Free fall to earth from lunar distance, how long does it take?

[running]

Ok so I only need to check that the moon is still in orbit every 4 days to have an advanced warning that it's comming down.

Thanks! that will save me some time.

[Doozler]

I'm still having difficulties grasping how standard orbital mechanics can be applied to a situation where two bodies are initially orbiting each other and one of those bodies suddenly stops moving.

The situation where both bodies suddenly stop can be thought or as just a "funny kind of orbit", where the semi-minor axis is zero.

If you only stop the moon not the earth (relative to the fixed stars or something), then there is still an elliptical orbit as the system still has some angular momentum, you'll end up with a very narrow "orbit" with a small-but-not-zero semi-minor axis.