Gravitational Potential Reference Point

[Pratik Saha]

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

 

[sophiecentaur]

Hello and welcome to PF

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.

 

[jbriggs444]

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.

 

[sophiecentaur]

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'?
Both approaches have their place, I think.

 

[jbriggs444]

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.

 

[Pratik Saha]

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...

 

[Pratik Saha]

Thanks a lot to everyone for sharing their opinion on this topic! :)