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    Re: equinox
    From: Fred Hebard
    Date: 2004 Mar 24, 21:22 -0500

    On Mar 21, 2004, at 10:56 PM, Herbert Prinz wrote:
    
    > Paul Hirose wrote:
    >
    >> Here's what I got from the JPL Horizons program. Note that 06:50:04
    >> TT is about
    >> 06:49:00 UTC. The USNO MICA program was pretty close to Horizons,
    >> about 2
    >> seconds of TT different.
    >
    > Again the same mistake: Paul solved for dec = 0, instead of lon = 0.
    > The correct
    > time is 6:49:42 TT, corresponding to 6:48:38 UT.
    >
    > Fred,
    >
    > I tried to forward to the list two of my own messages and one written
    > by George
    > Huxtable  at the occasion of the spring and fall equinoxes of 2002.
    > Maybe, this does
    > not work, if the list server does not permit it. If the messages don't
    > get through,
    > you might want to check the archives for these times.
    >
    > Herbert Prinz
    >
    
    Herbert,
    
    Here are some messages you and George Huxtable wrote in March and
    September of 2002 on this question.  I copied them from the web
    archive.  I don't know that they're the ones you had in mind, but
    they're pretty close.
    
    Fred
    
    From: Herbert Prinz (hprinz{at}XXX.XXX)
    Date: Sat Mar 16 2002 - 15:31:00 EST
    
      The astronomical definition for equinox is "The instant at which the
      apparent longitude of the Sun is 0deg (or 180deg)". This may or may
    not be
      the moment at which the declination of the Sun is 0 deg. The reason
    being
      that the latitude of the sun need not be 0 (this year it will be 0.06"
    at
      time of equinox) and that the Earth is wobbling around a little.
    
    According to MICA, the next equinox will be on Mar 20 at 19:17:12 ET.
      Assuming 64 seconds for delta T this gives 19:16:08 UT. However, the
    Sun
      will have crossed the equator 4 seconds earlier than this.
    
    This subtle difference is of no significance to the navigator, but it
    is of
      utmost importance to Rob Gendreau, who would miss the proper moment at
    which
      to balance his eggs, if he followed an official ephemeris.
    
    Subject: Re: September Equinox computation
    From: Herbert Prinz (hprinz{at}XXX.XXX)
    Date: Tue Sep 24 2002 - 13:48:17 EDT
    
      Pierre Boucher wrote:
    
     > Which method would you use to PRECISELY compute (hh-mm-ss) the
    September
     > equinox?
     >
    
    Pierre,
    
    If this were an astronomy list, I would say that according to the
    definition
      of equinox, you compute the ecliptic longitude of the Sun from a
    sufficiently
      accurate ephemeris for two reasonable guesses t1 and t2 and then solve
    for t
      such that L(t) = 180deg, either by interpolation or by iteration,
    dependent on
      whether you do it manually or with a computer.
    
    But I assume that you are asking how to do do it with the means that the
      modern average celestial navigator has at his disposal. The answer is
    that you
      can't do it to the required precision.
    
    For starters, modern nautical almanacs don't tabulate ecliptic longitude
      anymore. (Thanks God!). The next best thing is to solve for SHA =
    180deg (or
      RA = 12 hours) and the worst thing you can do is to solve for Dec =
    0deg.
      Neither is strictly correct, but using the SHA will get you
    THEORETICALLY
      within a few seconds of the correct time whereas using Dec will get
    you there
      within a minute, or so.
    
    In practice, however, you must compute SHA from the difference of GHA
    Sun and
      GHA Aries from your Nautical Almanac, which means that you have to
    interpolate
      a value that changes only 2.5' per hour from two values that are
    burdened by
      two rounding errors each of up to 0.05'. On top of this, the entries
    for GHA
      Sun in the Nautical Almanac are shifted on purpose by as much as 0.1'
    from
      their correct value. (This has nothing to do with "Selective
    Availability"; it
      facilitates the use of the interpolation table without a need for
      v-correction.) In late September, the entries are too high by 0.1' on
    average.
    
    In short: You can't even rely on getting within a minute of the correct
    time
      of equinox with the Nautical Almanac.
    
    Herbert Prinz
    
    Subject: Re: September Equinox computation
    From: George Huxtable (george{at}XXX.XXX)
    Date: Wed Sep 25 2002 - 06:35:51 EDT
    
      Searchers after the exact moment of Autumn equinox appear to be
    looking for
      the moment when the declination of the Sun is exactly zero, passing
    from
      North to South, and also the Right Ascension of the Sun is exactly 12
    hours
      or 180 degrees. In this, they are almost certain to be disappointed.
    Those
      two events are unlikely to occur at exactly the same moment.
    
    If the Sun was always exactly on the plane of the ecliptic, then they
      would: but in general that is not exactly the case. Because the earth
    is
      perturbed slightly in its path around the Sun by the attractions of the
      Moon and other planets, the Sun's latitude (its displacement out of the
      plane of the ecliptic) is not always exactly zero, but can vary up to
    1.2
      seconds of arc.
    
    Note that the effect referred to above is an actual physical shift of
    the
      Earth out of the plane of its orbit round the Sun, by up to 5,000-odd
      miles, not a shift of the Earth's polar axis such as precession and
      nutation cause.
    
    The moment of autumn Equinox is defined by the Sun's apparent geocentic
      longitude (and consequently its Right Ascension also) being 180
    degrees,
      and NOT by its declination passing through zero. A change in Sun
    ecliptic
      latitude of 1 second of arc would, I think, alter the declination of
    the
      Sun by a similar amount. The Sun's declination around the equinox is
      changing at very nearly 24 minutes a day. (I like to remember this by
      thinking of the maximum rate of travel of the Sun's geographical
    position,
      North or South, as almost exactly 1 knot).
    
    So a shift in the Sun's position from the ecliptic of 1.2 seconds of arc
      would change the moment of zero-crossing of declination from the
    moment of
      the equinox by about 72 seconds of time.
    
    I have not tried to estimate what the ecliptic latitude of the Sun
    would be
      at the 2002 autumn equinox, but for anyone that wishes to, Meeus in
      chapters 27 and 25 provides all the necessary information.
    
    I have no wish to sail under false colours, and pose as an authority on
      such matters. All that I have said here has been taken from Meeus'
      excellent work "Astronomical Algorithms", of which I claim only a
    partial
      understanding. So the conclusions above are somewhat tentative, and
    stand
      to be corrected by anyone who knows more than I do.
    
    George Huxtable.
    
    
    

       
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