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(Message started by: BNC on Jan 26th, 2003, 4:17am)
Title: Earth rotation
Post by BNC on Jan 26th, 2003, 4:17am
This one is not really a riddle. It is, however, interesting...
note: requires a bit of physics

As we all know, the earth completes a rotation every ~24 hours. This rate is decreasing! (that is, it takes longer and longer to complete one "day").
Why is that?
Will the earth stop rotating at some point?
Title: Re: Earth rotation
Post by towr on Jan 26th, 2003, 7:11am
The moon slows the rotation down, at least that's what I think I've been told, or picked up somewhere..
At some point the earth may stop turning, but there isn't really any way to be sure.. If the moon flies of into space (which could at some point happen since it's moving away from earth, and a large comet/asteroid might one day hit it), then it won't slow down the earths rotation..
On the other hand chances are when the sun burns out there won't be much left of earth, and if earth isn't around it can't turn..
Title: Re: Earth rotation
Post by BNC on Jan 26th, 2003, 10:42am
Close. The slowing mechanism is due to the tides, and is called "tidal braking".

But lets assume the moon will stay in orbit, no comet will hit it (or earth), etc.... Will earth stop rotating?
Title: Re: Earth rotation
Post by towr on Jan 26th, 2003, 11:18am

on 01/26/03 at 10:42:18, BNC wrote:
Close. The slowing mechanism is due to the tides, and is called "tidal braking".
And what causes those tides?
right.. the moon..
Title: Re: Earth rotation
Post by BNC on Jan 26th, 2003, 11:29am

on 01/26/03 at 11:18:12, towr wrote:
And what causes those tides?
right.. the moon..


And that's why I said.... "close".....   ;)

Off-course you're right...I'm sorry if I offended you, or if my answer hinted you're wrong. English isn't my native language.
Title: Re: Earth rotation
Post by Speaker on Jan 27th, 2003, 12:45am
I have heard that the earth is slowing in its rotation due to the redistribution of mass on the surface of the planet. Specifically, that water being held behind dams, at a higher altitude, is further from the axis of rotation and is resulting in a decrease in the speed of rotation.

This is the same principle that causes an ice skater to speed up when he folds his arms across his chest, and to slow down when he extends his arms.

My information, although I cannot indicate a source, described how the degree of deceleration is what might be expected if the estimated mass of the water behind dams were positioned at a distance from the center of the earth equal to its average or mean altitude. And that is coincides with modern development of dams for hydroelectric power.

But, maybe this is an urban legend promulgated by the Oil companies :o But, I don't think so.  
Title: Re: Earth rotation
Post by towr on Jan 27th, 2003, 1:04am
actually, I think, since most dams aren't on the equator, and thus the water can't flow there (furthest form the axis), it would be relatively closer to the axis, and the earth would speed up..
Title: Re: Earth rotation
Post by BNC on Jan 27th, 2003, 3:34am
Hmm, never heard about the dams influence. Tidal breaking is a "confirmed fact" (as far as these things can be confirmed, or considered facts). Currently the earth slows down at a rate of about 1-2millisecond per century. ~240 million years ago, the day on earth was ~23 hours long -- and that's confirmed by observing fossilized marine animals, such as coral, which show both daily growth rings and annual growth rings). 900 million ago the day may have been as short as 18 hours.

Question remaining: will earth stop eventually?
Title: Re: Earth rotation
Post by towr on Jan 27th, 2003, 5:43am
well.. the earth rotation slows down and the moon speeds up. When the angular velocity of the moon around the earth is the same as the earth's angular rotation velocity, then I suppose they would continue at that pace.. (There would also be no tides, since the moon is always at the same side of earth).
On the other hand, the moons angular velocity decreases as it goes faster and get's further away from earth..

Meh.. I dunno.. And I'll be long dead if it were to happen anyway :p
Title: Re: Earth rotation
Post by Chronos on Jan 27th, 2003, 4:27pm
Given enough time, the Earth and Moon would be in a situation like Pluto and Charon, with each locked to the other.  So the same face of the Earth would always face the Moon, and vice versa.  Since the Moon would still be orbiting the Earth, and hence turning, at this time, the Earth would also still be turning.

In actuality, though, the Sun will die out, and probably take the Earth and Moon both with it, long before this has a chance to happen.
Title: Re: Earth rotation
Post by Lythan gany on Jan 29th, 2003, 9:49pm
:)hi! how are u?
Title: Re: Earth rotation
Post by Yang He on Jan 29th, 2003, 9:53pm
:)hi! how are u?

      I know for a fact that the moon is slowly moving away! Well if you know that the circumference (pardon my spelling) is equal to pie(math term) times d(diameter) anyway the farther it goes away the longer the distance it has to travel around the earth and vola! it takes longer to travel a long distance! If you want to know more just mail me and I would be happy to answer.

