A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Jan 18, 12:41 -0800
Tony, why re-calculate the positions of the Sun and planets? These numbers already exist. Using equations that appear to determine the planets positions is "so 80s"... Follow the example of the publishers of the almanacs themselves: They don't use algorithms by Meeus or similar. They use the JPL numerical integrations (suitably reduced) as the primary source for the published almanacs. It's a database lookup. You can do the same in your calculator almanac. Just tabulate the positions of the Sun, Moon, planets and navigational stars at uniform intervals. Then your algorithm is simple:
x(t) = x(i) + dx_dt(i)·(t-ti),
or in words, plain linear interpolation by elapsed time between tabulated values at known time. That's the entire "algorithm" for the computation. All of my apps and nearly all of my software products in the past fifteen years have used this methodology. Those books of orbital algorthms by Meeus and others are now obsolete, as far as I'm concerned, in their primary function, and they have been obsolete for a long time. But they're loaded with invaluable detail and bits of information, and I feel lost if I don't have my dog-eared copy of his "Astronomical Formulae for Calculators" close at hand. If you don't have a copy of that little book, Tony, find one. It's been over thirty years since Roger Sinnott wrote the forward to the Willman-Bell edition, and yet a lot of it rings true today. I'm including an image of the cover (note Roger Sinnott's name on there).
For navigatonal purposes, you'll need to decide what accuracy you require and that will determine the interval for tabulation if you decide to travel this route. Nonetheless, you should have no problem reducing each day to about 1k of data or even half as much. Is that too much? This is where we get into fantasies about time away from port, the projected lifetime of our calculators, and so on. Do you really need a database in your calculator that can last for fifty years? Well, no, probably not, even if it's fun to ponder that sort of longevity. How about a year? Can you comfortably reload data once a year? Probably. How about two weeks? Or does that cross a line (I would think so since you might forget to update the almanac data when you really need it)? And note that even if you adopt this methodology, you'll still need to do "some" computation since you'll tabulate the almanac data in some baseline coordinates, probably ecliptic coordinates, and then you'll do various coordinate rotations to get out GHA and Dec or altitude and azimuth.