# NavList:

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

**Re: Lunars using Bennett**

**From:**George Huxtable

**Date:**2008 Apr 4, 15:23 +0100

D. Walden's note about using Bennett's tables to work lunars was interesting, but misleading. There would be nothing wrong with the notion, in principle, if the tables were much more precise than they are. But. There were two conclusions for the assiduous reader to pick out. 1. The remarkably close agreement between the corrected lunar distance between Moon and Sun centres, calculated from Bennett's tables by Walden as 46 deg 08', and that calculated more precisely by Frank Reed's online calculator to be 46 deg 07.4', a discrepancy between them of only 0.6 arc-minutes. That apparent agreement is entirely fortuitous. As Alex has pointed out, each pass through a Bennett solution of a navigational triangle involves a potential error of the order of 1 arc-minute. In the method Walden describes, four such passes are called for, in various directions. What's more, each prediction for position of each body involves summing several numbers, each presented no more precisely than to the nearest minute. Refraction corrections, parallax corrections, and semidiameters are given only to the nearest minute. And these potential errors sum up; not arithmetically but quadratically, as statistical errors generally do. D.Walden can reach no conclusions about potential errors in using the Bennett tables for that purpose, until he has checked out enough predictions to see what the resulting scatter amounts to (say, 10; at least 4, anyway). His one-off "bull's eye" signifies no more than I would achieve if I scored a bull's eye at my first throw at a dartboard. It would be a lucky accident; no more than that. I predict that he will see an overall range of scatter of 3 to 4 minutes or so. That would render it pretty useless for lunar distances, the deduced longitudes covering a range of longitudes getting on for 2 degrees.. So come on, D Walden, spend a bit more time with your tables, and let's see what scatter you come up with. By the way, there's an entry "HP = 58", in a line listing Sun data, which should presumably apply to the Moon instead. I've no reason to think it's been applied incorrectly in practice, but it may confuse readers. I can't check out any predictions from the tables, as my own copy expired in 2007. 2. The enormous discrepancy between the predictions, above, and the reported lunar distance measurement, between centres of Moon and Sun, of 46 deg 30'. This is stated as "Error in lunar - 26' ", but actually seems to correspond to a difference of 22 or 21.6 minutes. As a consequence of this, Walden writes- "surprisingly, final watch errors may be within 3 minutes or so". Not so, however. Lunar distance changes only slowly, at about 30' in each hour. So a difference of 21.6, 22, or 26 minutes in lunar distance calls for an error in watch timing of best-part of an hour, not "within 3 minutes or so"! It would correspond to a position error of some 11 to 13 degrees of longitude. And if that's really the case, it should then be necessary to redo the lunar distance calculations with a better estimate for time, because all the predicted positions will have been so grossly in error. But where does this supposed watch error, and this reported lunar distance comes from? Walden doesn't tell us whether he is reporting an observation that was actually made, or just contrived out of his head. I presume it was contrived, solely because of the round-number whole degrees that were used for latitude and longitude. And if so, and if the lunar distance and the time were no more than invented ones, then does the discrepancy between so-called observation and calculation have any significance at all? I think not. Walden may like to know that Bennett has written a paper proposing use of his tables for lunars, in exactly the same manner as he has, which appeared in "Navigator's Newsletter", issue 79, spring, 2003. It was titled "Lunar Distances - A Simple and Concise Solution" (though it was neither simple nor concise, occupying more than 5 A4 pages). Unfortunately, it contained many errors and also misprints, some (but not all) of which were corrected in the next issue. More seriously, it dressed up discrepancies that appeared, between observation and calculation, as due to an erroneous watch, out by 8 minutes of time. However, analysis of the detailed results has proved that the watch was not at fault. Presumably, then, at least part of that error in the result, which amounted to about 4 arc-minutes in the lunar distance, was due to using Bennett''s book of tables for a purpose for which they were not designed, and for which they were nowhere near sufficiently accurate. By the way, in that paper Bennett described a way of adapting use of his tables to deal with lunar distances greater than 90 degrees, which escaped D Walden. George. contact George Huxtable at george@huxtable.u-net.com 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 unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---