Decay of earths rotation

[chilehed]

Anyone know of a good discussion of the rate of decay of the earth’s angular velocity?



A while back I did some calculations using a viscous damping model. The time constant (based on the known daily loss of angular velocity) resulted in a very short age of the earth; I forget the exact numbers but the surface velocity at the equator exceeded the escape velocity far more recently than would be acceptable to old earthers (<100M years?).



I never could figure out how to model the change in the earth’s eccentricity as a function of velocity, nor did I have any idea how that would affect the time constant (especially at a time prior to the earth forming a single mass). I also didn’t know how to account for changes in angular momentum due to accretion or other mechanisms. And of course, viscous damping may not be the right place to start.



Any thoughts?



www.catholic.com

 

[Chi_Cygni]

The rotation of the Earth is no problem for a 4.5 Gyr lifetime.

The Earth's rotation slowing down does not give spuriously high rotation rates in the past. If you get this you are doing the math wrong.

By 'eccentricity' I assume you mean the oblateness of the Earth and are not referencing it's orbit. That isn't easy to calculate because you need an accurate model of the Earth and physical properties of different types of rock etc.

Anyways the Earth's oblateness would change that much so it's not a necessary parameter in a simple model - any effects of this would be a small correction. As would accretion. What accretion are you even referring to?

In fact - how did you end up with problems for the Earth?

Only if you used erroneous numbers could you have got this.

 

[JohnR7]

Anyone know of a good discussion of the rate of decay of the earth’s angular velocity?


The slowdown or spindown rate of the earth is due to friction from the tide. The tide is caused by the moon. The moon is moving away from the earth, and at one time the moon could have crashed & bounced off of the earth.

The universe or macro world is not as accurate as the atomic or micro world. Every few years they have to adjust the atomic clocks. Atomic time is fairly consistant, but our solar system is not as consistant. It can fluxuate more than half a second every two or three years.

 

[chilehed]

The Earth's rotation slowing down does not give spuriously high rotation rates in the past. If you get this you are doing the math wrong.

Hence my question - I rechecked my calculations several times (but we all know that doesn't always help).

By 'eccentricity' I assume you mean the oblateness of the Earth and are not referencing it's orbit. That isn't easy to calculate because you need an accurate model of the Earth and physical properties of different types of rock etc.
Anyways the Earth's oblateness would change that much so it's not a necessary parameter in a simple model - any effects of this would be a small correction.QUOTE]

No, it's not easy to calculate, that's what I said, but you seem to be sure of the answer. How is that? And yes, I was referring to the shape of the earth itself, not it's orbit.

As would accretion. What accretion are you even referring to?

The earth's momentum changes as it gains mass from things falling onto it. Nowdays it's not a significant factor most of the time (thank God), but the most widely held opinion is that it was in the past.

In fact - how did you end up with problems for the Earth?

Only if you used erroneous numbers could you have got this.

Well, as I said, I calculated the time constant of decay from the daily angular velocity loss. I suppose I may have had the wrong rate, but at the time the source seemed reliable. Perhaps I should go back and try again.

The slowdown or spindown rate of the earth is due to friction from the tide. The tide is caused by the moon. The moon is moving away from the earth, and at one time the moon could have crashed & bounced off of the earth.

I imagine that a significant component of it is due to viscous flow in the earth's interior, as well as magnetic field effects.

 

[fungle]

I got lost with the tides. More confirmation?

 

[Vegan Charity]

Anyone know of a good discussion of the rate of decay of the earth’s angular velocity?

A while back I did some calculations using a viscous damping model. The time constant (based on the known daily loss of angular velocity) resulted in a very short age of the earth; I forget the exact numbers but the surface velocity at the equator exceeded the escape velocity far more recently than would be acceptable to old earthers (<100M years?).

If I could see the algorhythm, and the numbers you used, I could show you where the error occurred.

I never could figure out how to model the change in the earth’s eccentricity as a function of velocity, nor did I have any idea how that would affect the time constant (especially at a time prior to the earth forming a single mass). I also didn’t know how to account for changes in angular momentum due to accretion or other mechanisms. And of course, viscous damping may not be the right place to start.



Any thoughts?

