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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Longhand Sight Reduction
From: Peter Monta
Date: 2014 Jun 12, 12:18 -0700
http://en.wikipedia.org/wiki/Lattice_multiplication
but turned on its side and with the low-order terms dropped. The aim was to calculate one or two places beyond the least-significant digit of the inputs, then round. Almost always this will give the same result as rounding the full-precision product (and for even lower expected error at very small additional cost, one can add a bias term before rounding to represent the dropped terms). Computer arithmetic people worry about this sort of thing because the factor-of-2 savings is very attractive; I'm sure there was historical precedent too, before log tables took over the medium-precision market.
Perhaps it's better just to do the full-precision multiplies. The aim was to have a very robust, simple, desert-island-derivable method with no complications. Your polynomial approximations sound fine, but our desert-island resident would have to devote time to reproduce them without high-tech aids (of course, if you're on a desert island, you have plenty of time).
So no-table sight reduction seems tractable. The other part of this is the almanac, and here we really have to memorize a few numbers. The minimal set might be something like (ra,dec)@J2000 of half a dozen bright stars plus the expression for sidereal time at Greenwich (including an estimate of the current delta-T). The Sun seems a bit too complicated to memorize to any usable accuracy, let alone the Moon and planets; but any of these bodies could be used as "transfer standards" by measuring them against the stars.
Here are my assumptions, which are of course pretty absurd:
- available: sextant; chronometer showing UTC; pencil and paper
Cheers,
Peter
From: Peter Monta
Date: 2014 Jun 12, 12:18 -0700
Hi Hanno,
The multiplications show each partial product separately in the array. It's less compact than the usual method, but somehow I find it more reliable to add up everything at the end. It's essentially the lattice method:http://en.wikipedia.org/wiki/Lattice_multiplication
- not available: tables or any other computational aid; almanac
- known: micro-almanac of a few stars; sight reduction algorithmHanno, just read your reply: yes, exactly, Napier's bones. The desert-island guy might well want to make a set.
