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

[Nousher Ahmed]

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.

 

[axmls]

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.

 

[Dale]

If there is such a technique, I am not aware of it either.

 

[sophiecentaur]

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.

 

[David Lewis]

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.