Does Potential Energy = 0 at Earth Centre?

[FizixFreak]

assuming the Earth is perfectly round, uniform density all over, and their is no gravitational interference from an outside object, like the moon, then yes. everything has to be perfectly placed into position. it works on paper but nothing can ever be measured and placed this exact. a grain of sand passing by at a distance of the center of the Earth to the moon would throw the balance off. so my answer is potential energy can never = 0

That is EXACTLY what i though when i first saw this thread if you really start seeing things on a universal level i think the conditions can never allow potential to be zero but on a global level things are quite different.

 

[Martha]

http://wiki.answers.com/Q/What_is_the_gravitational_potential_energy_at_the_center_of_the_earth

"Ideally, if the Earth were a perfect sphere, the gravitational potential energy would be zero. In the center of a sphere all other points within the sphere have an equal and opposite counterpoint. They work to cancel each other out.

However, the Earth is not a perfect sphere so there would likely be a gravitational pull towards the area with the greatest mass."

 

[D H]

Just goes to show that you should never trust anything at answers.com. Not a thing.

That response is a pile of nonsense. The person is confusing force with potential.

 

[arkyy]

Sorry, I've read through this and I'm still a little confused.

Potential energy aside, what is the gravitational potential at the centre of the Earth (assuming constant density, and perfect spherical shape), and defining gravitational potential as the work done per unit mass moving an object from a distance of infinity to that point.

A lot of the information in this thread suggests that gravitational potential is at a maximum (a negative maximum) on the surface of the earth.
But if there is a gravitational force within the Earth's surface, this suggests to me that the potential must be greater within the Earth's surface, because the work done in getting from the surface to that point should be negative, and would be added on to the potential from getting from infinity to the surface.

In summary I'm asking what is the gravitational potential at the centre of the earth, and what is the potential slightly outside this point.

 

[sophiecentaur]

The GPE gets more and more negative but.instead of going down to -∞ (for a point mass), it follows a parabola which levels out to a minimum at the centre.

I plotted this on a spreadsheet. Also, I was interested / surprised to see that the difference in GPE from surface to centre seems to be half the GPE at the surface (wrt ∞). The analysis gives you this factor of 1/2 when you integrate the force on the way up to the surface (you get an r²/2) yet there is no corresponding 1/2 when you integrate the force going from the surface to ∞. I am assuming uniform density of course.

The vertical scale is in arbitrary units of energy, (btw)