Question

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 1.96×10^4 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 1

let the density be ρ

mass of pluto = (4/3)*π*r1^3*ρ

mass of charon = (4/3)*π*r2^3*ρ

centre of mass from centre of pluto = [0*((4/3)*π*r1^3*ρ) + (1.96*10^4)*((4/3)*π*r2^3*ρ)]/((4/3)*π*r1^3*ρ + (4/3)*π*r2^3*ρ)

= (1.96*10^4)*(r2^3)/(r1^3 + r2^3) = 1.96*10^4*625^3/(1185^3 + 625^3) = 2507.75 km