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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Fix by Occultations
From: George Huxtable
Date: 2009 Feb 7, 23:58 -0000
From: George Huxtable
Date: 2009 Feb 7, 23:58 -0000
In my last posting, I wrote- "I don't know at what date such "signs" units were dropped in favour of straight 0� to 390� notation, but they had certainly gone by 1864, probably much earlier." ================= If you worried that "straight 0� to 390� notation" was yet another odd way to measure angles, think again. In was just a slip-of-the-keyboard for 360. Sorry about that. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ----- Original Message ----- From: "George Huxtable"To: Sent: Saturday, February 07, 2009 11:51 AM Subject: [NavList 7292] Re: Fix by Occultations Brad, trying to find the longitude of the Moon, had written- " I just couldn't understand why the latitude was so small, and assumed it was due to the heliocentric nature. " and Frank added- "It would probably be useful to you to get a copy of the Nautical Almanac from that period. Then you'll be able to see exactly which data were being published. There are a bunch of old Nautical Almanacs on Google Books. I've got some links to some examples here: http://www.fer3.com/Mystic2008/navbooks1.html and there are many more available at Google Books if you search around a bit." ===================== Old almanacs are certainly instructive, and interesting in themselves, now that they are becoming readily available. Moon longitudes and latitudes were given in the early nautical almanacs at just two moments each day, Noon and Midnight. Initially this was at Greenwich apparent time; from 1834, Greenwich mean time. There are one or two problems anyone needs to be warned about when delving into old almanacs for ecliptic longitudes. Although Right Ascension was measured, in degrees up to 360� (or sometimes, in hours up to 24h), Eastwards around the sky starting at Aries, celestial (ecliptic) longitude was not measured in quite the same way. Longitude was also measured Eastwards around the sky from Aries, but around a different arc tilted at 23 and-a-bit degrees, and to measure it in just the same units, 0� to 360�, would have been simple and logical. Instead, however, in early almanacs it was always measured in "Signs", each 30� wide, so there were 12 such signs around the circle. The first such sign was a block labelled with the sign-of-the-Zodiac name of Aries, 0� to 30� in longitude, the starting point of the whole thing, 0� in Aries, being literally "the first point of Aries", which today, we shorten to just the word "Aries". Then, after Aries, the next Zodiac sign is Taurus, 30� to 60�, and so on. The list is - S range 0 0� to 30� Aries 1 30� to 60� Taurus 2 60� to 90� Gemini 3 90� to 120� Cancer 4 120� to150� Leo 5 150� to 180� Virgo 6 180� to 210� Libra 7 210� to 240� Scorpio 8 240� to 270� Sagittarius 9 270� to 300� Capricornus 10 300� to 330� Aquarius 11 330� to 360� Pisces and then restart at Aries again. Unfortunately, emailese can't show those fancy symbols that go with the names, so I will add them as an attachment, taken from the first Almanac , for 1767. They can be useful, because some early almanacs didn't provide a useful "Sign-nunber" S, as Maskelyne did in his nautical almanac, nor a sign-name, but just the symbol itself. In which case, you need to know the symbol to put a given longitude into a sensible range of degrees. The symbols varied a bit, over time and in different countries. The Sun, which has an ecliptic latitude close to zero, travelling round the line of the Ecliptic itself, stays within a sign for about a month. The Moon, with longitude increasing by about 12� per day, is in and out of a sign in about two and a half days. I don't know at what date such "signs" units were dropped in favour of straight 0� to 390� notation, but they had certainly gone by 1864, probably much earlier. Another problem is this. Because predicting a Moon longitude and latitude, by hand-calculation, involved such immense labour, Maskelyne asked for them to be calculated as seldom as possible, and settled on an interval of 12 hours. But his lunar distances needed to be provided at 3-hour intervals, so Moon longitudes and latitudes were also needed, for that purpose, at 3-hour intervals. So interpolations were needed, between those Noon and midnight values, but the Moon's motion is such that simple linear interpolation would have been hopelessly inaccurate. What Maskelyne had to do was, effectively, to fit a curved line to the nearest four predicted values, and then to interpolate using that. So we, like Maskelyne, can't interpolate between the noon and midnight predictions without using similar tricks. How accurate were those predictions anyway? They were provided to the nearest arc-second, but that's simply because that was the next unit of angle smaller than an arc-minute. The claim was that they were good to a half-minute, but I doubt if they came reliably within that error-limit for many years. As a random example, for Greenwich apparent noon 12 March 1767, the Nautical Almanac gives Moon long 4S 17� 58' 28", so we have to multiply the 4 "signs" by 30 and add 17 to get a longitude of 137� 58' 28", taking the 28" with a grain of salt. All in all, you are far better nowadays to get predicted positions, Moon, Sun, or Planets, for those early dates, from a modern prediction program. It's odd but true that we know now where those bodies were, then, far better than they did at the time. However, I don't know where you will find modern predictions showing ecliptic latitudes and longitudes directly. If somebody does, please say. My own Skymap display program will display a grid of ecliptic lat and long on top of a picture of the sky, but won't show the calculated values. What I think you have to do is to obtain precise modern predictions for RA and dec, then convert to ecliptic long and lat using the Meeus expressions I copied into an earlier posting. But if you are trying to work to great precision be sure to use the contemporay value for the Earth's orbital tilt. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---