# Calculation of Earth's precession

*From*: "El Enrrabadore-mor" <enrrabadore@xxxxxxxxxxxxxx>*Date*: Thu, 15 May 2008 20:26:35 +0100

Earth is a gyroscope.

Earth precesses at a rate of 2.45*10^-12 rad/s measured

by astronomers (25,800 Years per turn).

Mach Principle says that without a force / torque a gyro

won't precess. Precession is due to inertia caused by the

centrifugal force of the spinning mass.

Centrifugal force requires a rigid point in space.

Hence, without a rigid fixed point in space gyroscopic

effects cannot occur.

Nevertheless, Earth precesses and many other celestial

bodies precess too, inclusive relativistic pulsars.

As far as I was taught by the experts, relativity pretends

to have field equations that can explain pulsars precession.

Experts also claim that relativity reduces to Newton

Theory for small relative speed, like the Earth for instance.

That's amazing, because if that were true, all we had to do is

to use the obvious simplification of relativity field equations

and get the gyroscope equations.

Since physics has no good equations for the gyroscope,

how am I supposed to believe on relativity field equations?

Earth is precessing and the only cause one can figure

to cause a torque is the gravity force over Earth bulge.

One can assume that Earth's orbit is a fixed line in

space, made of points where one can pick up an

instantaneous fixed point.

A little trigonometry and math is enough to show that

such torque is a sine square function over one Year,

so that to cause Earth's precession on average.

To understand what I'm talking about, it will be good

to read the following explanation by the middle of

the link below:

http://mb-soft.com/public/precess.html

The chapter on "Precession of the Earth's Axis"

explains it very well, starting at 6th paragraph,

and also adds a 19-Years nutation due to the Moon.

So, due to the Earth's equatorial bulge, one must have

nutation changes with 1-Year period and 19-Years

period, respectively (see article).

The problem is very well explained and everybody can

understand it (just read the article above).

The article was written by a physicist that claims:

1 - To have calculated a value of 25,700 Years period of

Earth precession, due to Sun-Moon only, to compare

with the actual measured value 25,800 Years, which

obviously is a very good approximation.

2 - That torque caused by Sun-Moon over the Earth's

bulge is a sine squared function, like this:

- Zero at 21 March.

- Maximum at 21 June.

- Zero at 21 September.

- Maximum at 21 December.

Therefore a net torque on average was calculated.

The claims made by the physicist caused obvious

predictions - A continuous motion due to nutation

over the Year, which doesn't cancel out on average,

since it was that same average term the heart of the

explanation.

By the end of the article, the physicist complains

about the following:

QUOTE:

"Assorted comments have been received since this

page was first placed on the Internet in 1998. I have

been somewhat amazed to find that there are many

people who claim that there is no such motion of the

Earth, that it is too slow of a process to have ever

been confirmed! Wow! I have been sometimes

tempted to ask if those people also believe in a

"flat Earth"!

END QUOTE.

The Earth's precess and one should be able to

calculate the torque and the precession rate to

be close to that of the actual value measured.

The Earth looks like a gyroscope that have found

a fixed orbit/point in space to cause precession

due to applied external torques on the equatorial

bulge.

And of course that Earth's equatorial bulge is

due to centrifugal force - a REAL force that

had REAL consequences at the equator.

What's an interesting point is how the physicist

gets the right result with the wrong equations.

In the chapter "Deeper Math regarding Precession

Beginning" the equation used was Euler's equation:

T3 = I3 dw3/dt + (I2 - I1) w2 w1

being I1 w1 the gyroscopic moment.

The right equation must be:

T3 = I3 dw3/dt + I1 w2 w1 sin(theta) +

+ (I1 - I2) w2^2 sin(theta) cos(theta)

Or else, since I3 dw3/dt and the last term

(I1 - I2) w2^2 sin(theta) cos(theta) are both

much smaller then T3 = T3max sin(theta)

and I1 w2 w1 sin(theta), we can use instead

an approximate solution:

T3average sin(theta) = I1 w2 w1 sin(theta)

T3average = I1 w1 w2

The whole math explanation on the article above

is a mess, since it considers T3=0 (no external

torques) and all the article explanation was about

the calculation of T3 non-zero on average.

(A sine squared term that changes over time

was explained during 90% of the article, but

now it simply is gone (T3=0).

The physicist calculated a torque due to

the Sun T3 = 1.44*10^22 Nm, and for

the Moon the twice of that value, addictive.

By the end of the article he puts T3=0.

Then it mixes the axis 3 and 2 (typo?).

The formula used (see the numbers used

and what they mean) was:

I3 w3 = (I2 - I1) w1 theta2

(the integral of the above formula,

assuming T3=0).

It's a nice cooking of Euler's equation.

Actually a very good cooking in general.

The final part of the article is pure crap and

a sort of magic cooking of values.

In fact, the physicist of the article claims:

- Conservation of Angular Momentum appears

to be violated, where it is always true otherwise.

As the precessional motion begins, angular momentum

"appears" where it had not existed before. This is unique

in the field of Physics!

- And of course, it is up to take energy out of

that violation: http://mb-soft.com/public2/earthrot.html

Basically the physicist looks like a crank.

Even so, that crank is the best that Physics have, so far,

(the article was pointed to me on this thread by

someone that looks like a non-crank physicist).

Now, since dw3/dt is very small and negligible,

if the calculations of I1 and I2=I3 are right, and

T3average = 4.55*10^22 Nm (Sun+Moon) I should

be able to calculate Earth's precession w2.

w2 = T3average / I1 w1 =

= 4.55*10^22 / (8.7*10^37 kg m^2 * 7.292*10^-5 rad/s) =

= 7.17*10^-12 rad/s

The actual value measured is 2.45*10^-12 rad/s

Yep, one must forget the Moon because on average the

torque is zero (one needs to look careful on the error made by

the physicist on Moon's analysis - it's due to the Moon's

eccentric orbit and it cancels on average), and one gets the

correct value:

w2 = T3average / I1 w1 =

= 1.44*10^22 / (8.7*10^37 kg m^2 * 7.292*10^-5 rad/s) =

= 2.27*10^-12 rad/s

(To be compared with 2.45*10^-12 rad/s measured).

Voilá, Earth's precession explained with NON-ZERO

torque as it should.

T3 was calculated by the physicist of the article for

the Sun (Moon is out because on average is zero,

according to my analysis of the problem).

The Earth total inertia moment (of the whole sphere)

is 8.7*10^37 kg m^2, as said in the article.

Earth's daily (24 hours) angular velocity is 7.292*10^-5 rad/s,

as said in the article.

And I got the right value without any cooking or crap.

.

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