$[20$ points$]$ The Moon is moving away from the Earth at a rate of about $3\mathrm{.}8$ centimeters per year. This

changing orbital distance comes as a result of the Moon$$s tidal influence on Earth$$s oceans, which

causes the Earth and Moon to exchange angular momentum. Earth has a mass of $6\mathrm{.}0$x$1024$ kg$,$ is

roughly spherical with an average radius of $6,371$ km$,$ and makes one rotation on its axis every $24$

hours. The Moon has a mass of $7\mathrm{.}4$x$1022$ kg and orbits the Earth in a circular orbit of radius $385,000$

km once every $27\mathrm{.}3$ days. You may assume the Earth$-$Moon system is closed and that the Moon$$s

orbital period does not change.

A$.[10$ pts$]$ By how much does the angular momentum of the Moon change over the course of one

year?

B$.[10$ pts$]$ How much does the length of one Earth day change by in one year as a result of the tidal

interactions with the Moon