Moon tidal locking inevitable by now?

Hi! I wasn't sure whether to start a new thread or tease this one out
a bit. I am not a mathematician nor an astronomer, just a layman
trying to figure this out:

A question has been plaguing me as a friend and I discuss "tidal
lock." Putting the physics of tidal lock aside (the Earth "commands"
the moon to do this as I understand) I am wondering what the odds of
tidal lock occurring would be if the Earth were not forcing the
situation. In other words, what would be the odds of the moon orbiting
and spinning at the same rate by happenstance?

If the orbit took even 28.3 days and the spin took 27.31 days, it
wouldn't be very many years for us to see the other side. The odds
must be infinitesimally small for them to go on like that for
millennia, is that correct? Is there any math that could prove this?

Thank you for any wisdom.

On Monday, March 3, 2014 3:19:02 AM UTC-5, wrote:
A question has been plaguing me as a friend and I discuss "tidal
lock." Putting the physics of tidal lock aside (the Earth "commands"
the moon to do this as I understand) I am wondering what the odds of
tidal lock occurring would be if the Earth were not forcing the
situation. In other words, what would be the odds of the moon orbiting
and spinning at the same rate by happenstance?

I don't think there's enough information to answer your question.

Tidal lock, as the name suggests, is a tidal force. The moon is an
imperfect nearly spherical body, and not a perfect test particle. I
think your question could be simplified to ask, what if the moon were
small enough that tidal forces upon it were negligible. Then there
would be negligible tides on the moon, negligible tidal dissipation in
the moon, and so no change in the rotation rate of the moon.... and no
tidal locking.

Even if that were the case, the moon still raises tides on the
*earth*. This is a dissipative process. The rotation rate of the
earth would be changed, and the earth-moon orbit would be changed.
In other words, the earth moon system is not fixed, even if one can
ignore tidal locking of the moon's rotation rate.

So then the question becomes: of all the possible starting points for
the earth-moon system, what fraction of them will evolve to have
exactly today's orbital parameters? I don't think we have enough
information about possible starting points or exact evolutionary
processes to make a good estimate to answer this question.

And furthermore, asking for an exact match to today's parameters is
guaranteed to give an infinitesimally small answer, because there are
infinitely many possible orbits. Common practice is to ask for the
probability over a finite range of parameters. (or, to quote the
differential probability)

CM

In article ,
Craig Markwardt wrote:
I don't think we have enough information about possible starting points
or exact evolutionary processes to make a good estimate to answer this
question.

We have enough moons in our Solar System to at least get some idea of
under what conditions it should be probable or improbable.

On Mon, 03 Mar 14, " wrote:
If the orbit took even 28.3 days and the spin took 27.31 days, it
wouldn't be very many years for us to see the other side. The odds
must be infinitesimally small for them to go on like that for
millennia, is that correct? Is there any math that could prove this?

This is just a mathematical question. Suppose the fastest possible
lunar rotation is once-around per hour (can't be bothered to calculate
true bound where the surface reaches escape velocity), so the full
range is between once-per-hour prograde and retrograde -- assuming
axial tilt is normal to orbital plane here.

Next, for the moon to appear to be locked to Earth-orbit over millenia
means the synchronicity hasn't varied more than 5% over 4000 years
(roughly), so over 4000 years a once-per-hour rotation is 35 million
rotations x 2 = 70 million range from prograde to retrograde, out
which we select 10% (5% prograde to retrograde) of one of those
values, so that's 1 possibility out of 700 million, taking each
possibility to be a 10% slice of a fixed number of rotations over a
4000 year period.

So the odds of this happening randomly are 1 / 700,000,000.

Eric