A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Fred Hebard
Date: 2004 Mar 24, 21:22 -0500
From: Fred Hebard
Date: 2004 Mar 24, 21:22 -0500
On Mar 21, 2004, at 10:56 PM, Herbert Prinz wrote: > Paul Hirose wrote: > >> Here's what I got from the JPL Horizons program. Note that 06:50:04 >> TT is about >> 06:49:00 UTC. The USNO MICA program was pretty close to Horizons, >> about 2 >> seconds of TT different. > > Again the same mistake: Paul solved for dec = 0, instead of lon = 0. > The correct > time is 6:49:42 TT, corresponding to 6:48:38 UT. > > Fred, > > I tried to forward to the list two of my own messages and one written > by George > Huxtable at the occasion of the spring and fall equinoxes of 2002. > Maybe, this does > not work, if the list server does not permit it. If the messages don't > get through, > you might want to check the archives for these times. > > Herbert Prinz > Herbert, Here are some messages you and George Huxtable wrote in March and September of 2002 on this question. I copied them from the web archive. I don't know that they're the ones you had in mind, but they're pretty close. Fred From: Herbert Prinz (hprinz@XXX.XXX) Date: Sat Mar 16 2002 - 15:31:00 EST The astronomical definition for equinox is "The instant at which the apparent longitude of the Sun is 0deg (or 180deg)". This may or may not be the moment at which the declination of the Sun is 0 deg. 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. According to MICA, the next equinox will be on Mar 20 at 19:17:12 ET. Assuming 64 seconds for delta T this gives 19:16:08 UT. However, the Sun will have crossed the equator 4 seconds earlier than this. This subtle difference is of no significance to the navigator, but it is of utmost importance to Rob Gendreau, who would miss the proper moment at which to balance his eggs, if he followed an official ephemeris. 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 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.