Is Potential Energy Infinite at Any Point for Point Masses?

[MicroCosmos]

Hi everyone, first post here.

Today i crushed into a question. I was going to write it down here, then i crushed into another one.
Lets say we want to know the potential energy of a body relative to a center of gravity.
I will refer to gravitys acceleration as "g" and to mass as "m". "k" will be some constant unit.

If we take a near, lower height(h) as reference it would be "m·g·h" because g doesn't change with h.

But if i want to reference to the center of gravity, because of g(h) = k/h², i can't use that anymore. I suppose i need ∫m*g(h) dh from 0 to the wanted height. That supposes potential energy is infinite at any point !

Some ideas? Am i doing something wrong?
Thanks!

 

[jbriggs444]

The inverse square force law applies for point masses and for spherically symmetric masses acting on outside objects. Once an object dips into the interior of a gravitating body, the portion of the gravitating body higher in altitude than the object ceases to have any net effect. See Newton's spherical shell theorem.

So let's say that we are talking about a point mass. Then yes, the potential energy measured against a reference at the gravitating point is infinite. You can take that as a clue that you should be selecting a different reference point, that the laws of classical physics cannot hold for point objects or both.

The alternate reference point that is normally chosen is one infinitely far away. So that potential energy is always negative and gets more negative the closer you get to the center.

 

[MicroCosmos]

Yes, i meant point masses. Okay, that clears everything, thank you very much!

 

[jtbell]

So let's say that we are talking about a point mass. Then yes, the potential energy measured against a reference at the gravitating point is infinite. You can take that as a clue that you should be selecting a different reference point, that the laws of classical physics cannot hold for point objects or both.

Or that point masses don't really exist!

 

[lychette]

Or that point masses don't really exist!

what ?

 

[Khashishi]

Fundamental particles like electrons are thought to be point masses. But classical mechanics breaks down at those scales.