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Subject: Re: September Equinox computation
From: Herbert Prinz (hprinz@XXX.XXX)
Date: Tue Sep 24 2002 - 13:48:17 EDT
Pierre Boucher wrote:
> Which method would you use to PRECISELY compute (hh-mm-ss) the September
> equinox?
>
Pierre,
If this were an astronomy list, I would say that according to the definition
of equinox, you compute the ecliptic longitude of the Sun from a sufficiently
accurate ephemeris for two reasonable guesses t1 and t2 and then solve for t
such that L(t) = 180deg, either by interpolation or by iteration, dependent on
whether you do it manually or with a computer.
But I assume that you are asking how to do do it with the means that the
modern average celestial navigator has at his disposal. The answer is that you
can't do it to the required precision.
For starters, modern nautical almanacs don't tabulate ecliptic longitude
anymore. (Thanks God!). The next best thing is to solve for SHA = 180deg (or
RA = 12 hours) and the worst thing you can do is to solve for Dec = 0deg.
Neither is strictly correct, but using the SHA will get you THEORETICALLY
within a few seconds of the correct time whereas using Dec will get you there
within a minute, or so.
In practice, however, you must compute SHA from the difference of GHA Sun and
GHA Aries from your Nautical Almanac, which means that you have to interpolate
a value that changes only 2.5' per hour from two values that are burdened by
two rounding errors each of up to 0.05'. On top of this, the entries for GHA
Sun in the Nautical Almanac are shifted on purpose by as much as 0.1' from
their correct value. (This has nothing to do with "Selective Availability"; it
facilitates the use of the interpolation table without a need for
v-correction.) In late September, the entries are too high by 0.1' on average.
In short: You can't even rely on getting within a minute of the correct time
of equinox with the Nautical Almanac.
Herbert Prinz
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