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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: About Lunars, part 4**

**From:**George Huxtable

**Date:**2002 Mar 21, 00:29 +0000

I have received a message directly, off-list, from Chuck Griffiths, and presume that he would wish it to be posted up. Here it is, with a response from me. ==========================Envelope-to: george---.u-net.com From:MIME-Version: 1.0 Date: Wed, 20 Mar 2002 08:08:18 -0500 Subject: Fwd:Re[2]: About Lunars, part 4 To: george---.u-net.com George, I posted this to the list last night but it looks like the server is having a little trouble keeping up again. I'm most interested to hear your thoughts on correcting for Venus' parallax as you had me convinced that Letcher ignores the parallax of the other body because it's negligible. Chuck ____________________Forward Header_____________________ Subject: Re[2]: About Lunars, part 4 Author: Chuck Griffiths Date: 3/19/02 8:46 PM I guess I should have thought to include more information. Here we go: Height of eye was about 10 feet, I used -3.1 for dip. Almanac information: 00:00:00 on 19 March Moon GHA 125-58.0, Dec N 15-55.3 Venus GHA 163-28.7, Dec N 4-26.2 01:00:00 Moon GHA 140-30.3, Dec N 16-5.3 Venus GHA 178-28.4, Dec N 4-27.5 HP 55.1 I didn't correct for Venus parallax, I thought that there wasn't a good way to work planet parallax into the Letcher method. For SD I used George's recommended method of calculating augmented SD from HP. Chuck ======================= Copied below once again is Chuck's earlier mailing of 19 March, which contains the rest of the necessary information. ======================= First, I have a set of observations from last night that I'm hoping you might have a look at George, and see if it looks like I'm still headed in the right direction. From approximately 27-42.0 N, 82-44.2 W I took a set of observation as follows: (All times GMT 19 March followed by altitudes Degree-Minutes) Venus 00:11:41 7-50.6 Moon 00:12:48 44-52.6 Venus 00:14:02 7-25 Moon 00:14:02 45-25.6 Lunar Distances 00:14:59 37-43.4 00:15:27 37-43.2 00:16:01 37-43.0 Venus 00:16:36 6-43 Moon 00:17:31 43-51.6 Venus 00:18:09 6-24 Moon 00:19:09 43-30 I roughly averaged the sights and used the following for my calculations: Venus 7-5.6 Moon 44-12.5 Distance between 37-43.2 >From which I calculated: B .69733 P 38.43635 R 6.65151 d 37.97333 D 38.72479 SD 15.1995 HP 55.1 D1 (00:00:00) 38.58036 D2 (01:00:00) 39.03829 T 00:18:55 v. real time of observation of 00:15:29 So, based on the fact that the Moon was rather high and, by my observations, was moving at an apparent speed of about 24 arc minutes an hour can I assume that some of my error is due to "parallactic retardation"? Or, did I make some more basic mistake? ================================ From George- If the apparent Moon was moving at 24 arc-minutes per hour and Chuck has measured GMT to within 3 minutes 26 sec of time, then he has measured the lunar distance within 1.4 minutes of arc, if all the calculations are correct (I haven't checked). An error of 3 minutes 26 sec in GMT would correspond to an error in longitude (at 15 deg per hour) of 51 arc-minutes. These are not bad values at all, especially for a first try at lunars, and singlehanded. One factor to check (I haven't done so) is to ensure that the average time of measurement of the Moon and Venus altitudes corresponds well with the average time for the Lunar distances. Parallactic retardation doesn't in itself cause errors, in that these effects are corrected for in the parallax calculations. But it does degrade the accuracy of the whole process (by up to a factor of 2 when the Moon is very high), which is not quite the same thing. I hope the information provided above is useful grist to Arthur Pearson, and to anyone else who might wish to have a go with Chuck Griffiths' observations. Above, Chuck said- "I'm most interested to hear your thoughts on correcting for Venus' parallax as you had me convinced that Letcher ignores the parallax of the other body because it's negligible." Well, if that's what I said, then it wasn't quite what I intended. Letcher ignores the parallax of the other body whether it's negligible or not. It is unable to take into account the horizontal parallax of the other-body, only that of the Moon. Or at least, I know of no way to get it to do so. It's a weakness of Letcher's method. But for bodies other than the Moon, the HP is usually small enough