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Moon tidal locking inevitable by now?
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Charles Packer
Jul 10, 2012, 7:04:48 AM7/10/12
to
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
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
Hans Aberg
Jul 10, 2012, 4:39:44 PM7/10/12
to
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
> 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.
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"
"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
> odds for the moon to be still rotating faster than
> its orbital revolution at this late date.
homogenous body (density only depending on the radius), it is hard to
see how it could even be locked in.
Hans
Phillip Helbig---undress to reply
Jul 11, 2012, 4:48:14 AM7/11/12
to
In article <mt2.0-30419...@hydra.herts.ac.uk>, Hans Aberg
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.
<haber...@telia.com> 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.
> 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,
> homogenous body (density only depending on the radius), it is hard to
> see how it could even be locked in.
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.
Hans Aberg
Jul 11, 2012, 7:37:02 AM7/11/12
to
On 2012/07/11 10:48, Phillip Helbig---undress to reply wrote:
> In article <mt2.0-30419...@hydra.herts.ac.uk>, Hans Aberg
> <haber...@telia.com> 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
> In article <mt2.0-30419...@hydra.herts.ac.uk>, Hans Aberg
> <haber...@telia.com> 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.
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
Eric Flesch
Jul 11, 2012, 7:37:55 AM7/11/12
to
On Tue, 10 Jul 12, Charles Packer <mai...@cpacker.org> 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
>in its history. I'm curious as to the odds that the
>moon might not yet have become locked by now.
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
Phillip Helbig---undress to reply
Jul 11, 2012, 7:59:41 AM7/11/12
to
In article <mt2.0-10237...@hydra.herts.ac.uk>, Hans Aberg
OK; now I get it. I'm not sure which effect is the larger.
Jonathan Thornburg [remove -animal to reply]
Jul 11, 2012, 2:28:09 PM7/11/12
to
Hans Aberg > <haber...@telia.com> 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).
> 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 <hel...@astro.multiclothesvax.de> 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"
> OK; now I get it. I'm not sure which effect is the larger.
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]" <jth...@astro.indiana-zebra.edu>
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
Steve Willner
Jul 12, 2012, 2:14:20 AM7/12/12
to
In article <mt2.0-20955...@hydra.herts.ac.uk>,
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.
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Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
Phillip Helbig---undress to reply <hel...@astro.multiCLOTHESvax.de> 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
> OK, the swinging happens only if it is locked, and locking happens only
> if there is inhomogeneity,
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 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
Phillip Helbig---undress to reply
Jul 12, 2012, 3:43:28 AM7/12/12
to
In article <mt2.0-14757...@hydra.herts.ac.uk>, Steve Willner
Inhomogeneity certainly speeds up the process, though.
<wil...@cfa.harvard.edu> writes:
> In article <mt2.0-20955...@hydra.herts.ac.uk>,
> Phillip Helbig---undress to reply <hel...@astro.multiCLOTHESvax.de> 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).
> In article <mt2.0-20955...@hydra.herts.ac.uk>,
> Phillip Helbig---undress to reply <hel...@astro.multiCLOTHESvax.de> 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.
Inhomogeneity certainly speeds up the process, though.
Hans Aberg
Jul 12, 2012, 5:11:12 AM7/12/12
to
On 2012/07/12 08:14, Steve Willner wrote:
> In article <mt2.0-20955...@hydra.herts.ac.uk>,
> Phillip Helbig---undress to reply <hel...@astro.multiCLOTHESvax.de> 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
> In article <mt2.0-20955...@hydra.herts.ac.uk>,
> Phillip Helbig---undress to reply <hel...@astro.multiCLOTHESvax.de> 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.
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
Lord Androcles, Zeroth Earl of Medway
Sep 30, 2012, 8:15:37 AM9/30/12
to
"Hans Aberg" <haber...@telia.com> wrote in message
news:mt2.0-10237...@hydra.herts.ac.uk...
orbit being elliptical.
http://en.wikipedia.org/wiki/Libration
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news:mt2.0-10237...@hydra.herts.ac.uk...
