs to escape the gravitational pull of a larger object. This escape velocity is measured from the gravitational potential reference point.

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