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    Re: A Nautical Almanac question
    From: Stan K
    Date: 2016 Nov 24, 17:51 -0500
    Dave,

    You ask why I care.  It just bothered me that different respected references say different things.  But I am feeling a little better about it now.

    I do not have a 2007 Almanac, but looking at NavSoft's for your example, I see that, as you said, the d at the bottom of the page is 1.0, but the 1200-1300 d is 0.9.  If I counted correctly, using the rounded values of the differences between the hourly declinations, I get an average 0.97222..., which rounds to 1.0, in agreement with the bottom of the page and in disagreement with the 1200-1300 value.  The question is whether unrounded values would give a different result.

    Interestingly (at least to me) when I use Celestial Tools, which uses the 1200-1300 value, I get a d of 1.0, not 0.9.  The value of declination at 1200 is 1º12.1599..'S (which rounds to the Almanac value of 1º12.2'S, in agreement with the NavSoft Almanac); at 1300 it is 1º13.133...'S (which rounds to the Almanac value of 1º13.1'S, in agreement with the NavSoft Almanac).  The difference between the unrounded values is 0.9734, which rounds to 1.0.  So it appears that the d value at the bottom may be the result of the difference in the unrounded declinations at 1200 and 1300.

    My intuition agrees with yours, that the two values, the average and the unrounded 1200-1300 difference, are identical when rounded to tenths of minutes.  My belief now is that the references that refer to "average" or "mean" are telling the truth, only they are not saying that the average is actually calculated by taking the difference between the unrounded declinations at 1200 and 1300. 

    Stan


    -----Original Message-----
    From: David Fleming <NoReply_Fleming@fer3.com>
    To: slk1000 <slk1000---.com>
    Sent: Thu, Nov 24, 2016 3:30 pm
    Subject: [NavList] Re: A Nautical Almanac question

    Stan K asked
    Is the d value listed at the bottom of the sun and planets columns of the daily pages of the Nautical Almanac the average (or mean) hourly change in the sun's declination for the three days listed (as stated in the Nautical Almanac and other references) or the amount the declination changes between 1200 and 1300 on the middle day of the three shown (as stated in Bowditch)?
    Why do you care?  Why do you doubt the editors of the NA in their description.
    Looking at Sept. 26, 2007 NA for the Sun, d at bottom of page is 1.0 but 1200-1300 d is .9.  That does not answer your question if you are referring to the higher precision numbers that are rounded to produce the table.
    But my intuition tells me that the two answers to your question are identical when rounded to a tenth of a minute.  The d are first differences in tabullated values of dec and are not large.  The difference between your answers depends on the second difference of the values from which the tabulated values are obtained.  The rate of change of dec is small and relatively constant taking a whole year to cycle, so that the second differences are likely orders of magnitude smaller.
    DaveF
       
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