Gravitational Potential Energy: A Basic Explanation

[ian2012]

A very basic question:

Why is the definition of gravitational potential energy, bringing an object from infinity (or any point of reference) to zero, the negative of the line integral of F.dr ? I am assuming since potential energy in an attractive field , which is defined to be negative, the integral was fixed to lead to this result... or is there a more mathematical reason?

 

[tiny-tim]

Hi ian2012!

potential energy (gravitational electric or whatever) is defined as minus the work done …

and work done = integral of force "dot" displacement …

so PE = -W = -∫ F.dr

(and it has to be minus so that the work-energy theorem works)

 

[ian2012]

thank you for your post

 

[rcgldr]

Object infinity zero

In the case of gravity from a point source, potential energy = -G m M / r. Because of this, using infinity as a reference point makes since, becaue - G m M / ∞ = 0, and all GPE's at finite distances from a gravitational point source would be negative.