# Definition of Gravitational Potential Energy

#### Bertknight

Can anyone explain to me the definition of gravitational potential energy? I mean, i understand that it is 'the total work done in bringing a mass from infinity to the point' for any mass at a point, but it just seems too vague. For instance, why is it zero at infinity and negative nearer to the gravitational body?
and why do we have to start counting from infinity, not from the gravitational body itself?

#### HallsofIvy

"Potential" anything is a function whose derivative is that anything. That is, "potential energy" is the anti-derivative of the energy function. An anti-derivative always involves an arbitrary constant. For potential energy, it is purely a convention that the arbitrary constant is set by taking potential energy to be 0 "at infinity".

1 person

#### oz93666

For potential energy, it is purely a convention that the arbitrary constant is set by taking potential energy to be 0 "at infinity".
I'm not sure that's correct ....

Suppose there are only two masses in the Universe . The condition of maximum potential energy is when they are infinity apart ...

Minimum potential energy is when their centers of mass coincide.

1 person

#### Woody

I agree Oz,
it does seem a totally backwards convention to use,
But HallsofIvy usually knows what he is posting about
and it wont be the only bizarre and totally counter-intuitive convention I have encountered.

Sometimes it seems that the "oldtimers" who initially set these conventions were being deliberately contrary.

1 person

#### neila9876

positive vs negative

Actually, we can start from the infinite or the center of the gravitatioal body. It's only the difference between negative and positive values. If we start from the infinite, we can get an approximate feasible way to set out. If we start form the center of the gravitational body, we set out from a nearly impossible mission. In another hand, in the infinite the gravity is zero, if we take potential energy is also zero, then we feel more natural in logic.

#### topsquark

Forum Staff
Just to put my four cents worth (two cents worth + inflation):

There are many points to use to talk about a 0 potential energy for any system. I've seen GPE set at the Earth's surface, at it's core, at the Sun, and out at infinity. I think that the best answer is a blend of Oz and HallsofIvys concepts. It's like finding the sum torques on a system of forces... You just pick one that's useful. (I do agree with HallsofIvy when he gave the Mathematical definition of a PE. There's nothing for me to add to that.)

-Dan

#### neila9876

cent vs cent

In APPLICATION the zero point of GPE could even set on the toe of that dragon. But I would rather to think about the DEFINITION in pure physics.
GPE is the experience of the difference of "curvature of space time". In the infinity, space time is "flat" (no curvature). So, the zero point of GPE defined in the infinity is reasonable in physics and nature. Non cent vs Non cent. FAIR.

#### topsquark

Forum Staff
In APPLICATION the zero point of GPE could even set on the toe of that dragon. But I would rather to think about the DEFINITION in pure physics.
GPE is the experience of the difference of "curvature of space time". In the infinity, space time is "flat" (no curvature). So, the zero point of GPE defined in the infinity is reasonable in physics and nature. Non cent vs Non cent. FAIR.
No offence intended but I have a feeling that General Relativity is a little too abstract at the level of HS.

-Dan

@dragon:
Oh...

#### benit13

Just to put my four cents worth (two cents worth + inflation):

There are many points to use to talk about a 0 potential energy for any system. I've seen GPE set at the Earth's surface, at it's core, at the Sun, and out at infinity. I think that the best answer is a blend of Oz and HallsofIvys concepts. It's like finding the sum torques on a system of forces... You just pick one that's useful. (I do agree with HallsofIvy when he gave the Mathematical definition of a PE. There's nothing for me to add to that.)

-Dan
This is exactly what we do in practise. Once a convenient fiducial value is identified and adopted by practitioners, it usually leads to a convention or standard reference value. A good example is the Rydberg energy.

1 person