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**1. Homework Statement**

we know the mass of the moon, Mm, and the earths, Me, and also the initial distance between their centers as the moon orbits the earth, Rem.

Now if the earth’s angular velocity about its own axis is slowing down from a initial given angular velocity, ωi to a final angular velocity (due to tidal friction), ωf

Find the final orbital distance between the earth and moon as a consequence. Ignore the rotation of the moon about its own axis and treat it as a point object in circular orbit about the center of a fixed (but spinning) earth.

**2. Homework Equations**

t=Iα torque

L=Iω or r x p angular momentum

T=2π √ r3/GM orbital period

**3. The Attempt at a Solution**

I do not conceptually understand why a change in the earths rotation would even change the radius of the moon's orbit around the earth. From the 3rd equation I wrote we see that r does not depend on the earth's rotation. Why would it even make a difference how fast earth is rotating?