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Re: North Pole



Gary Turner wrote:

Maybe clarify the posts b/w John and Michael (then again, I could be
completely wrong!)-

Naaa. By the end, we agreed on the physics; we were
just quibbling about terminology ("the celestial sphere").

In contrast Gary is discussing serious physics:

The precession is the rotation of one vector about another.

OK. I never thought of it that way before, and I
don't consider that the "definition" of precession,
but it is a true statement about precession.

The precession
of the Earth's spin axis is typically considered to be the rotation of that
angular momentum vector (associated with the Earth's spin) about a vector
perpendicular to the ecliptic (defined by the Earth's orbit) - the Earth's
orbital angular momentum vector

Not so fast.... Over the short term (18 years or so) the
precession is dominated by the _moon_. The earth's angular
momentum bivector undergoes a rotation in the plane of the
earth/moon orbit. Over the long term (26,000 years) the
sun gets into the act. Both contributions are readily
observable.

To talk about the precession of the orbital plane, you would have to have a
second reference vector

Yes and no:

1) We could _talk_ about precession of the orbital plane
in absolute terms. We could use the precession itself
to define the second vector; it need not be some a_priori
"reference" vector.

Remember, angular momentum is absolute. It doesn't have to
be relative to anything. (This is dramatically different from
straight-line momentum.)

If for technical or pedagogical reasons you wanted a "reference
vector" you could make one from scratch using a plain old
gyroscope.

2) OTOH if we move beyond mere talk to actually physically
_causing_ the precession, we would need a pretty hefty cause.
Precession involves adding angular momentum to something
that already has angular momentum.

http://www.monmouth.com/~jsd/how/htm/motion.html#fig-angular-precession
The thing causing the precession doesn't need to accumulate
angular momentum forever, but it does need to accumulate
it over a half-cycle or so. So if it is going to cause
precession of the earth's spin, it will have to be bigger
than a breadbox.

The angle between the ecliptic and spin axis does not change
(significantly).

Actually it does, due to the moon. But that averages
out over a multi-century timescale. All in all, if
the pole is considered a pencil drawing on the sky
(what *I* call the celestial sphere :-) it can be
described as drawing a series of short-wavelength
S-turns superimposed on the longer Platonic cycle.

The angle between a plane and a vector always causes
problems IMHO,

Huh? What problems?

Or.. . Represent them both by bivectors (or, failing that,
represent them both by pseudovectors) and there will be
even less problems.

This posting is the position of the writer, not that of Willow, Xander,
or Buffy.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.