Center of mass of Pluto and Charon system without masses

[elsternj]

Homework Statement

Pluto's diameter is approximately 2370km , and the diameter of its satellite Charon is 1250km . Although the distance varies, they are often about 1.93×10⁴km apart, center-to-center.
Assuming that both Pluto and Charon have the same composition and hence the same average density, find the location of the center of mass of this system relative to the center of Pluto.

Homework Equations

x_cm=m₁x₁+m₂x₂ / m₁ + m₂

The Attempt at a Solution

Well the center of Pluto and its satellite would be half the diameter so it's center of mass, I am assuming, would be

Pluto: 1185km
Charon: 625km

where i am confused is that i don't have the masses or any actual coordinates. I'm assuming that the masses would end up canceling out? But can somebody guide me as to where to go from here? How do I get the coordinates with the distance they are from each other? Is my equation even right?

 

[PhanthomJay]

The equation is correct, where x1, x2, and xcm are the distances from any arbitrarilly chosen reference point. It is simplest to choose that reference point at the center of one of the masses. Note that the mass of a sphere is is a function of its diameter cubed.

 

[elsternj]

So am I to assume that this is one dimensional? ..For I have no idea the angle at which these spheres are from one another. Say I choose Pluto to be the reference point. Make that x position to be 0 and then Charon's position to be the given distance?

 

[PhanthomJay]

So am I to assume that this is one dimensional? ..For I have no idea the angle at which these spheres are from one another. Say I choose Pluto to be the reference point. Make that x position to be 0 and then Charon's position to be the given distance?

Yes and Yes.