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Fred Hebard , at the prompting of Herbert Prinz, has dug out of the
archives my posting of two years ago, as follows-

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Subject: Re: September Equinox computation
>From: George Huxtable (george@huxtable.u-net.com)
>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.

====================

It's a bit cruel to throw my words of two years ago back at me now, but I
am hardly in a position to complain about that! Indeed, I would say most of
it again today. But why, I wonder, did I concentrate so hard on the
displacement of the Earth from the plane of the ecliptic (the Earth's
ecliptic latitude), and say so little about the shift of the plane of the
Earth's equator, due to nutation; an effect which is several times greater?

Nutation causes the spin-axis through the Earth's Poles, and thus the plane
of the Equator, to wobble about its mean value by up to about 15
arc-seconds. It's caused, mostly, by the attraction of the Moon and the Sun
on the Earth's equatorial bulge.

The official vernal equinox occurs when the apparent Sun is along the line
of intersection of the two planes; the mean equator and the true ecliptic.
But the actual Sun declination at that moment depends on the nutation,
which shifts the equator from its mean position, and the small amount by
which the Earth is off the plane of the ecliptic. That declination will
vary, from one Spring to another, and in general will not be exactly zero.

Michael Dorl has written (twice) about the shift in the direction of the
Sun, due to the 8-minute or so transit-time of the light from it.

It's true that if an event occurred on the Sun, it would not be observed on
Earth until 8 minutes later, in which time the Earth would have rotated 2
degrees. But that has little to do with the problem. What we are observing
is to do with the intersection between two planes at the Earth, not the
Sun, and the definition of equinox is when the APPARENT direction of the
Sun (i.e. affected by the parallax caused by the velocity of light) is
along the intersection of those planes. The TRUE direction of the Sun will
indeed be different from that apparent direction, by about 20 arc-seconds,
due to the light-time, and that is indeed something we need to be aware of
when calculating positions of planets from the Earth..

Jim Thompson provided a useful explanation, but he has got a bit tied up (I
think) with some terminology about the Sun. We are used to using the words
Mean Sun and Apparent Sun, to describe the differences between Mean and
Apparent Time, in which the Mean Sun is an invention that goes round the
sky at a uniform speed. But I think that's not the sense in which Jim
Thomson is using those terms. I hope I am not misunderstanding him.

George.


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01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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