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Subject: Re: September Equinox computation
From: George Huxtable (george@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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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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