$.$ a$)$ Write an equation for the spin angular momentum of the Earth assuming a polar moment of inertia

C $=0\mathrm{.}33$M ER$2$

$,$ and orbital angular velocity E$.(2)$

b$)$ Write an equation for the orbital angular momentum of the Moon, assuming a circular orbit of radius

r$,$ lunar mass MM$,$ and orbital angular velocity M$.(2)$

c$)$ 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. $(4)$

d$)$ Write the equation for the spin energy of the Earth. $(2)$

e$)$ Write the equation for the orbital energy of the Moon. $(2)$

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