Moon tidal locking inevitable by now?

The moon's rotation on its axis has approximately the
same period as its revolution around the earth as a
result of tidal forces that locked this rate earlier
in its history. I'm curious as to the odds that the
moon might not yet have become locked by now. In lieu
of spending time figuring out what range of parameters
to plug into the formula given in the "Tidal Locking"
Wikipedia article, I'd like to know simply if there
are any moon formation scenarios that give plausible
odds for the moon to be still rotating faster than
its orbital revolution at this late date.

--
Charles Packer
http://cpacker.org/whatnews
mailboxATcpacker.org

On 2012/07/10 13:04, Charles Packer wrote:
The moon's rotation on its axis has approximately the
same period as its revolution around the earth as a
result of tidal forces that locked this rate earlier
in its history. I'm curious as to the odds that the
moon might not yet have become locked by now.

By measurement, it is known that the moon is in fact swinging back and
forth a bit, suggesting that indeed it has an inhomogeneity that causes
a locking.

In lieu
of spending time figuring out what range of parameters
to plug into the formula given in the "Tidal Locking"
Wikipedia article, ...

"Tidal locking".

...I'd like to know simply if there
are any moon formation scenarios that give plausible
odds for the moon to be still rotating faster than
its orbital revolution at this late date.

So the odds is zero, it seems. By contrast, if the moon was perfectly a
homogenous body (density only depending on the radius), it is hard to
see how it could even be locked in.

Hans

In article , Hans Aberg
writes:

By measurement, it is known that the moon is in fact swinging back and
forth a bit, suggesting that indeed it has an inhomogeneity that causes
a locking.

So the odds is zero, it seems. By contrast, if the moon was perfectly a
homogenous body (density only depending on the radius), it is hard to
see how it could even be locked in.

I don't follow you here. As you note in the second bit quoted above,
some sort of inhomogeneity is necessary for locking. It is locked,
there is inhomogeneity, the near side looks different than the far side
etc. No problem. But what does the "swinging back and forth a bit"
have to do with inhomogeneity? Locking occurs when the period of
revolution equals the period of rotation. However, since the orbit is
not a perfect circle, sometimes the Moon is moving slower than average
and sometimes faster, but the speed of rotation (at least at this order)
remains constant. Thus, one can sometimes peak around the eastern limb
of the Moon, at other times around the western limb. (Add to this the
fact that the orbit is tilted so that we can sometimes see over the
poles then altogether we can see about 59% of the surface, though only
50% at any one time, of course.)

OK, the swinging happens only if it is locked, and locking happens only
if there is inhomogeneity, so swinging happens only if there is
inhomogeneity, but you seem to be implying some more direct connection
between swinging and inhomogeneity.

On 2012/07/11 10:48, Phillip Helbig---undress to reply wrote:
In article , Hans Aberg
writes:

By measurement, it is known that the moon is in fact swinging back and
forth a bit, suggesting that indeed it has an inhomogeneity that causes
a locking.

So the odds is zero, it seems. By contrast, if the moon was perfectly a
homogenous body (density only depending on the radius), it is hard to
see how it could even be locked in.

I don't follow you here. As you note in the second bit quoted above,
some sort of inhomogeneity is necessary for locking. It is locked,
there is inhomogeneity, the near side looks different than the far side
etc. No problem. But what does the "swinging back and forth a bit"
have to do with inhomogeneity? Locking occurs when the period of
revolution equals the period of rotation. However, since the orbit is
not a perfect circle, sometimes the Moon is moving slower than average
and sometimes faster, but the speed of rotation (at least at this order)
remains constant.

The rotation is not exactly constant, so that sometimes it is a bit
faster, and then it slows down, and the moon adjusts its position like a
pendulum around a balance point. In particular, one can see more than
one half of the surface of the moon from earth over time (and more what
any effect from the ellipticity of the orbit would give).

