# Dimensional analysis universal gravitation

Firstly, I admit that my math skills are fairly rusty. I also admit that this is a homework problem. It is not to be turned in for a grade however.
The problem is to determine the SI units of G in the following equation:

F = GMm/r^2

(where F is force (mass * acceleration), M and m are the masses of two objects, and r is a distance)
which is, of course, Newton's law of universal gravitation.
I would be greatly appreciative if someone could walk through the steps needed to make this determination.

TD
Homework Helper
Work it out for G:

$$F = G\frac{{m_1 \cdot m_2 }}{{r^2 }} \Leftrightarrow G = \frac{{F \cdot r^2 }}{{m_1 \cdot m_2 }}$$

I suppose you now the units of the RHS, LHS has to be equal

Thanks for that. The answer in the back of the book is quite different, however. It is given as m^3/kg*s^2. I'm working on it. Do you think you could go into more detail? Again, my skills are a little rusty. Also, how'd you get the math font into your message?

TD
Homework Helper
I just worked it out for G. Now you have to replace the right hand side by all their units and simplify to find the unit of G.

$$1N = kg \frac {m}{s^2}$$