How to derive the formula for Gravitational Potential Energy?

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Discussion Overview

The discussion revolves around the derivation of the formula for gravitational potential energy, specifically the expression -GMm/r. Participants explore the historical and mathematical aspects of how this formula is established, including the role of empirical observations and calculus.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how scientists derived the formula -GMm/r for calculating work required to move an object from an infinitely large point.
  • Another participant suggests that the derivation involved experimental observation and adjusting the constant of proportionality G.
  • A different participant challenges the notation used, indicating that "G" should not be included in a certain context.
  • One participant provides a mathematical approach using integral calculus to derive the gravitational potential energy formula from the gravitational force.
  • Another participant asserts that Newton's law of gravitation is empirical and cannot be derived from other fundamental laws, emphasizing that this applies to all basic laws of physics.

Areas of Agreement / Disagreement

Participants express differing views on the derivation process, with some focusing on empirical observations and others on mathematical techniques. There is no consensus on a single method or understanding of the derivation.

Contextual Notes

The discussion includes references to historical context and the nature of empirical laws, but lacks clarity on specific assumptions or definitions related to the derivation process.

Tommy1995
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How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?
 
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How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?

Experimental observation and number fudging to find the constant of proportionality G.
 
Tommy1995 said:
How did scientists derive the formula -GMm/r=Ep

not "G"...
 
Tommy1995 said:
How did scientists derive the formula -GMm/r=Ep

They used integral calculus.

$$PE_{grav} = - \int^r_\infty {F_{grav} dr^\prime}
= - \int^r_\infty {\left( -\frac{GmM}{{r^\prime}^2} \right) dr^\prime}
= - \frac{GmM}{r}$$
 
Newton's law of graviation is emperical - it can't be derived from some other fundamental law or set of equations. This is the case with all the basic laws of physics - nature is the way it is.

If you want to read more about the history try here and related pages:

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
 
Thanks ya'll!
 

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