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Thanks Bill

I seem to recall reading the terms upper and lower branches of the local
meridian.  Can you define please?

> Not sure this is relevant, but remember that stellar aberration -- the
> annual
> movement of stars' apparent positions due to the speed of the earth in
> orbit
> as a fraction of the speed of light -- will appear to affect the SHA of
> Polaris
> more than other navigational stars, even though its actual position is
> not
> affected more greatly.  This is simply because you divide the position
> change
> by cos(declination) to get change in SHA.

Good to learn that. Did not know, so hard to remember. 

> I would guess that longer-term
> changes in SHA for these stars are related much more to the earth's
> precession than to stars' proper motion, though again I'm not sure this is
> relevant to your question.

Precession was my best guess as to the prime mover.  If the first point of
Aries can move that much in a 2000+ years, and Vega? will be our next pole
star, and it seems to have a 26,000 cycle...
>
> Looking at a list of star SHA's, it appears Kochab's SHA is pretty close
> to 180d away from Polaris's.

That was my take, but I'm just a beginner.

> I suppose the ways to use this info are:
> a) when you think Polaris is east or west of the pole, use its altitude
> directly as your latitude...

Think we are on the same track. My SWAG was if I subtract Polaris's
declination from 90d, I get the distance from the pole. That multiplied by
the sine and cosine of the cardinal angle gives me the rectangular
coordinates (horizontal and vertical corrections).  Or punch in a
polar-to-radial on the calculator using the distance from the pole and the
LHA--or a guess.  I think that in the first case (sine and cosine) the
coordinates need to be swapped, as trig moves CCW from cardinal 90d, and
cardinal moves CW from trig 90d.  An application of sine x = cosine (90-x).
Same with polar to radial--use the x value as vertical, and the y value as
horizontal correction and correct + and - signs for the quadrant or by
simple inspection.

   

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