for the approximation to be acceptable. The Sun's HP is around 0.15 arc-minutes. I have checked the distance between the Earth and Venus at the date of Chuck's observation (19 March 02) by pocket-calculator, and this is 1.6 AU (AU = Astronomical Unit: 1 AU being the mean distance between Earth and Sun). So the HP of Venus at that date is 0.15 / 1.6, or just less than 0.1 arc-minute. This follows because Venus is away on the other side of the Sun from the Earth. This is fortunate because it implies that in those circumstances there will be no great error in using Letcher's method. However, when Venus is near perigee, its distance to the Earth can be as little as 0.25 AU, which would increase its HP to 0.15/0.25, or 0.6 minutes, at which time Letcher's method could give serious errors. However, when Venus is closest to the Earth, it's also near the Sun in the sky, so Venus is quite invisible near perigee. Mars is another matter. Having a larger orbit than that of the Earth, when near perigee it is opposite to the Sun, so is highly visible. At perigee it can come within 0.4 AU of the Earth, so its HP can reach nearly 0.4 arc-minutes. What this means is that users of Letcher's method, observing Mars or Venus at times anywhere near to perigee, should do so with their eyes open. The table on page 259 of the Nautical Almanac should be consulted, where the value of p will indicate the maximum error in lunar distance that can be caused by that Letcher approximation. The observer will at least be aware how big that error can be, although unable to allow for it using Letcher's method. For example, with Steven Wepster's Mars lunar, taken on 8 April 2001, the Earth-Mars distance happened to be .84 AU, so the HP of Mars would be 0.15 / 0.84, or 0.18 arc-minutes. If Steven had used Letcher's method (which he didn't), he would have to take into account a possible error of up to .18 arc-min (either way) because of the approximation. Most navigators would, I think, regard that as acceptable. For any other object in the sky, Jupiter, Saturn, or any star, parallax can be taken as zero. ======================= A suggestion : any takers? For anyone that's really keen to squeeze out all the information that can be got from Chuck's observations, it can I think be taken a step further. Once the GMT is agreed, then dec and GHA for Moon and Venus at that time can be established (using interpolation, as we have two values from the Almanac, 1 hour apart, for each of these quantities). From this, the location of the observer can be deduced. For a first shot (as we have no idea yet where Chuck was observing from) the geographical positions of Moon and Venus at that time could be marked on a globe. Chuck's measured altitudes for these bodies should be corrected in the ordinary way (ie corrections as for altitudes, not corrections as for lunar distances), and then the corrected altitudes converted to zenith distance by taking the 90-degree complement. Now draw circles of that radius about the two GPs on the globe. These intersect in two places, so you have to guess which one is most likely. This paragraph could be bypassed if we had a rough idea of whereabouts Chuck lived, in advance. Having done that, choose an AP near or at one of those places, calculate altitudes and intercepts for Moon and Venus, and where they cross will be our best guess at where Chuck lives. If it has all gone right, you should get a position within 2 or 3 miles in latitude. In longitude, if you are within 30 minutes, that will be very good going. You will realise that the above procedure, in this section, really has nothing to do with lunars, except that it has used the GMT derived from a lunar, and has used the observations of altitude, as taken for a lunar, for a different purpose. If you used Letcher's method to calculate your lunars, than you will realise one disadvantage of that method. It bypassed the need to work out individual altitude corrections for the two bodies, so those will have to be calculated anew. With other methods, you will have done much of the work in finding the altitudes corrections already, in the process of correcting the lunar distance. I haven't tried working out these figures myself, but it seems to me that all the information should be there to establish where Chuck Griffiths lives, if not to the nearest block... George Huxtable. ------------------------------ george---.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------