Re: EASTER NUT

Interesting discussion. It inspired me to find some numbers.

On Fri, 28 Mar 2008 15:54:09 -0500, David Williams wrote:

-> Remember, the *entire* crust of the earth is only about 50 miles thick,
-> and the radius of the earth is about 4000 miles, making the crust only
-> about 1.25% of the radius. The core of the earth is believed to consist
-> mainly of nickel-iron and spinning; thought to be the mechanism that
-> generates the Earth's considerable magnetic field - very much stronger
-> than any of the other rocky planets. Unless the core is absolutely
-> uniform in consistency, there will undoubtedly be shifting of mass as
-> it spins. Even if it is uniform, precession of the spinning mass would
-> cause some shifting, just as the earth itself wobbles. The amount of
-> material in the core is hundreds, perhaps thousands, of times more
-> massive than the entire crust of the earth, let alone just the water, which
-> is only a tiny fraction of the mass of the crust itself. And the core is
-> moving fairly rapidly (hence the magnetic field), which the crust isn't.
:-)

But is the core material moving *radially* at any significant speed? It
would have to do so in order to change the earth's radius of gyration
(or moment of inertia).

http://www.hno.harvard.edu/gazette/1996/08.15/PuttingaNewSpin.html
The whole Earth spins completely around once a day, while the inner
core rotates an extra three degrees or so each year. In approximately
120 years, the planet within completes an extra lap (360 degrees).

How smooth and stable the "surface" of the core is might affect its
moment of inertia; but maybe not measurably based on the following.


Remember that the moment of inertia is <sigma>M.R^2. If R changes, i.e.
material moves toward or away from the axis of rotation, the moment
will change, but the change will be bigger if R is already large. So
moving material in the crust will have a larger effect than a similar
motion in the core.

Some numbers here:
http://nasaexplores.nasa.gov/show_912_student_st.php?id=04021991438

Assume the mass of the Earth is 5.98 x 10^24 kg, and its radius is
6.37 x 10^6 m.

From table on same page: moment of intertia for a uniform sphere is
2/5 m * r^2.

That's too high because most of the earth's mass is at the center.
Let's use 1/3 the actual radius to compensate.

I = 2/5 * 5.98e24 kg * (1/3 * 6.37e6 m)^2 ~ 1e40 kg-m^2

Let's park an extra billion metric tons (1e15 kg) of stuff at 10,000
meters above sea level.

The added moment of inertia is:
I_extra = 1e15 kg *( 6.38e6 m)^2 = 4e28 kg-m^2

Angular momentum = I * w

w = 2pi/day

Angular momentum is conserved. The value before adding the mass must
equal the value after parking the extra stuff at 10,000 meters.

I_1 * w_1 = I_2 * w_2

I_1 *2pi/day_1 = I_2 * 2pi/day_2


day_2/day_1 = I_2 / I_1

The amount of day lengthing due to the added mass would be
(1e40 + 4e28) / 1e40 = 1 + 4e28/1e40 = 1 + 4e-12

4e-12 * 86400 seconds per day ~ 4e-7 seconds per day

About an extra half-microsecond per day.


I think I read that the earth's rotation speed changed measurably when
the earthquake occurred that caused the big tsunami in Asia a couple
of years ago.

I heard that, too. And I believed it, too. I didn't research it
beyond what was said on the "newcast" by a scientist who sat in front
of a computer and talked about how it changed the rotation of the
earth. Maybe it made the "news" more interesting -- or provided some
less-horrific aspect to focus on.

http://earthquake.usgs.gov/eqcenter/eqinthenews/2004/usslav/neic_slav_faq.html
The length of the day can be measured with an accuracy of about 20
microseconds and calculations of the source properties of the
earthquake showed the change in the length of the day to be -2.676
microseconds, or in other words, less than can be effectively
measured.

It would take 50,000 days (more than a century) for a change of 20
microseconds in the length of a day to accumulate to one second.

HTH

Adam

--
Posted via a free Usenet account from http://www.teranews.com

.

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