For this problem, please work out your solution on paper. Then upload your solution to all

parts of this problem. You must upload it as a pdf$,$ png$,$ or jpg file. Please show all your work

and pay attention to the units the problem asks for.

Pluto and its moon Charon orbit a common center of mass with a period of $P=6\mathrm{.}387$ days.

The mass of Pluto is $0\mathrm{.}0021M_{o+}($where $M_{o+}$ is the mass of the Earth$).$ with a radius of $0\mathrm{.}178$

$R_{o+}($where $R_{o+}$ is the radius of the Earth$).$ The mass of Charon is $0\mathrm{.}00026M_{o+}$ with a radius

of $0\mathrm{.}095R_{o+}.$ You may assume circular orbits for this problem.

A$.$ Using Kepler's third law, calculate the distance between the center of Pluto and the center

of Charon $($this is the semi$-$major axis of the orbit of the Charon$-$Pluto system$).$ Give your

answer in units of meters.

B$.$ Using your answer from part $($A$),$ calculate the distance from the center of Pluto to the

Center of Mass. Give your answer in units of meters.

C$.$ Compare your answer for the distance of Pluto from the Center of Mass with the radius of

Pluto. Which is larger? $($Discuss whether or not the center of mass of the system within

Pluto or does it sit outside the planet?$).$ Note that one of the posed definitions of a

"planet" includes that statement that the center of mass of its system must lie within its

radius. Does Pluto satisfy this?