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Re: Lunars with SNO-T
From: George Huxtable
Date: 2004 Oct 25, 13:00 +0100
From: George Huxtable
Date: 2004 Oct 25, 13:00 +0100
Alex reported his first lunars, as follows- >AP: N 40d27.2' W 86d55.8' >GMT: 4:00 Oct 24, T=58F Pressure 29.75 >Observation from my balcony, height 12ft, >Sextant SNO-T, index correction 0.0', inverting scope. >One of the 6 observations was immediately rejected >because it did not follow the pattern of increasing >distances. I reduced with Frank Reed's on-line calculator. >First, each measurement, and then their average. >The third line is the error in the distance, the fourth line >is the error in the longitude: > >Moon-Altair: > >GMT 4:06:49 4:09:58 4:13:10 4:17:12 4:18:57 >DIST 51d22.2' 51d23.3' 51d23.8' 51d24.1' 51d34.3' >ERD 0.0' +0.5' +0.3' -0.2' -0.4' >ERL +0.3' +13.5' +8.7' -7.3' -12.2' > >AVERAGE GMT: 4:13:13 AVERAGE DIST: 23.54' >ERROR IN DISTANCE: 0.0' ERROR IN LONG: 0.4' > >Moral: DO average:-) ============================ Congratulations to Alex for an outstanding set of observations. He has quickly got his lunars down to a fine art. Some niggles, however... 1. Presumably there's a typo in the 5th reported lunar distance, and it was actually 51d24.3', and not 51d34.3' as stated. 2. Alex stated- >One of the 6 observations was immediately rejected >because it did not follow the pattern of increasing >distances. I think this is over-simplistic, if that was the only reason for its rejection. It would be interesting to see the details of the rejected observation, and HOW MUCH it was out from that pattern of increasing distances.. When lunar distances, which change only slowly, are being taken at short intervals, then very small changes in the lunar distance are expected between observations. In the set given above, the total change in LD is about 2' of arc over a period of 12 minutes of time. If two observations were taken with a 2-minute interval, then an increase in LD between those observations would be expected to be about 0.3 arc-minutes. Looking at Alex's set, and doing a rough plot-in-the-head, rather than on paper, it seems that a scatter of the points, of something like 0.2' about the best straight line, would be expected. So if one observation happened to be 0.2' high, and the next one 0.2' low, that would more than cancel the expected increase of about 0.3', and break the monotonic sequence of always-increasing. This would cause the second observation to be rejected, although statistically, it's as valuable as the rest. Anyway, if you reject a point just because it breaks that sequence of always-increasing, can you be sure that you are rejecting the right observation? If its predecessor happened to have an unusually-high positive error, then it would be likely to put the NEXT observation, even if a perfectly normal one, out of the always-increasing sequence, and cause the wrong one to be rejected. In my view, all observations should be accepted, unless they are clearly blunders, and detecting such blunders should be a main purpose of making a plot. 3. It would be meaningful to give the averaged error for the 5 observations to an extra decimal place, in which case it would be 0.04', not 0.0'. 4. The scatter of errors in distance, and the resulting scatter of errors in longitude, shows that Alex has made a remarkably consistent and accurate set of observations. But the errors just happen, on averaging, to cancel out to nearly zero. This was fortuitous! It was Alex's lucky day. He happened to deduce a longitude which was only 0.4 miles from where he knew he was, from a set of longitudes that individually showed a scatter of about 10 miles or so. Averaging 5 such measurements should reduce the statistical error of the average, to 10 miles divided by root-5, or about 4.5 miles. So don't be misled by the precise result of 0.4 miles. Such things happen, by chance, once in a blue moon: perhaps, for Alex, never again! Averaging is indeed a powerful tool for reducing errors, but don't expect it to produce the same magic effects that happened on this one occasion. Eighteenth-century navigators at sea were very content if their longitudes came within 30 miles of the truth. On Alex's balcony, taking every precaution, he would indeed do well to achieve a result that's consistently within 5 miles. ======================= The comments above are not intended to detract in any way from Alex Eremenko's considerable achievement, made in a very short space of time. I look forward to the time when he can measure lunars at sea from a small vessel. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================