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    Re: A simple question, I hope, on almanac SHA
    From: Stan K
    Date: 2013 Apr 12, 20:42 -0400

    -----Original Message-----
    From: Frank Reed <FrankReed@HistoricalAtlas.com>
    To: slk1000 <slk1000@aol.com>
    Sent: Fri, Apr 12, 2013 1:28 pm
    Subject: [NavList] Re: A simple question, I hope, on almanac SHA

    Hi Stan,
    I was giving someone else a hard-time recently about non-descriptive subjects, so I've modified this subject to provide just a hint of what your question was about. I hope you don't mind! :)  Not at all.  It was way past my bed time when I wrote it, and only realized how bad a subject it was after I pressed Send.
    You wrote:
    "The SHA of stars changes very slowly, so the Nautical Almanac uses a single value for the three days of a daily page. I would have to believe that this is the value for 1200 UT of the middle day (rounded to 0.1'), but I have not been able to find this, or something contrary, documented anywhere."
    I would guess you're right, too. I was having dinner here on the island last night with Herbert Prinz (delicious seafood at Jamestown Fish), and a text message came in during dessert with your message so I offered it up for discussion. We spent hours talking about navigation and astronomy and NavList, so SHA trivia fit right in! We agreed that your suggestion is almost certainly correct. HP also pointed out that, of course, this is documented somewhere in technical publications on the Nautical Almanac, but good luck digging it up. I certainly cannot find it in the Almanac itself.  Even Bowditch was no help (see below).  I suggested that you could determine this by re-calculation. Find as many cases as you can where the SHA changes by 0.1 minutes from one page to the next. Then find some source that calculates SHA's for every hour (my site does) and as long as they're using nearly identical input data and nearly identical precession and nutation models (How can I be sure of that?), you should be able to find cases where the SHA flips its tenths digit on just the right date. Here's the link for my web-based software that does this: http://reednavigation.com/lunars/nadata_v5.html. Other NavList members, including Paul Hirose, have similar tools available.

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    Excerpts from Bowditch give specific information about the planets...
    The time of transit of the planets for the middle day
    is given to the nearest whole minute, with SHA (at UT 0000
    of the middle day) to the nearest 0.1'...
    but are not specfic about the SHA of the stars.
    On the left-hand page, successive columns list GHA
    of Aries, and both GHA and declination of Venus,
    Mars, Jupiter, and Saturn, followed by the Sidereal Hour
    Angle (SHA) and declination of 57 stars.

    (Note that for the planets the Almanac uses UT 0000 of the middle day, not UT 1200, which somehow surprises me.)

    I checked every reference I have, and the best I can find is one that says the SHA of a star does not change more than 0.1' over the course of three days.

    Regarding that other item I mentioned, the Sun altitude correction being a single value for a six-month period, given the same limb and apparent altitude, this is also giving me heartburn.  These things come up in casual discussions and keep me awake at night.  The Sun altitude correction is made up of refraction, parallax, and semi-diameter.  Refraction is only a function of the apparent altitude - the time of year has no bearing.  Parallax is tiny to begin with, and the difference throughout the year is insignificant.  The only thing that would have an effect is semi-diameter, so I figured there had to be a value, perhaps the mid-point between the largest and smallest values of semi-diameter over the six-month period, that could be applied to the refraction and parallax to get the values in the table.  Well, that didn't work, so I played with the value but could not find a value that worked for the entire range of apparent altitudes.  And a value that worked fairly well for a range of altitudes for the lower limb was not even close for the upper limb.  Then I happened to look at the table from a different year, and found that the break points, the apparent altitudes where the correction changed by 0.1', were, for most of the range of altitudes, different by 1' than the table I started with.

    The only thing I could come up with was possibly refraction causing the Sun's to be compressed vertically at low altitudes, but the problem was noticeable at higher altitudes also, and doesn't explain the differences from year to year.

    Any help in getting me a good night's sleep would be appreciated.

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