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Author
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Topic: britney spears vs celestial formulae
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rick
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posted January 19, 2008 01:50 PM
i'm one of those who, while waiting in line at the grocery, would rather rehearse formulae than look at celebrity magazines in the rack
the drill for dec sun, arc-time, and the equation of time are easy
1) how do i connect the eq of time with gha - 175 as shown on the emergency nav card?
2) how is the n(x) table generated?
thanks -
rick
From: boston
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David Burch
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posted January 19, 2008 03:22 PM
Well... that is likely a habit that will serve you better than the magazines in the long run.
One way to think of the EqT is as the difference between 180 and the GHA of the sun at 1200 UTC, which is an angle that you then convert to time as 15° = 1h, 15' = 1m to get the EqT in its conventional time format.
Thus if you have any way to figure the GHA of the sun you can apply that definition to get the EqT. The long term approximate almanac of the sun we provide on the card happens to use GHA-175 as the base approach, but that is purely a math trick to make it always positive. You could make such tables using GHA - 172 or GHA - 160 just as well.
The idea of using 175 means we shift what we compute by 5° because 5° = 5/15 = 1/3 of an hr which is 20 min which is always bigger than 16m which is the maximum value of the equation of time. Put another way, the GHA of the sun at 12Z is never more than 5° different than 180... ie you could not use this trick with GHA - 177.
From: Starpath, Seattle, WA
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rick
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posted January 21, 2008 03:17 PM
ah - very sneaky - now i see - requires conceptualizing gha at 00 gmt instead of 1200
thanks
and should i assume that the n(x) table is generated from some long trig function that only a true geek (as opposed to a pseudogeek like me) would want to know?
rick
From: boston
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David Burch
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posted January 21, 2008 07:41 PM
My apologies, i forgot question (2).
The N(x) table was developed some time in the 80s when we made the Emergency Navigation Card. It was a modification of some thing like the Ageton method, which is turn is something like what is now included in the Nautical Almanac, called the NAO Sight Reduction tables. We simply formulated it slightly differently and shortened the tables by including less entries. And yes, it is a special solution to the spherical triangle using some trig identities--mathematical work, but not that complicated if someone who has worked with even basic trig. There are wonderful websites online these days that offer excellent reviews of all the trig required for this. If you desire more spcific information, i would have to dig out my old notes on this.
For those interested in the various solutions possible, go back to Bowditch in 1977 edition or earlier. That book outlines several possible solutions and i am sure it was our main reference at the time. After the 1977 edition they stopped including these details.
For the most part, it reflects the fact that we had too much time on our hands in those days!
For what it is worth, however, it does still represent the world's shortest sight reduction tables that will in fact reduce any sight.
--david
From: Starpath, Seattle, WA
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