> The rotation is not exactly constant,
The angular velocity IS constant. The libration is a result of the
orbit being elliptical.
http://en.wikipedia.org/wiki/Libration
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Hans Aberg
Oct 1, 2012, 3:15:29 AM10/1/12
to
On 2012/09/30 14:15, Lord Androcles, Zeroth Earl of Medway wrote:
> "Hans Aberg" <haber...@telia.com> wrote in message
> news:mt2.0-10237...@hydra.herts.ac.uk...
>> The rotation is not exactly constant,
>
> The angular velocity IS constant.
The angular varies, as the orbit is elliptical; see section "Libration"
> "Hans Aberg" <haber...@telia.com> wrote in message
> news:mt2.0-10237...@hydra.herts.ac.uk...
>> The rotation is not exactly constant,
>
> The angular velocity IS constant.
here:
https://en.wikipedia.org/wiki/Orbit_of_the_Moon
However, the areal velocity is constant:
https://en.wikipedia.org/wiki/Areal_velocity
> The libration is a result of the
> orbit being elliptical.
> http://en.wikipedia.org/wiki/Libration
tidal locking, though.
Hans
Steve Willner
Oct 1, 2012, 1:20:26 PM10/1/12
to
In article <mt2.0-28563...@hydra.herts.ac.uk>,
Try a better source. The Wikipedia article discusses only "geometric
libration," not all of which is a result of the elliptical orbit.
There's also "physical libration," though it is much smaller. See,
for example:
http://astro.ukho.gov.uk/data/tn/naotn74.pdf
"The actual rotation state has small periodic variations from this
mean state caused by dynamical perturbations, and these cause the
physical librations of the Moon's orientation."
"Lord Androcles, Zeroth Earl of Medway" <Sept...@2012.org> writes:
> The angular velocity IS constant.
Almost but not quite.
> The angular velocity IS constant.
Try a better source. The Wikipedia article discusses only "geometric
libration," not all of which is a result of the elliptical orbit.
There's also "physical libration," though it is much smaller. See,
for example:
http://astro.ukho.gov.uk/data/tn/naotn74.pdf
"The actual rotation state has small periodic variations from this
mean state caused by dynamical perturbations, and these cause the
physical librations of the Moon's orientation."
Lord Androcles, Zeroth Earl of Medway
Oct 4, 2012, 3:35:51 PM10/4/12
to
"Hans Aberg" <haber...@telia.com> wrote in message
news:mt2.0-6884...@hydra.herts.ac.uk...
>The angular varies, as the orbit is elliptical;
The ROTATION of the Moon has a CONSTANT angular velocity, INDEPENDENT
of the orbit. That'¹s the rotation on its own axis. The orbital
velocity is not constant.
IF the moon had a circular orbit no libration would be seen, but if
the Moon had a highly elliptical orbit it would linger at apogee and
visibly turn due to its CONSTANT angular velocity.
The angular velocity of the Moon is constant, the orbital velocity
varies. The difference causes libration.
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Lord Androcles, Zeroth Earl of Medway
Oct 4, 2012, 3:36:18 PM10/4/12
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"Steve Willner" <wil...@cfa.harvard.edu> wrote in message
news:mt2.0-18694...@hydra.herts.ac.uk...
'Step 1 : The apparent positions of the Moon and Sun have been
calculated using methods described in
Section B of The Astronomical Almanac.'
Moon = 57?.364896851
I'd prefer the apparent positions to be measured, not calculated.
Perhaps you can explain how an exercise in numerology to a trillionth
of a degree with no tolerance is a `better source', Steve.
To within the limits set by observational accuracy, The angular
velocity IS constant. The libration is a result of the orbit being
elliptical. Or maybe the flea on the elephant's back is a significant
contribution to the mass of the beast when it stomps on the mouse,
although I doubt the mouse will care.
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news:mt2.0-18694...@hydra.herts.ac.uk...
>Try a better source. The Wikipedia article discusses only "geometric
>libration," not all of which is a result of the elliptical orbit.
