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Re: Lat. and Lon at LAN
From: George Huxtable
Date: 2004 Jan 8, 17:07 +0000
From: George Huxtable
Date: 2004 Jan 8, 17:07 +0000
Fred Hebard said- >I'm glad George addressed this question. I had been wondering why he >and Herbert Prinz had been saying that noon shots were so bad for >establishing LAN, but didn't work through the math as George has. > >One quibble. With local noon moving at a rate of 15 arc-minutes per >time-minute, would not an error of 5 time minutes would put one out 75 >arc-minutes rather than 20? I might not mind being out 8 to 20 >arc-minutes at the equator but 30 to 75 would be a fair amount. > >On Jan 8, 2004, at 9:38 AM, George Huxtable wrote: > >> So there's no way for an observer to time the noon sight within a few >> seconds, as Doug claims. If the time of LAN could be determined within >> 5 >> minutes, then it would establish longitude within about 20 >> arc-minutes. Not >> a great result. In the unlikely event of a timing precision to 2 >> minutes, a >> longitude determination to 8 arc-minutes would result. ======================== Thank you, Fred, for correcting my arithmetic. I don't know how I got it all so wrong. I was over-generous to Doug's procedure by a factor of nearly 4! Not only that. Fred didn't mention that there was exactly the same arithmetic error in the second problem, that of North-South velocity of the ship affecting the moment of maximum altitude, for which, in the 20-knot example I gave- >If lat = +51deg and dec = - >23.5deg, this works out at 511 sec, or all of 8.5 minutes late. Unless >corrected for, this will give rise to an error (not an uncertainty this >time, but an actual error) of 34' in the longitude! The time-error of 8.5 minutes late would really have given rise to an error of 127.5 minutes in longitude, a serious business indeed. 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. ================================================================