                                               Best Regards Yang He,
Title: Re: Earth rotation
Post by Pietro K.C. on Jan 30th, 2003, 1:48pm
Didn't know about the dams either... I would never had thought they had enough mass to be of any effect.

Anyway, I've also heard that the Earth is gaining mass at the rate of about a dozen tons a day (could be wrong) due to spatial debris that is continually falling. With angular momentum conservation, the increasing mass would slow down Earth.

If anyone would care to estimate the rate of mass increase that would account for the observed slowing, the Earth's mass is about 6 X 1024. Me, I'm too lazy right now.
Title: Re: Earth rotation
Post by wowbagger on Jan 31st, 2003, 5:10am
Well, I'm not sure about the effect of water held behind dams on the speed of rotation of the earth. However, I think I read somewhere that such a redistribution of mass might be important with respect to the earth's precession (and nutation) as there is much more water dammed on the northern hemisphere than on the southern.

For those really interested, here's a piece of info I unearthed: http://dgfi2.dgfi.badw-muenchen.de/dgfi/DOC/poster_99_seite12.pdf.
Disclaimer: This poster is very technical. It does, however, seem to investigate the effect of the "Three Gorges Dam" on the rotation of the earth.

On the original question:
The "tidal braking" mechanism is quite well-known, I would say. (At least among those who know what brings about the tides in the first place - or the seasons etc.)
As for the second part, I agree with Chronos.
Title: Re: Earth rotation
Post by aero_guy on Jan 31st, 2003, 12:27pm
I agree, but thought the earth is slowing, the moon is not accelerating.  The energy is lost to heat and such when the tidal forces change the shape of the earth, or at least its oceans, not transferred to the moon.  The moon already went through this process and came to a "stop" long ago, matching its rotation with its orbit.  In fact, every moon in the solar systems has already braked to its respective planet.

Another interesting side note: The moon's orbit is somewhat eliptical so there is a small wobble in which side is face us over an orbit.  The same forces that matched its rotation to its orbit are now making the moon's orbit more circular.  And for the next question: I have no idea whether it will come close to circular before the sun dies.
Title: Re: Earth rotation
Post by James Fingas on Jan 31st, 2003, 1:43pm
Aero Guy,

Although you can lose energy to heat, you can't lose angular momentum. That is to say, the earth/moon system can't stop rotating unless we consider tidal braking with the sun (don't ask me how big an effect this is), and even then, the earth/moon/sun system would still be rotating, unless we consider...

I guess the relevant question is: rotating with respect to what?
Title: Re: Earth rotation
Post by aero_guy on Jan 31st, 2003, 8:01pm
pesky basic laws of physics always getting in the way of a good explanation, should have caught that, thanks.
Title: Re: Earth rotation
Post by towr on Feb 1st, 2003, 5:50am

on 01/31/03 at 12:27:37, aero_guy wrote:
I agree, but thought the earth is slowing, the moon is not accelerating.
Acually the moon is accelerating, causing to move further and further away from earth.. Which also decreases it's angular velocity around earth, meaning it can never reach geostatic orbit (since it's allready much slower than 360 degrees per day)
Title: Re: Earth rotation
Post by aero_guy on Feb 3rd, 2003, 3:39am
OK, I admit the earlier comment was wrong, but when you say it can never reach geostatic orbit are you taking into account the slowing of the earth's rotation?  Which is slowing faster, its speed around the earth or the earth's rotation?
Title: Re: Earth rotation
Post by towr on Feb 3rd, 2003, 4:08am
you've got a point there.. I don't really know..
Title: Re: Earth rotation
Post by BNC on Feb 3rd, 2003, 4:44am
from http://www.astronomy.ohio-state.edu/~ryden/ast161_8/notes32.html

2) Tidal forces are gradually slowing down the Earth's rotation.
Friction heats things up (as you know if you've ever tried to warm your hands by rubbing them together). Thus, the friction between the ocean's tidal bulges and the solid earth beneath heats up the ocean. It's a small effect, but it's there. Energy can't be created out of nothing. Where did the energy to heat up the ocean come from? It came from the kinetic energy of the Earth's rotation on its axis. Thus, as the oceans gain energy, in the form of heat, the Earth loses rotation energy, and the rotation slows down. This process - the slowing of rotation due to the presence of tides - is called tidal braking.
Tidal braking doesn't work very rapidly. Currently, the length of the day here on Earth is increasing by roughly 2 milliseconds every century. During the Triassic period, about 240 million years ago, the Earth's day was only 23 hours long, and consequently there were 381 days per year.  

Just as the Moon creates tidal bulges in the solid Earth, so the Earth creates tidal bulges in the solid Moon. Tidal braking, resulting from the big tidal bulges raised by the massive Earth, has ALREADY slowed the Moon to the point where it is ``locked in'' with the same side always facing the Earth. The fact that the Moon's period of rotation is equal to its period of rotation is not a coincidence, but is due to tidal braking.


