[Jack Simth]

Originally posted by Suicide Junkie:
Star masses can also be found by looking at colour, age, size, etc.

Getting the mass from the color, age, size, etc. implicitly uses G, as the plasma physics that produce such results include gravitational effects from the mass of the star. Again, G is used to calculate G, and as such is circular logic and is not reliable. Mind you, G is probably constant throughout the universe - but there isn't any good way to be certain of that until we get out there and measure things up close. Until then, G is constant makes for a good working theory, but it can't be proven.

Originally posted by Suicide Junkie:

And having a third body in the system to observe helps a lot.

G can be calculated from the masses, distance between, and the observed acceleration.

For that, the masses have to be known. Getting the masses uses G, although sometimes it is implicit rather than explicit. Again, G is used to obtain G, which is circular reasoning; not reliable. Mind you, G is probably constant throughout the universe - but there isn't any good way to be certain of that until we get out there and measure things up close.

Without knowing both the masses and G, some simple numerical manipulation on the gravitational formulas can tell you that the distance and acceleration alone won't help:

F = G(M*m)/(d^2)
F' = G'(M'*m')/(d'^2)
A = F/m = (G*M)/(d^2)
A' = F'/m' = (G'*M')/(d'^2)
If A = A' and d = d', then
(G'*M')/(d^2) = (G*M)/(d^2)
-> (G'*M') = (G*M)

Example: Suppose G' = 2G:
-> 2G*M' = G*M -> 2M' = M -> M' = M/2

Then M' = M/2 results in the same acceleration for the same distance. The number of bodies won't make a difference for this aspect of things.