A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2010 Apr 3, 16:57 -0700
Peter H, you wrote:
"A fitting formula has a smaller "footprint" compared to a large table. I find this to be a convenient memory-saving approach, especially in Excel."
And Antoine, you wrote:
"using the generally VERY MUCH SMALLER "footprint" given by the fitting formulae or equivalent is the way to go."
Heh. You guys haven't tried it. :-)
Here's a challenge for you (hypothetical --I don't really mean it as a challenge): On whatever device and/or computing environment you favor, how many bytes does it take to represent the values of Delta-T for the period from, let's say, 1750 to 1950 using a table and simple linear interpolation only? And how many bytes does it take to do the same thing with those polynomials from Espenak's NASA web page? Note that the latter includes SIX different polynomials one of which is 7th order. And let's suppose that we want the values to agree with no more than 1 second difference for dates before 1875 and no more than 0.25 seconds difference for dates after 1875. Feel free to set your own rules. Can you come up with a set of rules where the polynomials win?? Frequently with data like this, a table is all you need.
But of course this is just calculational minutia and I don't really expect you to bother with it. I'm only commenting on this because I have in fact considered the options.
Antoine, you wrote of my wisdom and brilliance:
"Thanks to his superior and far seeing approach we are all able to benefit from a number of his recent innovations in which computations are almost finished before they are ever started. "
Yes, I have already completed my computation for the meaning of life, the universe, and everything, and you didn't even have to ask. Do you want to hear it? You're not going to like it... It's concise at least. I think it would even fit in the spare memory on one of your favorite calculators. :-)
"If you only have limited storage, or if your environment constraints require you to fit ALL your software into a small hand-held calculator without losing ANY accuracy - at the sole expense of a much increased computation time, while still achieving a sufficient speed compatible with sailing or even real time Jet Aircraft operations - then using the generally VERY MUCH SMALLER "footprint" given by the fitting formulae or equivalent is the way to go."
Absolutely! If you've decided to work with some device or environment with extremely limited memory then you should make this trade. But after all, you're talking about amusement here. If you're working on any normal computer or even a mobile phone today, this is no issue at all.
And you wrote:
"Frank seems to have a huge storage space compared to what some others have"
Interesting possibility but REALLY unlikely. I am no technological leader by any means. I own more sextants than computers even though I do code for my "daily bread". My mobile phone is 2.5 years old and literally starting to fall apart, yet it has 500 megabytes of storage, standard. My six-year-old camera has a gigabyte. Either of these devices could hold thousands of years of arcsecond accurate ephemeris data (properly stored, of course --not as plain text) with plenty of room to spare. My computer is relatively new since the one from 2002 failed last summer. It has a 300-gigabyte hard drive. Are these unusual numbers for NavList members?? I don't really think so. For what it's worth, the entire suite of data and applications to generate lunar distance data, clear lunars, and generate complete nautical almanac data from 1750 through the present on my web site occupies less than 14 megabytes. I understand that this would not possibly fit on an old programmable calculator, but that's not a constraint that would affect many people, and if it does, it's by choice --for fun rather than practicality.
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