Gravitational Potential Energy: A Basic Explanation

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Discussion Overview

The discussion revolves around the definition of gravitational potential energy, particularly why it is expressed as the negative of the line integral of force. Participants explore the mathematical reasoning behind this definition and its implications in the context of gravitational fields.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the reasoning behind defining gravitational potential energy as the negative of the line integral of force, suggesting that the negative value may be a result of the attractive nature of gravitational fields.
  • Another participant explains that potential energy is defined as the negative of the work done, linking it to the integral of force over displacement, and emphasizes the necessity of the negative sign for the work-energy theorem to hold.
  • A third participant provides a specific formula for gravitational potential energy in the context of a point source, noting that using infinity as a reference point leads to a potential energy of zero at that distance, and that potential energies at finite distances are negative.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants present different aspects of the definition and reasoning behind gravitational potential energy without resolving the initial question posed.

Contextual Notes

There are assumptions regarding the nature of gravitational fields and the choice of reference points that are not fully explored, as well as the implications of the work-energy theorem that remain unaddressed.

ian2012
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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?
 
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Hi ian2012! :smile:

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 :wink:

(and it has to be minus so that the work-energy theorem works)
 
thank you for your post
 
ian2012 said:
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.
 

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