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Topic: Earth rotation (Read 2042 times) |
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aero_guy
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Re: Earth rotation
« Reply #25 on: Feb 12th, 2003, 4:50am » |
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OK, I did a very brief analysis and it seems likely that there is a possibility of oscillation. Assuming that the effect of tidal forces is a rotational force linear with the difference of the moon and Earth's rotations, the earth's radial acc. is lin. based upon that difference. The moon's has a dependence upon r, and the r equation is a bit of a mess. In any case it looks somewhat familiar as a oscillatory equation. If anyone wants to take it further I'd be interested in seeing what you get. As it is, my assumptions about the damping are based upon nothing, so whatever the equations give aren't proof of squat. Oh well.
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James Fingas
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Re: Earth rotation
« Reply #26 on: Feb 12th, 2003, 11:12am » |
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As I see the process, it goes like this:
rotation of earth w.r.t. moon's position -> tidal slowing of earth, speed-up of moon's orbit -> expansion of moon's orbit -> reduced tidal forces
However, the reason I think this can't cause oscillation is that although the tidal forces are being reduced, they can never become positive (slowing the moon down). The only time that they could be positive would be if the earth started rotating in the other direction to the moon. However, it would have to pass through zero rotation for this to happen, and in the abscence of rotation, there is no force. Basically, I think when it gets to zero, it will stay there.
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aero_guy
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Re: Earth rotation
« Reply #27 on: Feb 12th, 2003, 12:18pm » |
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I think you are right. If the radial acceleration of the earth is directly proportional to the difference of the radial velocities, then that would require the moon change rotation speed after they equalize. The basic reason, mathematically speaking is, I think, that none of the forces are dependent upon the actual angle of rotation, only the rate of rotation. It is like a swinging door with a damper but no spring. It wants to stop immediately and doesn't care what the angle is. I guess I was invented "spring equivalent forces" where none existed. Thanks, though it may not seem so here, it is rare I make these kind of mathematical or physics related blunders. Ah well, ignorance has been squashed a llittle more.
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James Fingas
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Re: Earth rotation
« Reply #28 on: Feb 12th, 2003, 1:45pm » |
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aero_guy,
Actually, I am not really sure of myself either. When I was googling, I came across some sites that claimed that there could be resonance (and one even claimed oscillation!) with rotating and orbiting bodies. For instance, the rotation of Mercury is tide-locked with the sun, but not at 1 day/year (so to speak), but rather at 3 days every 2 years. How can this happen? I don't know. Another website I went to was even stranger (James goes searching for links):
http://www.mathpages.com/home/kmath273.htm
This page indicates that oscillation is possible, although personally I think the guy is on crack. The other thing that I don't understand at all is how people go and calculate an exact date for when the earth and moon pair will be tide-locked. But it seems to me that it would be an exponential decline, so there could be no one specific date.
On the other hand, if you look at the moon, it's not even slowly rotating. It's perfectly stopped, and it even seems to have some restoring force to keep it there (maybe that's why it can "librate", not that I know what "libration" is). Perhaps an egg-shaped object tends to align its longer axis towards gravity? With the lack of water, the moon could tend to settle in one particular egg shape, and the elastic properties of rocks could keep it in that shape.
Conclusion: I don't know anything, and it doesn't look like anyone else does either.
The only thing we can be sure of is the answer to the original question: no.
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Chronos
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Re: Earth rotation
« Reply #29 on: Feb 12th, 2003, 4:15pm » |
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Libration occurs because the moon's orbit is not perfectly spherical. Over the course of an orbit, its rotational speed about its own axis is essentially constant, but its orbital speed is not (it moves faster when it's closer to the Earth, and slower when it's further out). So sometimes the rotation lags behind the orbital motion, and sometimes, it leads.
As for Mercury's resonance, it has a permanent elongation. Every orbit, at perihelion (closest approach tothe Sun), that elongation is lined up radially, but in opposite directions each time. Since tidal force is strongest at perihelion, and any small variation would cause the long axis to not line up at perihelion, the present situation is stable.
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aero_guy
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Re: Earth rotation
« Reply #30 on: Feb 12th, 2003, 4:40pm » |
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Oooh, libration. I mentioned the phenomenon in one of my first posts, but I didn't know the name of it. I am checking the link, odd stuff, thanks.
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aero_guy
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Re: Earth rotation
« Reply #31 on: Feb 12th, 2003, 4:53pm » |
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OK, I read it. Summation: FOS. He actually used the same three minutes of logic I used earlier. LIke me he didn't go deep into the problem. The difficulty here is that for most physical oscillators, say a pendulum, there is a stable equilibrium point through which it rotates, just as with the moon, but with the pendulum there is momentum in the system to carry it through equilibrium point. In the moon example, it is the rates that reach an equilibrium, not the positions. Things in motion tend to stay in motion, but thing in acceleration do not stay in acceleration, which is what would be required to cause oscillation.
So, my vote is for exponential decay, but that itself is a guess as it depends on how the forces translate to the earth. It is definitely mono..... dang, what is that word? mono something decay, when the derivative is always negative?
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Icarus
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Re: Earth rotation
« Reply #32 on: Feb 13th, 2003, 5:32am » |
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The word is "monotonic".
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aero_guy
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Re: Earth rotation
« Reply #33 on: Feb 13th, 2003, 12:05pm » |
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I swear I have been senile since the age of 20.
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Icarus
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Re: Earth rotation
« Reply #34 on: Feb 13th, 2003, 5:10pm » |
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You were that late of a bloomer? Geez - how lucky can you get!
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"Pi goes on and on and on ...
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
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