How constant are constants? - ice skating

[harrisonorbit]

I recently read a thread that pointed to some constants that caught my attention. Before I go off the deep end with a question it would seem to be a good idea to understand exactly how constant are certain constants. I'm specifically curious as to the constants of:
Length of a day (sidereal day, solar day and or Stellar day)
Length of a year (Sidereal year/stellar year)

Also what could impact these figures? I mean..."global climate change" could effectively change the position of the mass of the earth. This changes it's physical properties and density.

Imagine if you will, the ice skater. When they pull their arms in the rate of rotation increases noticeably. They let their arms out and the speed decreases. (http://answers.yahoo.com/question/index?qid=20080424125806AAxYP2g")

So, if the water from the ice caps all melts and shifts to the oceans the the Earth's mass near the equator increases...I.E. ice skater letting arms out.

Wouldn't the speed of the planet's rotation change?

Decrease?

 

[DaveC426913]

Wouldn't the speed of the planet's rotation change?

Decrease?

Yes. By a small amount. I would guess on the order of < second per day.


BTW, those aren't constants; those are measurements.

 

[tony873004]

The length of a day aren't considered "constants" because, as you point out, there's things that can cause subtle changes.

I think you're right that the Earth's rotation would slow down if mass shifted from the poles to the equator. But it would be insignificant. The bulk of Earth's mass is below the surface.

Perturbations from the other plants, and the Sun's non-constant mass will cause small insignificant changes to the length of the year, so it's not constant either.

 

[harrisonorbit]

Well...someone needs to write a letter to these guys! Mis-leading poor saps like me...

http://hpiers.obspm.fr/eop-pc/models/constants.html#rotation"

Thank you for the response.

Now that I know the theory is plausible...how would I calculate (roughly speaking) how much the changes in mass would impact rotation speed?

Where I'm going with this...theoretically speaking, think way off in the future..global warming evaporates all the water off the planet surface and the water, for the most part (99.99% of surface water), is trapped in the atmosphere...not on the planets surface.

I'm curious as to how this would impact the length of a day and the length of a year.

PS, since constants aren't so constant, year not being a year and a second isn't quite a second unless you are on Earth time etc...what is a true universal constant for time that can be used in the equitations?

You guys are awesome! Thanks!

 

[D H]

Ignoring relativistic effects, a second is a second. The number of seconds in a day does vary because of changes in the Earth's rotation rate. Long-term variations result primarily by exchange of angular momentum between the Moon and the Earth. These changes will overwhelm the affects on the Earth's rotation rate resulting from the slight changes in the Earth's inertia tensor caused by global warming.

Nonetheless, the affects are observable if you look closely. For example, the Earth's land surface is concentrated in the northern hemisphere. Mass transfers from the Equator toward the North Pole during northern hemisphere winter and back again during northern hemisphere summer. This results in a seasonal variation of the length of day.

Length of a year (in seconds) varies only slightly, and slight changes in the inertia tensor will not have any measurable affect on the length of a year.

 

[harrisonorbit]

Awesome, thank you!

In regard to the Earth's liquid water mass I read:

The mass of all the water on the planet is estimated at 1.35 x 10^18 metric tons. The total mass of the planet is 6 x 10^21 metric tons. This gives a ratio of 1 to 4400. This comes out to 0.023%.

Now, to calculate what would happen if 0.023% of the Earth's surface mass relocated into the atmosphere.

I'm thinking out loud here...when the ice skater spins...it's only the arms that move in or out...not the core, the person's body. The water is on the outside of the planet...while only making up 0.023% of the mass...it's located on the outside...

The ratio isn't right...but if 0.023% of our year disappeared...again, this isn't right...we'd loose 0.08395 days or two hours out of the year!

I don't even know where to begin to give a real calculation!

Ideas?

 

[DaveC426913]

If Earth's oceans relocated to the atmosphere, a two-hour shorter year would be low on the list of Things to Worry About.

