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    Re: When is the Autumnal Equinox?
    From: Paul Hirose
    Date: 2011 Sep 07, 16:15 -0700

    Geoffrey Kolbe wrote:
    >> The equinoxes and solstices are the moments when the geocentric 
    >> apparent Sun reaches 0, 90, 180, and 270 degrees of ecliptical 
    >> longitude. See The Astronomical Almanac glossary:
    >> http://asa.usno.navy.mil/SecM/Section_M.html
    > If this is the case, how to the equinoxes precess?
    I'm not sure what Geoffrey is asking. I'm guessing he sees a 
    contradiction between the above definition of "equinox" and the 
    precession of the equinoxes. Actually, the two have almost nothing to do 
    with each other. "Vernal equinox" can mean (1) the time when the Sun 
    passes through a specified coordinate. But it can also mean (2) the 
    point on the celestial sphere where the ecliptic and the celestial 
    equator intersect, and which the Sun is near at the time of the vernal 
    "Precession of the equinoxes" refers the regular movement of (2). Due 
    mainly to the precession of Earth's rotation axis, the vernal equinox 
    (2) makes an approximate great circle in the sky every 26,000 years. And 
    since this point is the "Greenwich" of the equatorial (right ascension 
    and declination) and ecliptical (longitude and latitude) reference 
    systems, the coordinates of a body with respect to the equinox "of date" 
    change continuously. But this phenomenon occurs regardless of the 
    definition of "equinox" (1).
    I can understand a reluctance to accept a definition of (1) based on 
    longitude. It's practically unknown.  A few years ago I was irked and 
    disbelieving when someone corrected a "precise" equinox time I had 
    computed. But upon consulting the references I most respect, the Almanac 
    and the Explanatory Supplement, I had to admit I'd just learned 
    something new. I'm trying to pass it on.
    As further evidence I offer the astronomical data sheets from HM 
    Nautical Almanac Office:
    Here are their autumnal equinox times for the last 10 years. The times
    are UT. I've added the Sun's geocentric apparent declination and
    longitude. (Because the longitudes are all very close to 180°, I show
    only the seconds.)
           date  time    dec    lon
    2002-09-23 04:55  -00.1"  59.1"
    2003-09-23 10:47  +00.2"  00.5"
    2004-09-22 16:30  -00.7"  00.4"
    2005-09-22 22:23  +00.5"  59.6"
    2006-09-23 04:03  +00.2"  59.1"
    2007-09-23 09:51  +00.2"  59.5"
    2008-09-22 15:44  +00.9"  58.8"
    2009-09-22 21:19  -00.7"  01.0"
    2010-09-23 03:09  +00.9"  59.9"
    2011-09-23 09:05  -00.7"  00.9"
    A little experimentation shows that 5 of those times are in error by a 
    minute, if equinox is defined by declination. But all are correct if 
    equinox is defined by longitude.
    The thought crossed my mind that perhaps the table was based on the time 
    the Sun crossed the geodetic equator, not the celestial equator. So I 
    recomputed the last 5 years with polar motion (daily values are in IERS 
    Bulletin B). Well, three years got a little better, one stayed the same, 
    and one got a lot worse. So much for that hypothesis. It didn't make 
    much sense, but I had to be sure.
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