Re: Angular momentum considerations

On Aug 23, 7:18 pm, don findlay <d...@xxxxxxxxxxxx> wrote:
Stuart wrote:
This is a repost of a post I made nearly 5 years ago.

Its still relevant.

The Williams study I have referenced in this forum shows that the
history of
changes in the length of day inferred by tidal rythmites is
incompatible with
models which propose large changes in the Earth's inertia (greater
than a few
percent). At least one EEer chimed in that Willimas assummed a
constant mass
for the earth. I pointed out that if we assummed the Earh's mass grew
in
proportion to its size, the change in inertia would be (Rn/Rc)^5 where
Rc in
the Radius at the beginning of the Cambrian and Rn is the radius at
present.
Maxlow, an EEer, frequently cited by other EEers proposed a factor of
4 change
in radius since 600mya.

Even a factor of two change yeilds a lower bound change in Inertia of
32 for
the earth.

Most of you know that this alone implies that the rotation of the
Earth would
have been some 30 or so times faster at 600mya, which is at complete
odds with
the rythmite analysis.

But lets consider some other affects besides the obvious affect on the
Earth's
rotation. Well at least obvious to anyone but EE supporters.

Lets allow the Earth's mass to change. What does that do to the Lunar
orbit?

Lets assume circular orbits.. it makes tha analysis easier, and I
doubt it will
fundamentally alter the conclusions.

Lets assume the moon's orbit is perfectly circular.

Then GMeMm/R^2 = MmRV^2

Where G is the gravitational constant, Me is the mass of the Earth and
Mm is
the mass of the moon, R is the raidus of the lunar orbit and V is the
linear
velocity of the moon in its orbit.

Suppose the Earth moon system at some point in the past is described
by

GMe1=R1V1^2 (1)
where the subscript 1 denotes past.

At current

GMe2=R2 V2^2 (2)
where 2 denotes current.

We have Me2 > Me1.

While the Earth's mass is growing, the angular momentum of the lunar
orbit is
conserved (we'll ignore changes in lunar mass for now), as there are
no
external torques being applied to the system.

Thus we have at time 1

L=MmV1R1

and at time 2

L=MmV2R2

Thus we find that V2= V1*R1/R2 by conservation of angular momentum.
Plugging
this into equation (2) and dividing by equation 1 we have:

Me2/Me1 = R1/R2

Thus if Me2 > Me1, R2 < R1.

This means if the Earths mass has increased by a factor of two, the
radius of
the lunar orbit has shrunk by a factor of two. This result should not
be
unexpected. If you increase the mass of the earth, the force of
Earth's gravity
increases causing objects in orbit to spiral inward towards the Earth.
Of
course, EE theory demands a larger increase in mass than a factor of
2.

It should be noted that at current, the lunar orbital radius is
increasing at
some 4cm per annum.

If we change the lunar mass as well, at proportinally the same amount
as well
we get:

R2=R1/a^3 where a = Me2/Me2, Mm2/Mm1 (proof is left as an excercise
to the
reader)

Hence doubling both the lunar and terrestrial mass forces the radius
to change
by factor of eight, 4 times faster than by doubling the Earth's mass
alone...

So not only do we have an Earth spinning at least 30 times faster than
present;
but the moon was at least 8 times futher away. This means mucho more
days in a
lunar month.

All of this clearly at odds with data from tidal rythmites.

This is an utter and complete refutation of any hypothesis which
requires a
change by any more than a few percent in mass and/or inertia of the
earth and
moon over the phanerozoic.

There is simply no point in discussing this issue further.

Stuart

Hmm, ..perhaps more relevant to this discussion is how
< rotation inside the atom> : <atomic force>
= rotation outside the atom : <gravity>
..when the analogy of the atom as a microcosm of orbital dynamics is
readily made.

You need to come out your shoebox of 5 years ago, Stu


Yeah.

That analogy went out of business 80 years ago.

Stuart

.

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