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From: George Huxtable <george@hux.me.uk>
To: NavList@fer3.com
Sent: Tue, 27 April, 2010 4:20:33 PM
Subject: [NavList] Re: Star - Star Distances

Richard Reed wrote, about correcting star-star distances-

"John Karl's book has some more pairs than Bauer (12 I think, upto 113
degrees), with a refraction table for each, but no aberration tables."

============

A bit of care is needed, for those following that route, if using the first
printing (2007) of John Karl's book "Celestial Navigation in the GPS age".
Significant changes were made in that respect in the second printing of
2009 (which is still labelled as first edition).

In that first printing, a wrong assumtion was made. Taking an observer at a
known latitude and a star-pair A and B, it was assumed that if star A had a
known altitude, then that would also define the altitude of star B at the
same moment. The problem with that is that there are two distinct times of
any night when star A has that altitude. These times are equally before and
after the moment of culmination: when it's rising, somewhere to the East of
the observer, and when it's falling, somewhere to his West. And, at those
two times, star B will have two very different altitudes, so the assumption
in those tables breaks down.

As I understand it, John's first refraction correction table considered
(without saying so) only the case when star A would be rising, so it could
be used only when that star was somewhere to the East, not the West, of the
observer. Then, it would give the right answers.

John's later version, in the second printing, handles refraction quite
differently, and gets around that problem.

However, that leaves the question of star aberration, which can shift the
angle between star-pairs significantly, by up to half an arc-minute, or so,
either way, for the most-distant pairs, depending on the geometry of the
observation and the time of year. John, in the first printing of his book,
just accepted the value of aberration at one particular moment in the year
(New Year), which meant that for some star-pairs the worst-case aberration
could be doubled. More recently, he has changed this to ignore star
aberration altogether: a better solution, which limits that worst-case
error. John accepts, in his explanation, that for high-precision work, it's
necessary to take another approach which allows for aberration, as Brad and
Richard seem to be doing.

George.


contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Richard Reed" <richard.reed@idnetfreemail.co.uk>
To: <NavList@fer3.com>
Sent: Monday, April 26, 2010 9:53 PM
Subject: [NavList] Re: Star - Star Distances


Thanks for all that work!

John Karl's book has some more pairs than Bauer (12 I think, upto 113
degrees), with a refraction table for each, but no aberration tables.

For just one pair so far (I really need a tripod!), I went the long way and
got aberration-corrected Right Ascension and Declination from Solex 10.2.
I then used Frank Reed's calculations here:

http://www.fer3.com/arc/m2.aspx?i=015098&y=200404

Using Frank's distance formula on Regulus-Betelgeuse, 62 deg 26.6' in Karl,
without refraction, I got 62 deg 26.94' from both the Solex data and the US
Naval Observatory data.  I then used the Bennett refraction formula as
modified by George Huxtable and used Frank's refraction distance
correction.  I was quite happy to be within 0.2 minutes that time, but it's
only one shot.

Richard Reed

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