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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: My first Lunar
From: Giuseppe Menga
Date: 2008 Jul 16, 09:48 +0200
From: Giuseppe Menga
Date: 2008 Jul 16, 09:48 +0200
Well, looking at position finding as an optimization problem, where the model is highly non linear and the functional to minimize is not simply quadratic, but shows several local minima, mathematically nothing can be sayd other than, if you starts relatively close to one of these local minima you will find it as solution. Usually in these cases, after finding a minimum, you apply a random perturbation to the solution and try again to see if other minima (or a best minimum) exist: In this case I assume that all (two) minima have identical functional value so are undistinguishable just from the fitting. Giuseppe ----- Original Message ----- From:To: Sent: Wednesday, July 16, 2008 6:32 AM Subject: [NavList 5858] Re: My first Lunar Giuseppe, you wrote: "Dear Frank, using my clearing algorithm I found: time 22:19:38 GMT, pos 14�N 35.3', 61�W 41.3' LD 68� 13.13' (sextant LD 68� 19.40') The position is roughly 5 miles from yours Giuseppe" Sounds like a near-perfect match. Incidentally, the "best" GMT would appear to be about 22:19:34 according to my calculation, but 0.1' difference in the clearing process would correspond to 12 seconds difference in time so I don't consider a difference smaller than 6 seconds in time, in any analysis of lunars, to be meaningful. The "fix" from the two altitudes comes from two altitudes in nearly opposite azimuths so that the position is relatively indeterminate along azimuth 340/160. That is, you can shift the fix five miles or more along that direction and there would be little difference in the result. So again, that means your result is a near-perfect match with mine, which is re-assuring! And this brings up an interesting question. How can this analysis be producing different longitudes? Viewing a lunar as a sight for longitude, as in traditional, historical lunars, how can there be any ambiguity in the final longitude? The few miles difference that we're seeing here might be excused but what about the big difference in longitude between the position (presumably the correct one) west of Martinique and the other position inland in Guyana? The answer, of course, is that the longitude resulting from a lunar depends also on the local time. If these sights had been worked in the early 19th century, and there was no reliable time kept by a common watch, the altitude of Jupiter would probably have been worked to get the local apparent time. But that calculation depends on the latitude. So if you assume a different latitude, you get a different LAT and when combined with the Greenwich Time that comes from clearing the lunar, you would end up with a different longitude. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---