Gravitational Potential [Moved from Academic Guidance]

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Gravitational potential is considered negative by convention because it is often defined to vanish at infinity, making potential values for finite distances negative. This convention aligns with the idea that work must be done against gravity to move an object from a gravitational field to a state of zero potential. In practical applications, such as near the Earth's surface, gravitational potential can be expressed as positive when a reference point is set at ground level. The choice of reference point for gravitational potential can vary, leading to different interpretations of its sign. Ultimately, the negative convention is a matter of convenience in physics, facilitating calculations and understanding of gravitational effects.
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hey friends why is gravitational potential negative?
 
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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

\nabla U({\boldsymbol{x}}) = -\,{\boldsymbol{F}}({\boldsymbol{x}})

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 ||\boldsymbol x||\to\infty, in which case the potential for any finite x will be negative.
 
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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...
 
First things first: I corrected a sign error in my previous post.

Naty1 said:
Gravitational is negative by convention.
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:

\boldsymbol{F} \approx -mg \hat \boldsymbol z

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

U=mgz+C

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.
 
thanks for the help.
 
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