Answer to Question #169142 in Physics for Emilie Rashcovan

Question

Pluto’s moon, Charon, has an orbital period of 153 hours. How far is Charon from Pluto?  ​

Answer 1

We can find the distance from Pluto to Charon from the Newton's form of Kepler's third law:

$$\dfrac{T^2}{R^3}=\dfrac{4\pi^2}{GM},$$ $$R=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}},$$ $$R=\sqrt[3]{\dfrac{(153\cdot3600\ s)^2\cdot6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot1.3\cdot10^{22}\ kg}{4\pi^2}},$$ $$R=18824\ km.$$