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Gravitational Potential [Moved from Academic Guidance]

  1. Oct 16, 2008 #1
    hey friends why is gravitational potential negative?
  2. jcsd
  3. Oct 16, 2008 #2

    D H

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    Any potential energy (gravitational, electrical, ...) has an arbitrary constant term. Given some conservative force field F(x), any function U(x) for which

    [tex]\nabla U({\boldsymbol{x}}) = -\,{\boldsymbol{F}}({\boldsymbol{x}})[/tex]

    is a potential energy function U(x) of the force field F(x). Adding a constant to U(x) yields another function Uc(x)=U(x)+c whose gradient is the force field. Bottom line: You can pick any value you want for that constant. One obvious choice for gravitational potential is to make the potential vanish as [itex]||\boldsymbol x||\to\infty[/itex], in which case the potential for any finite x will be negative.
    Last edited: Oct 16, 2008
  4. Oct 16, 2008 #3
    Gravitational is negative by convention. The potential of a body is free space without gravity is taken to be zero...hence near a gravitational mass,say a plant or star, since work must be done to move the body from a strong gravitational influence to free space where it's zero, we say gravity imposes a negative potential...

    An analogous situation is on the surface of the earth...say on a beach where we take gravitational potential to be zero....climb out of a hole in the sand to reach zero potential...again gravitational potential is taken to be negative in the hole....

    I've not come across a clear explanation as to whether this convention is significant or just convenient...I think idea this matches DH post above....
  5. Oct 16, 2008 #4

    D H

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    First things first: I corrected a sign error in my previous post.

    Only in the case of a body in free space.

    Suppose I want to do elementary physics near the surface of the Earth. I'll choose coordinates such that the x and y axes are parallel to the surface and z is positive upwards. With this convention, the gravitational force is nearly constant:

    [tex]\boldsymbol{F} \approx -mg \hat \boldsymbol z[/tex]

    The potential functions that generate this constant force field are of the form


    Here, the "obvious" choice for a constant is C=0. In other words, u=mgz=mgh, which is what you were taught in elementary physics. Now potential is positive above the surface. So gravitation is not always negative by convention.
  6. Oct 23, 2008 #5
    thanks for the help.
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