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Pretend that we do not know gravitational law at all, and want to investigate the gravitational law by dimensional analysis:

Let's suppose the gravitational force are proportional to both masses, distance, hence:

[tex] F \propto m_1^am_2^br_{12}^c [/tex]

But obviously, there is no way to equal the dimensions, since the right side has no dimension of time at all. Making a constant

Hence I would like to pose: how do we obtain the gravitational law by dimensional analysis? If impossible, then when, and how dimensional analysis fails?

Let's suppose the gravitational force are proportional to both masses, distance, hence:

[tex] F \propto m_1^am_2^br_{12}^c [/tex]

But obviously, there is no way to equal the dimensions, since the right side has no dimension of time at all. Making a constant

*G*fitting the dimensions kind of sounds like a cheat to me here. It left me wonder if dimensional analysis fails.Hence I would like to pose: how do we obtain the gravitational law by dimensional analysis? If impossible, then when, and how dimensional analysis fails?

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