Pluto & Charon's Center of Mass - 6871.5 km

[rsala]

Homework Statement

Pluto's diameter is approximately 2370 km, and the diameter of its satellite Charon is 1250 km Although the distance varies, they are often about 1.99×104 km 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. answer in km.

Homework Equations

$$\frac{\Sigma m*r}{\Sigma m}$$

The Attempt at a Solution

i didnt know how to approach this problem since i didnt know the masses of the objects, so i treated each unit of kg in its diameter as 1 unit of m, so the mass pluto would be 2370,000*M...? (converted all units to meters, not sure if it matters)

so, since the question asks for center of mass relative to pluto center, i don't include plutos m*r since its initial position is 0.

$$\frac{1250,000*M*(1.99*10^{4}*1000)}{2370,000*M + 1250,000*M}$$

i guess m can factor out here.$$\frac{1250,000*(1.99*10^{4}*1000)}{2370,000 + 1250,000}$$

this equals 6871547 meters, 6871.5 km
this is incorrect, I don't think this is correct because i just have the feeling that i don't know what I am doing here

 

[PaintballerCA]

You made a very simple mistake.
You used the diameter of the objects and not the radius. Treat the objects as point masses, so the distance between the two objects surfaces plus the radius of each object is the total distance between the two.

EDIT: Also, notice that one is bigger than the other (one diameter is 2370km and the other is 1250km). Given this, one will be more massive then the other. How would you figure out how much more massive one is with respect to the other?

 

[Moetasim]

.

I would approach this problem by first determining the masses of Pluto and Charon using their diameters and average density. This information can be found through previous research or by conducting experiments. Once the masses are known, I can use the formula for center of mass, which is the sum of the individual masses multiplied by their respective distances from the center, divided by the total sum of the masses. This will give the location of the center of mass relative to the center of Pluto.

Therefore, it is not accurate to assume that each unit of kg is equal to 1 unit of m in this scenario. The correct approach would be to determine the actual masses of Pluto and Charon and use those values in the formula for center of mass. This will provide a more accurate and scientifically sound answer.