[JennyGracie (OP)]

Benny was asking,

In one of the earliest podcast it was said that the moon is slowly moving away from the earth, a few cm every century. Does this mean that someday the moon will pull away from the earth's gravitational field? If so when would that be?

Do you know the answer?

[Halc]

In one of the earliest podcast it was said that the moon is slowly moving away from the earth, a few cm every century. Does this mean that someday the moon will pull away from the earth's gravitational field? If so when would that be?

The combined Earth/moon system does not have enough angular momentum to do this.  Assuming the process is not interfered with, the moon will stop moving away when the day and month are both about 1400 hours long, at which point the tidal forces from the sun would start bringing it closer in again until the moon falls and hits the Earth.

Long long before any of this happens, the sun will grow and swallow the Earth with the moon, so none of this is in our future.

[chiralSPO]

In one of the earliest podcast it was said that the moon is slowly moving away from the earth, a few cm every century. Does this mean that someday the moon will pull away from the earth's gravitational field? If so when would that be?

The combined Earth/moon system does not have enough angular momentum to do this.  Assuming the process is not interfered with, the moon will stop moving away when the day and month are both about 1400 hours long, at which point the tidal forces from the sun would start bringing it closer in again until the moon falls and hits the Earth.

Long long before any of this happens, the sun will grow and swallow the Earth with the moon, so none of this is in our future.

This is my understanding as well.

[Kryptid]

until the moon falls and hits the Earth.

I don't think the Moon will actually hit us. At least not in one piece. Once it enters the Roche limit, it should break up into a planetary ring. I would expect the ring to slowly spiral in over time and be either burned up in our atmosphere or fall to the ground as meteorites.

All of this ignores the red giant phase of the Sun, of course.

[Halc]

Once it enters the Roche limit, it should break up into a planetary ring.

Yes of course.  Shouldn't have left that out.  So what is the length of the day when that happens?  Same as the orbital period at our Roche limit, so maybe 11 hours long.

Of interest is other planets.  Totally in isolation, they're incapable of spinning off a moon despite having plenty of angular momentum to do so.  But the further away the moon gets, the less the tides effect it, and it takes an eternity to push it to escape velocity.  But planets are not in isolation, so all it needs to do is shove the moon past its hill radius and the moon wanders off as a free agent, or possibly gets trapped by a Lagrange point.  I think that doesn't take infinite time.  Our moon (and Charon) are the only moons that cannot be spun away like that.  The others (at least the receding ones) are all far to small for the momentum limit to matter.
A few moons are falling in due to being inside geosync radius or having retrograde orbits.

[Janus]

Once it enters the Roche limit, it should break up into a planetary ring.

Yes of course.  Shouldn't have left that out.  So what is the length of the day when that happens?  Same as the orbital period at our Roche limit, so maybe 11 hours long.

The Moon will orbit somewhere between 3 and 7 hours. 7 hrs if we treat the Moon as a purely fluid object, and 3 hrs as a rocky one that doesn't deform at all under tidal forces.    Since The Moon isn't fluid, nor immune to some deformation, the break up point will fall somewhere in between.