First, you have to keep in mind that the Earth's rotation is getting slower, but the rate of slowing (a rate of a rate) is growing exponentially smaller.

If the rate of slowing were constant, that would violate the Law of Conservation of Angular Momentum as well as the Law of Rotational Inertia (if your calculations involved a constant rate of slowing, then that is where the error occurred).

The reason why the rate of slowing is growing exponentially smaller is due to the fact that the moon is getting further away. To illustrate this, imagine you are holding a dumbbell. There is a weight on both sides of the bar. You can put your hand between the weights and rotate it about it's Normal Axis. If you increase the distance between two weights, you cannot rotate the system about its axis as easily.

The earth's rotation is slowing at a rate of 0.005 seconds per year per year (at its current rate). This extrapolates to the earth having a 14-hour day 4.6 billion years ago, which is entirely possible. (This extrapolation takes into account of the potential Moon's mass.)

Keep in mind, the the rate at which the earth slows today is higher than average because the present rate of spin is in resonance with the back-and-forth movement of the oceans. What this means is that the earth is not a fixed system. In Physics, the oceans effectively make the earth an Open Inertial body. This means the Center Of Gravity between the Earth-Moon system is constantly shifting about, which explains not-so-constant spin of the Earth.

This information is verified via Empiricism because we know the Fossil rugose corals preserve daily and yearly growth patterns and show that the day was about 22 hours long 370 million years ago, in rough agreement with the 22.7 hours predicted from a constant rate of slowing (a non-constant rate of slowing puts the length of one Earth Rotation at about 22 hours).


I can only assume in the calculations involved were incorrect, did not take into accordance enough variables, and did not involve itself in Elementary Physics. (And really, why does it matter so much that the Earth be 6000 years old?)

 

[AlHailThePowerOfJesusName]

lol just be a yec ist like me, that'll solve all your problems.

 

[Bushido216]

lol just be a yec ist like me, that'll solve all your problems.

If I may be allowed to paraphrase:

"Just shut your mind off like me, that'll solve all your problems. You can just blindly accept what your Church Creation Champ (CCC) tells you and call everyone else a heretic, it's very simple!"

 

[AlHailThePowerOfJesusName]

If I may be allowed to paraphrase:

"Just shut your mind off like me, that'll solve all your problems. You can just blindly accept what your Church Creation Champ (CCC) tells you and call everyone else a heretic, it's very simple!"

congradulates Bushido216 for not flaming. God bless you

 

[lucaspa]

The earth's rotation is slowing at a rate of 0.005 seconds per year per year (at its current rate). This extrapolates to the earth having a 14-hour day 4.6 billion years ago, which is entirely possible. (This extrapolation takes into account of the potential Moon's mass.)

Chilehed, this is the essential part of all the posts. If you are getting a different answer than this, then
1. Your viscous damping model is wrong.
2. Your constants in your equations are wrong.
3. You made some arithmetic errors.

I'm willing to bet it's a combination of 1 and 2.

This information is verified via Empiricism because we know the Fossil rugose corals preserve daily and yearly growth patterns and show that the day was about 22 hours long 370 million years ago, in rough agreement with the 22.7 hours predicted from a constant rate of slowing (a non-constant rate of slowing puts the length of one Earth Rotation at about 22 hours).

Nice data!

 

[chilehed]

If I could see the algorhythm, and the numbers you used, I could show you where the error occurred...I can only assume in the calculations involved were incorrect, did not take into accordance enough variables, and did not involve itself in Elementary Physics. (And really, why does it matter so much that the Earth be 6000 years old?)

OUCH! You really know how to hurt a guy. Was that entirely necessary, seeing as how I basically said that I don't know what all the variables are, nor how to correctly model them?



Certainly, if the rate of deceleration is decreasing over time, than my calculation will give the results I got. But I’m not sure how that squares with your other statement that the current deceleration rate is higher than average – if you could direct me to a fuller treatment I’m sure it would all become clear. I majored in engineering, not math, but if I have enough time to sit and think about it I can usually get the gist of things if it’s not presented at too high a level.



And what did I say to give you the impression I'm trying to prove the earth is 6000 years old? If that was the case, I'd have trotted out my lame model as a proof, rather than asking for help because it doesn't make sense.

lol just be a yec ist like me, that'll solve all your problems.

