How much slower does the Earth rotate after the Moon recedes from an orbital radius of $400,000$ to $500,000$ km$?$ You$$ll need to use Kepler$$s law.

d$)$ Write the equation for the spin energy of the Earth.

e$)$ Write the equation for the orbital energy of the Moon.

f$)$ What is the energy change in the Earth spin and energy change in the lunar orbit for part c$?$