Hello Everybody, I am Meaningless and I had this doubt on Newtons laws of gravitation while deriving it. My textbook stated the following derivation 9 for any two masses m(adsbygoogle = window.adsbygoogle || []).push({}); _{1}, m_{2}, and radius 'r'

It stated that according to the law of product of masses,

F (Directly Proportional) m_{1}*m_{2}

And according to the inverse square law,

F (Directly Proportional) 1/r^{2}

Now here came my doubt..:

They then said that, When both Forces (F's) were combined, we would get,

F ( Directly Proportional) m_{1}m_{2}/r^{2}

But I thought of elaborating the ''combination'' and logically approached it. Here's what I got:

If F was directly proportional to the product of the masses, the it would be equal to the product of the massesand a proportionality constantwhich I took as 'k'.

Now similarly if F was directly proportional to the inverse of the square of the radius then it would be equal to the inverse of the square of the radius multiplied by aproportionality constantwhich I took as 'l'.

Now if I multiplied them I would get...

F^{2}= K*L*m_{1}*m_{2}/r^{2}

and if I rooted (square root) the entire equation on both sides I would get....

F = (SQRT)[K*L*M_{1}*M_{2}/R^{2}]

Which did not seem to match with F = Gm_{1}m_{2}/r^{2}

Now please tell me if:

1.There is any rule with the Proportionality that I am not aware of (or)

2.What my textbook has given is wrong

3. This was experimentally proved as an exception

4. If there is any other derivation for it

Any help will be appreciated. Thanks in advance :-)

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# B Regular derivation on The Universal Law of Gravitation?

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