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Re: accuracy of Cook's lunars
From: Frank Reed
Date: 2013 Jan 7, 12:30 -0800

Hanno Ix, you wrote:
"I wonder if the ephemeris especially of the moon as used by Cook can still be studied today. Naturally, Cooks errors cannot have been any smaller than the ones of those."

Even better. Although we can certainly study the tables (Mayer) that were used to generate the early Nautical Almanacs, we may as well jump straight to the product itself. Very nearly all Nautical Almanac editions from the first in 1767 through the early 20th century are available in full on Google Books. To compare these with correct values (as nearly as can be determined given some continuing small uncertainties in delta-T for that era), we need lunar distance tables given, preferably in degrees, minutes, and seconds, as was normal back then, and we need those tables for the rather unusual argument of GAT, Greenwich Apparent Time, which was standard before the switch to GMT which came in 1834 (and was considered seriously late by commentators at the time). Back in 2004 I made available online software which does just that. I am attaching an image of a portion of the tables for Sun-Moon lunar distances from August 1767 compared against data from my online app for the same dates, lined up to match the tabular format of the old Nautical Almanac. As you can see, there are cases where the difference is as large as 50 seconds of arc, but there are others where the difference is only 1 second of arc. For an "average" lunar this will add an uncertainty equivalent to an error of something like 0.25' in the distance. Whatever the observational error may be, this error would sometimes increase it and other times cancel it out. On average two sources of error add as the square root of the sum of the squares, so if they had, let's say, 0.25' error from observations, then the net error would be sqrt(2)*0.25 or about 0.35' (equivalent to 42 seconds in time or 10' in longitude). By 1805 the errors in the lunar distance tables had been significantly reduced. By 1875, they were nearly perfect for navigational use (though lunars were essentially obsolete at sea by that date, there were still a handful of practitioners, and there were definitely lunarians on land, exploring and mapping Africa, for example).

-FER

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