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Subject: Re: Towards a basis for Bruce Stark's Tables
From: John McKeel (jgmckeel-250927) (jgmckeel@XXX.XXX)
Date: Fri Jan 03 2003 - 11:22:01 EST
Good Morning Fred,
Just a quick point of clarification. Were you using an artificial horizon
with the Mark 3? I am using a Mark 2 twice a day to practice with in the
parking lot outside my office along with the Davis artificial horizon and
some used motor oil. My results are regularly within 2 miles and often much
closer than that. I have been able to do lunar sights and on the rare
morning, Venus, with the same results.
It wasn't that way when I began though. The Davis "telescope" is a bit
"persnickity" and the IC can change radically from sight to sight. I also
found Bruce Bauer's suggestions (The Sextant Handbook) for checking the SD
very helpful.
I am looking forward to the day when I can buy a "real" sextant. Having said
all that, I'll go back to "lurking" and learning. This new hobby and the
posts on this list have sent me back to the community college to take the
math classes I skipped in favor of Greek and Latin!
Cheers,
John McKeel
Phoenix
-----Original Message-----
From: Fred Hebard [mailto:Fred@XXX.XXX]
Sent: Friday, January 03, 2003 12:35 AM
To: NAVIGATION-L@XXX.XXX
Subject: Towards a basis for Bruce Stark's Tables
OK, some history of this major obsession of mine,
I used to sail and do coastal piloting, and always wanted to do celestial,
but have lived inland for 30 years. Then I noticed the price of a Davis
Mark 3 on the Celestaire site and bought it. Then of course spent hundreds
of dollars on sight reduction books when I couldn't get my position down to
better than 20 miles, trying to figure out what was going on. Thought maybe
elevation above sea level was involved, but in my case that's a half mile
difference in a 6000 mile radius of the earth; elevation affects lunar
parallax and refraction a bit, but not much more. Finally got my position
to about 2 miles once. Decided I needed a better sextant. Got a 1948 Husun
Mate on Ebay for a little more than $200 because the batteries had burst the
handle; but the enamel was not noticeably chipped in any of the photos and
all the parts were there. Found I would have to remove the index arm to
remove the handle for repair. Delayed doing that. Ran a lunar and got to
within 12 seconds of GMT! Maybe that Husun was OK, but handle needed
fixing. So removed index and fixed handle, but feared destruction of the
calibration due to a small blunder while removing index. To check
calibration, I would like some accurate interstellar distances, thus need to
apply Borda's method to correct for refraction. But how do all those tables
in Bruce Stark's book work? A far more abstruse question.
Table K, one of the big ones, is log(haversine()). Found a reference to
Gauss' formulas at http://mathworld.wolfram.com/SphericalTrigonometry.html .
They are similar to Napier's formulas. So one of those must be the formula
for the Gaussian table. It clearly is not the normal approximation to the
binomial.
I have gotten about as far as this as I have time, and sure would like to
see Bruce Stark's method laid out in detail. It appears to be a fairly
straight-forward application of log haversines to spherical triangle
trigonometry. He appears to be using Borda's method for clearing the
distance, and the standard method for computing intercelestial distances
(with no correction for refraction).
Here is as far as I've gotten with his method for computing intercelestial
distances. Let del(GHA) be the absolute value of the difference in GHA
between the two bodies, del(dec) be the corresponding value for
declinations. ~ is the operator for finding the absolute value of a
difference. Mdec is the declination of one body and Sdec the declination of
the second; logs are to the base 10; hav is haversine; archav its inverse;
and Gauss are values from his Gaussian table:
=archav{-Gauss[(log(hav(del(GHA))) + log(Mdec) + log(Sdec))
~log(hav(del(dec)))]
+ [log(have(del(GHA))) + log(Mdec) + log(Sdec)) ___or___
+ log(hav(del(dec)))]}.
The ___or____ function chooses the lesser of the two values.
So what is the Gaussian, and how do you hook all these guys together in
standard mathematical notation? Hopefully, this will help and inspire
somebody, maybe Bruce, to lay this out!
Thanks,
Fred
-- -------------------------------------------------------------------------- Frederick V. Hebard, PhD Email: mailto:Fred@XXX.XXX Staff Pathologist, Meadowview Research Farms Web: http://www.acf.org American Chestnut Foundation Phone: (276) 944-4631 14005 Glenbrook Ave. Fax: (276) 944-0934 Meadowview, VA 24361 As an Insight TechBuyer subscriber you are automatically entered for a chance to win our monthly prize. Sign-up for Insight TechBuyer today to start receiving our weekly e-mail newsletter that keeps you up-to-date on the latest technology products, exclusive product deals, technology services offerings, and keeps you posted about the latest news from Insight. Visit http://www.insight.com and select "Manage Subscriptions" under Resources to sign up for TechBuyer today.
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