Determining the mass of Pluto using its moon

[Softshow]

Homework Statement

On June 22, 1978, James Christy made the first observation of a moon orbiting Pluto. Until then, the mass of Pluto was not known, but with the discover of its moon, Charon, its mass could be calculated with some accuracy. Explain.


2. The attempt at a solution
"By knowing how large the orbit of the moon was, the mass of pluto could be calculated. In order to do this, the radius of the orbit of the moon is used because it shows the amount of gravity pluto is exerting on it. Because mass is proportional to gravity, and gravity to the size of the orbit, the mass can be calculated by looking at the size of the orbit."

I was given 4/5 credit for this with no direction as to where I went astray. I'm not sure if I was just too vague or I was simply incorrect, but any input would be greatly appreciated.

 

[voko]

Unless you explain what you did, how could anyone here find out where you went wrong?

 

[Softshow]

Sorry I didn't explain this better, this was not given as a mathematical problem, instead it was a problem which we were expected to try and talk through. No numerical values were given, making it completely impossible to actually determine the mass of pluto. We were simply expected to demonstrate our knowledge of the concepts at work relating to this problem.

 

[scoobmx]

I don't think the size of the orbit is the only factor. The period also has to be in there somewhere I believe.

 

[D H]

Gravity is not "proportional to the size of the orbit". Jupiter has moons with semi-major axes ranging from ~128,000 km to over 30 million km. The Earth has man-made satellites that orbit just a few hundred km above the surface (semi-major axis ~6700 km), geostationary satellites orbiting at 42,164 km, and of course the Moon at ~385,000 km.

 

[HallsofIvy]

One thing I have a problem with is your references to "gravity" as if it were a specific quantity:
"amount of gravity pluto is exerting on it" and "Because mass is proportional to gravity". I presume you mean "gravitational force" but you should still tell how one could determine the gravitational force the size or period of an orbit.