Dimensional analysis universal gravitation

[suetonius]

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]

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

 

[suetonius]

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]

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.

 

[EvLer]

$$1N = kg \frac {m}{s^2}$$
for font (LaTex) read first threads in General Physics forum

edit: where 1N is unit of force.