Earth and Moon

CJ in the solar system

Part III: Mickey on Earth

CJ approaches Earth. As he watches the planet, which is covered with lots of water, he feels that he needs to go to the loo. He decides to land and visit his friend Mickey. Mickey is glad to see CJ: "Hello CJ, why did you come all the way to Earth?" CJ says he is on his way to Pluto. Mickey looks concerned and replies: "I cannot approve of this journey, unless you help me launch a satellite." CJ fancies the idea "That sounds like fun! What do you want me to do?" Mickey tells CJ that he wants the satellite to float on the equator above the Galápagos Islands and shows CJ an email.

They want to know at which altitude CJ should drop off the satellite. CJ says: "Clare told me that the orbital period squared over the distance cubed is constant." "Actually," says Mickey "we know that

$$\frac{T^2}{a^3}=\frac{4\pi^2}{G(M+m)}$$

where G is the gravitational constant (about $6.7\times10^{-11}$N$\cdot$m$^2$/kg$^2$) and $M$ and $m$ are the masses of Earth and the satellite."

CJ leaves Earth's atmosphere and looks down at the blue planet. Then he drops off the satellite and continues his journey to Pluto

To be continued