Is there any mathematical proof of Newton law of universal gravitation?

Question

Is there any way to derive mathematically Newton's law of universal gravitation ?

How this formula so exactly follow the law of gravation?

If this is just a guess then why it is so accurate?

$F = Gm1m2/R2$

Answer 1

Excluding F, G, M, and m (you've already used those names in this expression), you could label that distance any letter from a to z or from A to Z or from $\alpha$ to $\omega$. Or whatever. It doesn't matter. It's a variable.

That said, there are conventions. It's best not to call that distance v, for example. The symbol v usually means a velocity or speed, not a distance. With regard to distance, you can find textbooks, etc., that label the distance as d, and then you will see $F = GMm\,/\,d^2$. Denoting a distance as d or r is in line with the naming conventions.