How do i find the units of the universal gravitational constant G expressed in terms of fundamental SI units?

You need to remember that in an equation, the meaning of the equal sign is that the numbers on the left and right must be exactly the same at all times for the equation to be valid. What you shouldn't forget also is that the units of those numbers must be exactly the same as well.

So in this case, you have two choices: either find the units on the left side (force), find the units that you've listed on the right, and figure out a way to apply units to G so that in the end, the right side has units of force as well.

An easier way might be to get everything on the left side of the equation except G, analyze the units, and then you have your answer. What I mean is this:

Put everything on the left side, so: F*r^2 / m1*m2 = G

Now, by the argument I just made, the left and the right side must have the same units, so we can find the units of G. These are:

(kg* m/ s^2)*(m^2)/(kg^2)

Then you do your canceling, and find that G has units of:

m^3 / [(s^2)*kg]

You can verify this by looking it up in a physics or astronomy book, or just googling.

Hope this helps.

Fr^2/m(1)m(2) = G

Mass X Mass = Mass Squared (M^2)

Force = Mass X Meters Per Second Squared = (MLT^-2)

Meters X Meters = Lenght Squared (L^2)

Do the math;

MLT^-2 X L^2 / M^2

T^-2 L^3 M^-1

Meters Cubed per Kilogram per Second Squared

(Or the density of the force of gravity)

1/100000 N

you look on wikipedia

G = 6.67428e-11 m³/kgs²

.