a$)$ Write an equation for the spin angular momentum of the Earth assuming a polar moment of inertia $C=0\mathrm{.}33M_E{R}^2,$ and orbital angula$$ velocity ${}_E.(2)$

b$)$ Write an equation for the orbital angular momentum of the Moon, assuming a circular orbit of radius $r,$ lunar mass $M_M,$ 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 $500,000km?$ 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 c$?(4)(16$ total$)$

Please solve this all the way through!!