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    Ecliptic coordinate system (was equinoxes)
    From: Jim Thompson
    Date: 2004 Mar 25, 21:43 -0400

    To understand "equinox" I needed to dig deeper into the ecliptic coordinate
    system, which so far I had largely been ignoring. I ended up with this:
    Jim Thompson
    Herbert Prinz wrote in 2002:
    "The astronomical definition of equinox is "The instant at which the
    apparent longitude of the Sun is 0o (or 180o)". This may or may not be the
    moment at which the declination of the Sun is 0o. 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."
    "Celestial (or ecliptic) longitude and latitude are spherical co-ordinates
    that are referenced to the plane of the ecliptic (i.e. the plane of the
    Earth's orbit around the Sun). This plane intersects the equatorial plane in
    a line that points towards the "equinox", also called "First point of
    Aries". By definition, this point has ecliptic longitude 0 and latitude 0.
    It also has RA 0 (or SHA 0) and Dec 0. Both planes are inclined to each
    other by ca. 23 1/2 deg."
    George Huxtable wrote in 2002:
    "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
    "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
    "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."
    Jim Thompson
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