>
>There's also "physical libration," though it is much smaller. See,
>for example:
>http://astro.ukho.gov.uk/data/tn/naotn74.pdf
"The actual rotation state has small periodic variations from this
mean state caused by dynamical perturbations, and these cause the
physical librations of the Moon's orientation."
Quite, but not almost.
>libration," not all of which is a result of the elliptical orbit.
>
>There's also "physical libration," though it is much smaller. See,
>for example:
>http://astro.ukho.gov.uk/data/tn/naotn74.pdf
"The actual rotation state has small periodic variations from this
mean state caused by dynamical perturbations, and these cause the
physical librations of the Moon's orientation."
'Step 1 : The apparent positions of the Moon and Sun have been
calculated using methods described in
Section B of The Astronomical Almanac.'
Moon = 57?.364896851
I'd prefer the apparent positions to be measured, not calculated.
Perhaps you can explain how an exercise in numerology to a trillionth
of a degree with no tolerance is a `better source', Steve.
To within the limits set by observational accuracy, The angular
velocity IS constant. The libration is a result of the orbit being
elliptical. Or maybe the flea on the elephant's back is a significant
contribution to the mass of the beast when it stomps on the mouse,
although I doubt the mouse will care.
--
This message is brought to you from the keyboard of
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Hans Aberg
Oct 4, 2012, 5:23:51 PM10/4/12
to
On 2012/10/04 21:35, Lord Androcles, Zeroth Earl of Medway wrote:
> The ROTATION of the Moon has a CONSTANT angular velocity, INDEPENDENT
> of the orbit. That's the rotation on its own axis.
The physical librations are caused by departure from this, and they have
> The ROTATION of the Moon has a CONSTANT angular velocity, INDEPENDENT
> of the orbit. That's the rotation on its own axis.
been measured. For example, Libration link mentioned before gives J. D.
Mulholland, E. C. Silverberg (1972), "Measurement of Physical Librations
Using Laser Retroreflectors".
Searching for "lunar laser ranging experiment physical libration" gives
a number of related hits.
Hans
Jonathan Thornburg [remove -animal to reply]
Oct 5, 2012, 3:23:32 PM10/5/12
to
Lord Androcles, Zeroth Earl of Medway <LordAn...@october2012.org> wrote:
> I'd prefer the apparent positions to be measured, not calculated.
If you really want that, you'll have to sacrifice a *lot* (many decimal
> I'd prefer the apparent positions to be measured, not calculated.
places) of accuracy. The best way to measure absolute angular positions
of astronomical objects is with an (automated) meridian circle, e.g.
http://en.wikipedia.org/wiki/Transit_circle#20th_century_and_beyond_.281900s_and_2000s.29
Alas, these are all set up to observe point sources (stars), not extended
sources like the moon.
Indeed, it's not obvious how to *observe* (without needing nontrivial
calculation as well) the moon's position -- you can at best locate the
lunar "disk" on the sky, but where is the moon's center of mass with
respect to that disk? You'll need a nontrivial dynamical model of the
moon's position and angular orientation, and of the observer-moon-sun
angle, to make that connection.
If you want high-accuracy modelling of the moon's orbit, lunar laser
ranging is your *big* friend. Today's accuracy's are a few *millimeters*
in range between a telescope on the Earth and a retroflector on the moon.
But to do anything useful with those numbers (indeed, even to know the
right distance-to-a-few-meters-accuracy range-converted-to-light-travel-time
to "listen" for the few reflected photons), you need a full model of the
earth-moon dynamics, including solid-earth and solid-moon tides and lots
and lots of relativistic effects. I cited a bunch of references in a
sci.physics.research posting on 24 April 2012, which can be found at
https://groups.google.com/group/sci.physics.research/msg/1e4e106ebd77528b?dmode=source&output=gplain&noredirect
Merkowitz's Living Reviews article
http://relativity.livingreviews.org/Articles/lrr-2010-7/fulltext.html
section 6 mentions about 170 parameters in such a dynamical model.
ciao,
--
-- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zebra.edu>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
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