Re: North Pole

["John S. Denker" <jsd@MONMOUTH.COM>]

Michael Edmiston wrote:
> John (Denker)... Sorry we're having problems, but I think
> you are using words interchangably that are not synonyms.
>
> You are using ecliptic and orbital plane as synonyms.  They are not.

But they describe the same physics.  If one precesses,
the other does.  So I use them interchangeably, even
though they are not nit-for-nit synonymous.

> The orbital plane is, well... the orbital plane.

OK.

> The ecliptic is the intersection of the orbital plane
> with the celestial sphere.

Exactly.

> The celestial sphere is polar defined.

No, the celestial sphere, to follow M.E.'s example, is
the celestial sphere.

The celestial sphere has physical reality quite independent
of what coordinates, if any, somebody imposes on it.

By way of analogy:
 -- Vectors are not defined by the coordinate system (if
  any) in which somembody (if any) chooses to project out
  components.
 -- Numbers have a reality independent of the base or font
  in which somebody (if any) chooses to write numerals.

I made it clear, I thought, that when I said the ecliptic
was not precessing, it was not precessing relative to the
fixed stars.

> Therefore, if the pole
> moves with respect to the fixed stars, then the stars
> change their locations on the celestial sphere.

No, the fixed stars are fixed.  This seems clear.  Obvious.
Tautological.  Changing your choice of coordinate system
does not cause things to move.

There are techniques for writing down the equations of
motion with respect to a changing coordinate system, but
these are far-from-elementary techniques.  If anybody
really wants to get into this, we can get into it.

For a discussion of the methods of (and the importance
of) the coordinate-free approach to doing physics, I
recommend Misner, Thorne, Wheeler _Gravitation_.

> And the orbital plane, as you said, stays with the fixed
> stars,

and so it does

> so that means the ecliptic goes to a new position on the
> celestial sphere.

On a couple of occasions they renumbered the area-codes where
I lived.  That doesn't mean that my house moved, or that my
phone moved, in any physical sense.  Relabeling the coordinate
system is not "motion" or "precession" according to any
physics I've ever heard of.

> There are two problems (1) physics definitions, (2) context of our discussion.
>
> (1) The ecliptic is defined as the intersection of the orbital
> plane with the celestial sphere.

OK.

> The celestial sphere is polar defined.

This is getting repetitive.  This is still wrong physics
for the reasons described above.

> Therefore the ecliptic is drawn on a sphere that is
> oriented with respect to the north pole.

The physics of spheres is not oriented.  Your chosen
coordinate system may be oriented in a way of your choosing.
Others may choose coordinate systems that they find more
convenient.  The sphere is unchanged by any such choice.

Correct physics is _always_ independent of choice of
coordinate system.

It's like dimensional analysis.
 == If the dimensions don't work out, it's "tilt, game over".
  The calculation is guaranteed wrong.
 == If the question of whether something moves depends on
  the choice of coordinate system, it's "tilt, game over".
  The calculation is guaranteed wrong.

> In you earlier post you specifically
> said your words (Yes, but that's almost trivial to observe...) in response to
> my statement about finding the solar system angular momentum.

I made a mistake there.  Perhaps I misread the sentence to
which I was replying.  Another way of saying the same thing
is that I re-organized my reply and inadvertently wound up
with the wrong antecedent to my relative pronoun ("that").
I intended taht passage to refer to the the earth's orbital
angular momentum.

> Please don't quote our discussions out of context.

I wasn't intentionally taking anything out of context.
What I wrote changed from note to note because the
second time I got it right.  I didn't notice until just
now that I got it wrong previously.

To clarify/summarize what I meant to say in both previous
notes:
 -- earth's orbital angular momentum: easy to observe and relevant
 -- total system angular momentum: hard to observe and irrelevant

I continue to believe that it is physically reasonable
and appropriate to determine where the earth's orbital
angular momentum points relative to the fixed stars.
I continue to believe it is almost trivial to do that
according to the method I described.  The only thing
that makes it less-than-entirely trivial is that you
can't see the fixed stars in the daytime, so you need
to interpolate a little bit.

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