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    Re: September Equinox computation
    From: George Huxtable
    Date: 2002 Sep 25, 11:35 +0100

    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.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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