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Re: Towards a basis for Bruce Stark's Tables
From: Fred Hebard
Date: 2003 Jan 5, 02:13 -0500
From: Fred Hebard
Date: 2003 Jan 5, 02:13 -0500
I worked out the basis for Bruce Stark's method of computing
intercelestical distances.
He uses logs and Gaussian addition logs to evaluate:
archav{ hav[del(dec)] + hav[del(GHA)]*cos(Mdec)*cos(Sdec) },
where del(GHA) is the absolute value of the difference in GHA between
the two bodies, del(dec) the corresponding value for declinations.
Mdec is the declination of one body and Sdec the declination of the
second; hav is haversine; and archav its inverse.
A haversine equals: [1-cos(theta)]/2. It also has the beneficial
property of equaling: sin^2(theta/2).
Using the same notation, the corresponding standard modern formula
using sines and cosines is:
arccos{ sin(Mdec)*sin(Sdec) + cos[del(GHA)]*cos(Mdec)*cos(Sdec) }.
I'm fairly sure that Stark's method for clearing the distance is a
log haversine version of Borda's method, so ably laid out by George
Huxtable last February
(http://www.i-DEADLINK-com/lists/navigation/0202/0149.html). If anybody is
interested, I will see whether I can uncover the haversine version of
Borda's method. Bruce's earlier post in this thread explains the
Gaussian addition logs used to evaluate the summation before taking
the inverse of log(haversine).
Note also that you could use Bruce's tables for sight reduction to a
tenth of a degree without interpolation, which might save some space
and mind strain.
It was a relief to get this done!
Fred
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Frederick V. Hebard, PhD Email: mailto:Fred@acf.org
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
