How to prove V=-(GM)/r without applying calculus?

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Discussion Overview

The discussion centers around the question of how to prove the gravitational potential formula, V=-(GM)/r, without using calculus. Participants explore the possibility of simplifying the explanation to make it accessible to younger audiences, while considering the implications of avoiding calculus in the derivation or proof of this concept.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to find a simple method to evaluate the gravitational potential without calculus, aiming for clarity suitable for a 12-year-old.
  • Another participant argues that proving the existence of gravitational potential is inherently linked to multivariable calculus, suggesting that understanding the concept without calculus may not be feasible.
  • A third participant agrees with the uncertainty regarding the possibility of deriving or proving the formula without calculus.
  • One participant suggests that the invention of calculus was necessary for addressing such problems, implying that learning calculus is essential for understanding these concepts.
  • A later reply mentions the use of computer-aided drafting (CAD) software as a means to visualize derivatives and integrals, though this does not directly address the original question of proving the formula without calculus.

Areas of Agreement / Disagreement

Participants generally express skepticism about the possibility of proving the formula without calculus, indicating a lack of consensus on whether a non-calculus approach exists.

Contextual Notes

Participants highlight the dependence on calculus for deriving gravitational potential and the challenges of simplifying complex concepts for younger audiences. There is an acknowledgment of the limitations in understanding without the foundational knowledge of calculus.

Nousher Ahmed
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In my textbook, gravitational potential , V=-(GM)/r, has been evaluated by applying calculas. I want to evaluate it with another simple way except calculas. I want to learn the simplest way to evaluate it in such a way that even a boy of 12 years old can understand it without facing any difficulty.
 
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I'm not even sure if that's possible. The fact that the potential exists is a direct consequence of a result in multivariable calculus, and the process of going from potential to field requires taking a derivative, and the reverse process requires integration. I mean, you can introduce the potential without calculus, but I'm not sure you can derive or prove it without calculus. The intuition for it can only be gained, I think, from the calculus.
 
If there is such a technique, I am not aware of it either.
 
Nousher Ahmed said:
I want to evaluate it with another simple way except calculas.
Why? A Calculus was invented by Newton and Leibnitz and others because there were not ways of doing it 'simply'. If you have a problem with calculus then the best way to deal with that is to learn about it and get to love it. You cannot do without it.
 
If you have computer aided drafting (CAD) software, a differential can be found by measuring the slope of a curve, and an integral by measuring the area under a curve.
 

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