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Re: North Pole



Michael Edmiston wrote:

John says the celestial sphere is not polar aligned, and I say it is.

That's a clear statement of the disagreement.

In the phrase "the celestial sphere" note the use of
the words "the" and "sphere". I consider this wording
to be !!not!! synonymous with "a celestial coordinate system".

John says the stars do not change their positions on the
celestial sphere. I say they do.

Again, clearly stated.

This boils down to the definition of celestial sphere.

Probably.

* * begin quotations * *

Just as we use the earth's poles and equator as reference marks on the earth, we can use corresponding reference marks on the sky.

I agree with that quote completely. It supports my
point. We _can_ choose a coordinate system. We can
also choose other coordinate systems. Or no coordinate
system.

On the earth, as in the sky, coordinate systems are chosen
on the basis of convenience. Examples include
-- the geomagnetic definition of north/south/east/west
-- on the SF Peninsula, "east" means toward the bay and "west"
means toward the ocean, while "north" means toward SF and
"south" means toward Silicon Valley, even when those directions
are inclined more than 45 degrees away from the corresponding
E/W/N/S directions as defined by the earth's spin. For example,
see
http://maps.yahoo.com/py/maps.py?Pyt=Tmap&&csz=Menlo+Park+CA+&Get%A0Map=Get+Map
in which Highway 101 is a north/south road.

The celestial poles and celestial equator are defined by the earth's rotation.

Again I agree with the quote. It supports my point.
It defines "pole" and "equator".
It does not define "sphere".
The sphere has a physical reality quite independent
of whatever coordinate system (if any) somebody imposes
on it.

In the northern sky, [stars] appear to revolve around a point
called the north celestial pole, the point on the sky directly above
the earth's North Pole.

That describes the motion on the timescale of a day,
to an excellent approximation. If we take a timescale
a million times longer, that approximation breaks down.
I think the author of that quote can be forgiven for
silently making that approximation. But it remains
an approximation, not a definition.

In fact, the celestial poles and equator are the basis for a
system of precise celestial coordinates much like the system of
latitude and lingitude on the earth,

Again I agree with the quote. It supports my point.
It speaks of poles and equator and coordinates. If
M.E. is seeking a definition of "the celestial sphere"
he must look elsewhere.

But we must beware. These critical reference marks on the sky
are moving, and that can tell
us something new about the motion of the earth.

Again this supports my point. Note the use of
the word "beware". That is a warning that the real
physics behaves one way, while the arbitrary "reference
marks" behave another way.

Also.... If the reference marks
are moving, we can ask "moving relative to what".
Correct answers include: the arbitrarily-chosen marks
are moving relative to the sky itself, moving relative
to the fixed stars, moving relative to the celestial
sphere, moving in absolute terms.

Note that angular momentum and (therefore) precession are
absolute, not relative. Observers in different reference
frames (with a relative velocity) might observe different
values for the straight-line momentum of an object, but
they will always measure the same _angular_ momentum.

Angular momentum is conserved. If you have chosen a
coordinate system in which angular momentum seems not
to be conserved, you have done something wrong. There
are (non-elementary!!) techniques for dealing with
accelerated coordinate systems, but they require carefully
redefining what one means by "fixed" and "moving" and
generally reformulating all the laws of mechanics. It is
just plain wrong physics to use an accelerated coordinate
system without doing the required reformulations.

...earth's axis [precesses] in a conical motion, taking about
26,000 years for one cycle. Because the celestial poles and the
equator are defined by earth's rotation, precession changes
these reference marks.

Again I agree with the quote.
It speaks of reference marks.
It does not define "the celestial sphere".

Over centuries precession has dramatic effects. For example,
it makes the celestial poles move across the sky. Egyptian records
show that 4800 years ago the north celestial pole was near
the star Thuban (a-Draconis). The pole is now approaching Polaris and
will be closest to it about AD 2100.

Again I agree with the quote.
Again I don't see the word "sphere" there.
Again "the sky" has physical meaning separate from "the poles".

* * end quotations * *

That's the definition of "celestial sphere" in all the astronomy
books.

Unless my computer is lying to me, the word "sphere" does
not appear in any of those quotes. Using those quotes to
define "the celestial sphere" isn't a definition as I
understand the concept of definition. Perhaps there is
a new way to define "define" that I am unware of.

This posting is the position of the writer, not that of Harry, Ron, or
Hermione.

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