--------------------------------------------------------------------------------

(3) Tidal forces are gradually increasing the size of the Moon's orbit.
Consider the tidal bulge of the Earth which is closest to the Moon. Friction, as noted above, drags the waters of the bulge in the direction of the Earth's rotation, so that the bulge is always leading the Moon in its orbit, like a carrot held in front of a donkey. The extra little gravitational force exerted by the tidal bulge upon the Moon gives the Moon an extra little acceleration. The Moon, as a result of this extra acceleration, spirals slowly outward.
Currently, the distance between the Earth and Moon is increasing by 3.8 meters (about 4 yards) per century. This is not very rapid (it's about the rate at which your fingernails grow) but over billions of years, it adds up. In roughly 10 billion years, the Earth-Moon system will look significantly different from its current appearance:


* The Earth will keep the same face turned to the Moon, just as the Moon currently keeps the same face turned to the Earth.
* The Earth-Moon distance will be about 50 percent greater than it is now.
* The length of the sidereal month, with the Moon on a larger orbit, will be lengthened to about 47 current Earth days. (This will also be the rotation period of the Earth and the rotation period of the Moon.)
Title: Re: Earth rotation
Post by Icarus on Feb 3rd, 2003, 7:04pm

on 02/03/03 at 04:44:30, BNC wrote:
In roughly 10 billion years, the Earth-Moon system will look significantly different from its current appearance:


* The Earth will keep the same face turned to the Moon, just as the Moon currently keeps the same face turned to the Earth.
* The Earth-Moon distance will be about 50 percent greater than it is now.
* The length of the sidereal month, with the Moon on a larger orbit, will be lengthened to about 47 current Earth days. (This will also be the rotation period of the Earth and the rotation period of the Moon.)


Alas - this overlooks one thing: In about 5 billion years the Sun will become a red giant. It's radius will swell up to slightly larger than the mean distance from the Earth to the Sun. So the Earth-Moon system will indeed look significantly different: it will no longer exist!
Title: Re: Earth rotation
Post by aero_guy on Feb 5th, 2003, 10:02pm
OK, did the whole 10 bill year thing take into account the slowing change in the rate of change?  Of course as the Earth and Moon near their ideal state they will change their orbits/rotations more slowly or do these numbers assume constant rate changes?  On second thought I am not sure about that.  Though the rate of change of the forces will be slower, they will have time to create greater deformations in the earth's surface which will take more energy to reverse.  Dang, this is complex.

Oh, and I was also wondering if the system is critially damped or not.  Will the Earth slow down a little too much, then have to speed up... and so on?  By guesswork I would say it was critically damped, but I am not about to figure it out.
Title: Re: Earth rotation
Post by James Fingas on Feb 6th, 2003, 1:05pm
Aero Guy,

I would guess that the Earth-moon pair is closer to a single-order system. Even if it were a second-order system, to talk about underdamped versus critically damped versus overdamped, you have to have an oscillator.

An oscillator always has at least two forms of energy storage (for example gravity and velocity, an inductor and a capacitor, etc.), and in this situation, I can only see one (rotational kinetic energy).
Title: Re: Earth rotation
Post by Chronos on Feb 8th, 2003, 4:10pm

Quote:
An oscillator always has at least two forms of energy storage (for example gravity and velocity, an inductor and a capacitor, etc.), and in this situation, I can only see one (rotational kinetic energy).
I, too, am not convinced that we can model the system as a damped oscillator, but there are indeed two forms of energy:  Rotational kinetic and gravitational potential.
Title: Re: Earth rotation
Post by aero_guy on Feb 12th, 2003, 4:50am
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.
Title: Re: Earth rotation
Post by James Fingas on Feb 12th, 2003, 11:12am
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.
Title: Re: Earth rotation
Post by aero_guy on Feb 12th, 2003, 12:18pm
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.
Title: Re: Earth rotation
Post by James Fingas on Feb 12th, 2003, 1:45pm
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.
Title: Re: Earth rotation
Post by Chronos on Feb 12th, 2003, 4:15pm
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.
Title: Re: Earth rotation
Post by aero_guy on Feb 12th, 2003, 4:40pm
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.
Title: Re: Earth rotation
Post by aero_guy on Feb 12th, 2003, 4:53pm
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?
Title: Re: Earth rotation
Post by Icarus on Feb 13th, 2003, 5:32am
The word is "monotonic".
Title: Re: Earth rotation
Post by aero_guy on Feb 13th, 2003, 12:05pm
I swear I have been senile since the age of 20.
Title: Re: Earth rotation
Post by Icarus on Feb 13th, 2003, 5:10pm
You were that late of a bloomer? Geez - how lucky can you get!


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