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chornedsnorkack
2009-Mar-16, 01:48 PM
If the Moon were librated through 180 degrees of longitude and brought to stop, what would its period of free libration then be? Shorter than now, exactly the same as now, longer than now, or imaginary?

NEOWatcher
2009-Mar-16, 02:38 PM
If the Moon were librated through 180 degrees of longitude ... or imaginary?
What would the orbit look like?

hhEb09'1
2009-Mar-16, 03:54 PM
JOOC, what is it's period of free libration now?

chornedsnorkack
2009-Mar-16, 04:30 PM
What would the orbit look like?
A slight displacement from exactly 180 degrees would start slowly increasing, then accelerate exponentially. This is what imaginary period of oscillation means.

NEOWatcher
2009-Mar-16, 08:17 PM
I always thought that the moon's libration was entirely due to the orbit and eccentricity.
After lookup up some of your phrases, I get into stuff over my head. Is there a simple explaination of the concept?

Hornblower
2009-Mar-16, 08:26 PM
Correction: If rotated 180 degrees and released in synchronous rotation, it will be in its other stable position and will not oscillate. An oblong object in such a position is stable with either end toward the Earth.

If rotated 90 degrees and released, it will be in an unstable equilibrium. If at exact dead center there will be no torque, but if it is the least bit off it will start turning away from this crossways position and oscillate like a pendulum. The closer to 90 degrees when released, the longer it will take to move appreciably.

I see no justification for calling this period "imaginary". It merely is indeterminate if the angle at release is exactly 90 degrees. As the release point approaches 90 degrees, the period increases without limit.

hhEb09'1
2009-Mar-17, 01:20 AM
If rotated 90 degrees and released, it will be in an unstable equilibrium. If at exact dead center there will be no torque, but if it is the least bit off it will start turning away from this crossways position and oscillate like a pendulum. The closer to 90 degrees when released, the longer it will take to move appreciably.The reason it's oblong though is because of the earth's tides. If they relaxed, the new orientation could be established.

Hornblower
2009-Mar-17, 09:51 AM
The reason it's oblong though is because of the earth's tides. If they relaxed, the new orientation could be established.

That is a good point. If the Moon is pliable enough, the tidal stress could stretch the short axis into a long one and arrest what otherwise would be a tendency to return to the previous orientation.

chornedsnorkack
2009-Mar-17, 10:29 AM
If the Moon were pliable enough, then the Moon would not stay same side to Earth, because repeated small displacements in longitude would not be restored and would accumulate over time.

Hornblower
2009-Mar-17, 12:46 PM
If the Moon were pliable enough, then the Moon would not stay same side to Earth, because repeated small displacements in longitude would not be restored and would accumulate over time.
I don't think so. For a small displacement the shape is not going to change much from the original tidelocked prolate spheroid, and my educated guess is that we will have a damped oscillation that will settle down at or near the original position.

Jeff Root
2009-Mar-17, 01:27 PM
If the Moon were pliable enough, then the Moon would not stay same
side to Earth, because repeated small displacements in longitude would
not be restored and would accumulate over time.
That would definitely happen if the Moon were perfectly uniform,
radially. But it isn't, of course. The biggie is that the Moon's crust
is thinner on the near side than on the far side. It is about 60 km
thick on the near side and 100 km thick on the far side.

-- Jeff, in Minneapolis

chornedsnorkack
2009-Mar-17, 01:30 PM
That would definitely happen if the Moon were perfectly uniform,
radially. But it isn't, of course. The biggie is that the Moon's crust
is thinner on the near side than on the far side. It is about 60 km
thick on the near side and 100 km thick on the far side.

Precisely. Moon lacks symmetry against 180 degree libration.

If the thick crust were turned to the nearside, would this change the period of libration?

Hornblower
2009-Mar-17, 03:53 PM
If the thick crust were turned to the nearside, would this change the period of libration?
In my opinion, no. As noted before, an asymmetrical oblong object will be stable with either the heavy end or the light end toward the Earth. A free libration around this position should have the same period either way.

Try Googling "moon free libration". You will find some papers illustrating just how complicated the problem is. One thing I found was a period of about 3 years for a free libration in longitude.

hhEb09'1
2009-Mar-17, 11:27 PM
That would definitely happen if the Moon were perfectly uniform, radially. But it isn't, of course. The biggie is that the Moon's crust is thinner on the near side than on the far side. It is about 60 km thick on the near side and 100 km thick on the far side.The way I always heard it (and I could be wrong about this, I can't find anything one way or the other right now) is that that asymmetry is not aligned with the earth now, that it's maybe 30 degrees off.

Jeff Root
2009-Mar-18, 12:11 AM
The way I always heard it (and I could be wrong about this, I can't
find anything one way or the other right now) is that that asymmetry
is not aligned with the earth now, that it's maybe 30 degrees off.
I expect that that is for the same reason that Earth's tidal bulges
are not directly under the Moon: rotation carries them forward.
The Moon's mass distribution may not be aligned exactly with the
Earth, but it is dynamically balanced so as to minimize angular
momentum or rotational energy or whatever it is that is minimized.

-- Jeff, in Minneapolis

grant hutchison
2009-Mar-18, 12:16 AM
This month's (April) Icarus contains Did a large impact reorient the Moon? (http://www.ipgp.jussieu.fr/~wieczor/MyPapers/Wieczorek_and_Le_Feuvre_2009.pdf) (962KB pdf), which suggests that the Moon will lock in either its current position, or the 180-degree-rotated position, and that it may have occupied both states over geological time.

Grant Hutchison