Hans

On Tue, 10 Jul 12, Charles Packer wrote:
in its history. I'm curious as to the odds that the
moon might not yet have become locked by now.

If the Moon had an independently-rotating core, as do planets with
magnetic fields, then that core could have kept the Moon unlocked. In
a previous posting titled "Tumbling Venus", I outlined evidence that
Venus has a large spinning core which has freed it from a previous
state of being rotationally locked to its orbit.

However, our Moon is modelled to have a warm but fixed core.

Eric

In article , Hans Aberg
writes:

The rotation is not exactly constant, so that sometimes it is a bit
faster, and then it slows down, and the moon adjusts its position like a
pendulum around a balance point. In particular, one can see more than
one half of the surface of the moon from earth over time (and more what
any effect from the ellipticity of the orbit would give).

OK; now I get it. I'm not sure which effect is the larger.

Hans Aberg wrote:
The rotation is not exactly constant, so that sometimes it is a bit
faster, and then it slows down, and the moon adjusts its position like a
pendulum around a balance point. In particular, one can see more than
one half of the surface of the moon from earth over time (and more what
any effect from the ellipticity of the orbit would give).

Phillip Helbig---undress to reply wrote:
OK; now I get it. I'm not sure which effect is the larger.

There's a detailed analysis of this in chapter 5 "Spin-Orbit Coupling"
of Murray and Dermott, "Solar System Dynamics" (Cambridge U.P., 1999).
The non-constant angular rotation of the moon (with respect to an
inertial reference frame) is known as "forced libration", and is
treated in Murray & Dermott's section 5.6.

Murray and Dermott give the amplitude of the forced libration as about
15 arcseconds. This is around 3 orders of magnitude smaller than the
elliptic-orbit effect.

It's also of interest to note that the forced libration's damping time
(i.e., the e-folding time with which perturbations in the Moon's angular
velocity decay) is only 3e7 years, a factor of ~150 less than the Moon's
age (4.6e9 years, determined from radioisotope dating of lunar rocks).
So there has been (much) more than enough time for the Moon's initial
spin to decay to its current rate.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

In article ,
Phillip Helbig---undress to reply writes:
OK, the swinging happens only if it is locked, and locking happens only
if there is inhomogeneity,

Why wouldn't a homogeneous body become tidally locked? The body
would be deformed into an ellipsoid by the tidal forces, and the
resulting non-spherical shape should result in locked rotation.

As to terminology, most sources distinguish between "optical" or
"geometric" libration on the one hand and "physical" libration on the
other. As Jonathan wrote, the former is by far the larger effect for
the Moon; the latter isn't even mentioned in the Wikipedia
"Libration" article. I couldn't find any simple discussion in a
quick web search, but http://astro.ukho.gov.uk/data/tn/naotn74.pdf
gives technical details.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

In article , Steve Willner
writes:

In article ,
Phillip Helbig---undress to reply writes:
OK, the swinging happens only if it is locked, and locking happens only
if there is inhomogeneity,

Why wouldn't a homogeneous body become tidally locked? The body
would be deformed into an ellipsoid by the tidal forces, and the
resulting non-spherical shape should result in locked rotation.

Right, assuming the body is deformable (which most are, to some extent).
Inhomogeneity certainly speeds up the process, though.

On 2012/07/12 08:14, Steve Willner wrote:
In article ,
Phillip Helbig---undress to reply writes:
OK, the swinging happens only if it is locked, and locking happens only
if there is inhomogeneity,

Why wouldn't a homogeneous body become tidally locked? The body
would be deformed into an ellipsoid by the tidal forces, and the
resulting non-spherical shape should result in locked rotation.

I defined homogeneous to mean that the density only depends on the
radius. If the body is deformed that would not any longer be true, as
some outer spherical shells would consist of both mass an nothing.

The reason such a definition is convenient is that Newton showed that
such a body under the gravitational inverse square law behaves as a
point particle. Thus, all effects that depart from that behavior is due
to some inhomogeneity as defined above.

Hans