 

[harrisonorbit]

Thank you for that astute observation. Very helpful, glad you brought that up.

 

[tony873004]

If the all the Earth's water relocated to the atmosphere (which it can't), it would not effect the length of a year. Period is 2*pi*sqrt(a^3/(G(M+m))). If you want to change the period of the year, you either have to change Earth's semi-major axis, or its mass. The distribution of mass is irrelavant. And even if you could change its mass, it would have an insignificant effect on the length of the year, as the Sun is over 300,000 times as massive as Earth, rendering "little m", the Earth's mass, in the above formula insignificant.

 

[Janus]

Awesome, thank you!

In regard to the Earth's liquid water mass I read:

Now, to calculate what would happen if 0.023% of the Earth's surface mass relocated into the atmosphere.

I'm thinking out loud here...when the ice skater spins...it's only the arms that move in or out...not the core, the person's body. The water is on the outside of the planet...while only making up 0.023% of the mass...it's located on the outside...

The ratio isn't right...but if 0.023% of our year disappeared...again, this isn't right...we'd loose 0.08395 days or two hours out of the year!

I don't even know where to begin to give a real calculation!
Ideas?

As pointed out, the year wouldn't change, only the length of the day would get longer.

For a rough, off the cuff, estimate, you can assume that the existing water forms a hollow shell of no thickness at the surface of the Earth and moving the water to the atmosphere forms a hollow shell at say, 80km above the surface. Then you can figure the moment of inertia of the water in both situations, and find the difference. This will give you the change in the moment of inertia in the Earth. Then, taking into account the moment of inertia of the solid Earth itself, you can determine what change in the rate of rotation the Earth would have to undergo in order to maintain angular momentum.

Without going into the details, I calculate that the change in the length of day would be less than 1 millisecond.

This shouldn't be taken as an accurate value, but more of an upper limit.

 

[harrisonorbit]

AWESOME! Now this is what I'm talking about...

Janus: Dead on! Just what I was thinking about.

tony873004: Thank you, the formula and explanation gives me a more realistic understanding.

Can it be said that the speed of rotation (length of a day) has NOTHING to do with the length of a orbit? (year)

If so, why do planets bother rotating?

Thank you all for your extreme patience!

 

[Tomtom]

The length of a day has nothing to do with the length of a year; in seconds.
However, if you measure the length of a year in number of days, and the speed of rotation of Earth increases, there will be more days in a year. Do you see the point?

Planets bother rotating because something set them off that way ;)

 

[harrisonorbit]

Ok, I grant you if the orbital speed stayed the same and the rotational speed increased, yes, there would be more rotations per year.

"Something set them off that way"

Ok - is that to say if the Earth started rotating (for some unknown reason) at twice the speed and we had 12 hour cycles (vs 24 hours) and we had 730 days (vs 365)...but the length of the year measured in seconds (not days) would stay exactly the same?

Just want to make sure I understand correctly.

Thanks!

 

[DaveC426913]

"Something set them off that way"

Ok - is that to say if the Earth started rotating (for some unknown reason)

The planets rotate because they were formed from masses of gas and dust, which, when summed will always have a net movement. You'd have to look long and hard to find a volume of dust and dust out there whose movement, once you added it all up, was exactly zero.

As the gas and dust accumulates in a smaller and smaller volume its angluar momentum is conserved so that the final solid planet - like the spinning skater - is rotating at a fair clip.

 

[Tomtom]

The length of a day has nothing to do with the length of a year; in seconds.
However, if you measure the length of a year in number of days, and the speed of rotation of Earth increases, there will be more days in a year. Do you see the point?

Planets bother rotating because something set them off that way ;)

100% correct ;) The amount of spin the Earth has, hasn't got anything (okay, perhaps very little for very perfectionist gravitational reasons) to say for the amount of time the Earth uses to spin around the sun.