Please, spare me. That's why you guys get smoked so bad whenever you debate a knowledgable evolutionist, right?

Chilehed, this is the essential part of all the posts. If you are getting a different answer than this, then
1. Your viscous damping model is wrong.
2. Your constants in your equations are wrong.
3. You made some arithmetic errors.

I'm willing to bet it's a combination of 1 and 2.

Coming from you, I count that as high praise. Thanks.

 

[Vegan Charity]

OUCH! You really know how to hurt a guy. Was that entirely necessary, seeing as how I basically said that I don't know what all the variables are, nor how to correctly model them?

[Hugs chilehed]



(Did that help?)

Certainly, if the rate of deceleration is decreasing over time, than my calculation will give the results I got. But I’m not sure how that squares with your other statement that the current deceleration rate is higher than average – if you could direct me to a fuller treatment I’m sure it would all become clear. I majored in engineering, not math, but if I have enough time to sit and think about it I can usually get the gist of things if it’s not presented at too high a level.

You have to keep in mind to take into accound the mass of the oceans. The oceans oscillate rather noticeably (called tides), this throws the center of gravity between the Earth-Moon system about.

Things always rotate on their center of gravity. Here is a test you can perform:

Take a wrench (or something which is ridgid and have has no moving parts), mark a red dot at its center of gravity. If you video tape the wrench falling in midair, the red dot will mark a parabolic path (you can check this by superimposing the frames of the video). The rotation of the wrench will be uniform (ignoring air resistence) because its a ridgid system.

However, when you have non-ridgid system (which is a system where the center of gravity can move about), the rotation of system is not uniform. Take a half-full (optimistic!) jug of milk. If you throw the jug in the air, you can see it rotate about pretty erratically. The reason why the jug rotates erratically is not only because its center of gravity is moving about, but also because it would have to conserve the net momentum.

The Earth-Moon system itself is non-ridgid, the Earth's Oceans (and possibly to an extent, the semi-liquid Mantel of the Earth) makes the earth itself a non-ridgid system within a non-ridgid system. A great deal of Physics later and that is why the current deceleration of the Earth is slightly faster.

I'll explain the Physics of why the significance of the Oceans as simplistically as I can: The Earth's Oceans move about seperate from the Earth. The net momentum of the Earth system is the same, but much of the Angular Momentum will be transferred from the rotation of the Earth to the movement Oceans. That is specifically (in Laymens - or almost Laymens - terms) why the deceleration would be slightly faster.

Does that explanation help?

(And the Moon moving away from the Earth is especially significant.)

 

[chilehed]

Thanks, I feel better now.
But something more advanced would be good. Assume I’m familiar with undergraduate level physics, vector mechanics and calculus.



As I recall I modeled it using the standard solution for the decay of damped vibrations, E(t)=E0e^-(b/m)t. The only unknown here is the damping coefficient b, which is pretty simple to solve for since.



But after having thought about what you’ve said, yes, the damping would certainly be time variant here, for a number of reasons (feel free to revise and extend):

• The rate of viscous losses due to the tides would have been greater in the past when the angular velocity was higher.
• The core temperature of the earth is due in part to tidal effects in the rock; at first it would have been relatively cool, so the viscosity of the mantle would have been higher before the core temp stabilized.
• Tidal effects would have been greater when the moon was closer.
• I’m also wondering if there’s a component due to a phase shift between the line of action of the gravitational pull and the actual position of the tidal peak. If the peak tide lags the line between the earth and moon, might that result in a moment that would retard the rotation of the earth? (This sounds pretty goofy to me since I’m used to treating objects as point masses when doing gravity calculations, but I haven’t had the opportunity to really sit down and think about it)

About the moon moving away from the earth, I’ve not thought about it much before but to me that means that it’s gaining orbital momentum, which has to be coming from somewhere. The light’s just now going on in my head about the gravitational coupling of two bodies, the center of gravity of the system and how the slingshot thing works, but I have to go to bed now. Why don’t you give me a bit more and I’ll compare notes.

 

[dan00000]

I'd say start from scratch again.

http://www.cnn.com/2004/TECH/science/01/01/leap.second.ap/index.html

 

[fungle]

Take out pluto. what happens to the earth?