# Conservation of Angular momentum

## Homework Statement

The moon will gradually slow down the Earth's rotation period. If the total angular momentum is conserved in an Earth-moon system, how long will the orbital period of the moon be when both bodies will keep same face toward each other? How far will the two bodies be from each other?

Hint: Use Kepler's 3rd law and a spreadsheet to find numerical solutions

## Homework Equations

$$L=m{\omega}r^2+I_e\omega_e$$

omega is the orbital angular velocity of the moon and omega_e is the angular velocity of the earth.

$$\tau^2=(\frac{4\pi^2}{G(M_e+M_m)}r^3)$$

Where tau is the period, M_m is the mass of the moon, and M_e is the mass of the Earth.

## The Attempt at a Solution

This is the last of a multiple part problem. I didn't have a problem with the other parts, but I'm not sure what to do here. I know that the final angular momentum will equal the current one, but from here it looks like I have 1 equation and 2 unknowns (omega final and r final). The phrase "use a spreadsheet" makes me think that it is going to end up being a differential equation that I can solve using Euler's numerical methods in excel or something like excel. Any ideas would be appreciated.