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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?

$F = Gm1m2/R2$

user127219
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    Duplicate of

    http://physics.stackexchange.com/q/137768 and other link therein.

     –  Oct 11 '14 at 07:59
  • Sorry for labelling it as duplicate. But please make your question clear. What you are saying and asking are totally meddled with each other and write a strong title; I thought you were asking that question but after reading the body, it is completely different. But since you are new, be aware next time! –  Oct 11 '14 at 08:18
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    I would guess it's because the most obvious application of Newton's law is to calculate the force on something orbiting a much heavier object in a roughly circular orbit. (E.g. planets around the Sun, or satellites around planets). In this case $r$ is the radius of the orbit. – N. Virgo Oct 11 '14 at 09:21
  • Debating one notation over another is non-constructive and off-topic, cf. this meta post. – Qmechanic Oct 11 '14 at 09:49
  • I prefer to that of @Nathaniel. However, I would say it is mostly due to historical reason. Old books wrote acceleration as $f$ but today we prefer $a$ to avoid confusion. However,it doesn't bother any physics. –  Oct 11 '14 at 10:38
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    There isn't a hint of that question in the question you wrote. If you had asked that, your question would have been closed as a duplicate of Why are so many forces explainable using inverse squares when space is three dimensional? – David Hammen Oct 12 '14 at 17:22

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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.

David Hammen
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