# NavList:

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

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Re: Star-star distances for arc error
From: George Huxtable
Date: 2009 Jun 26, 14:30 +0100

```Gary asked-

I don't follow the discussions of lunar distance very carefully. What
is the expected accuracy of the derived longitude in practice?

There's an unavoidable  factor of about-30 comes in, from the ratio between
the length of the month and the length of the day. So the Moon travels round
the sky, with respect to the stars, at only about half a degree per hour.
Greenwich time is determined from measuring that motion. So if you can
measure Moon position to 1 minute of arc, with respect to the star
background, then you can measure Greenwich Time to about 2 minutes-worth,
thus longitude to about 30 minutes.

If you could measure Moon position to half a minute of arc, which was about
the best anyone could hope for at sea, even in good conditions, then if
there were no other errors (in prediction, in correction, in deducing local
time from another observation), you could get longitude to about 15' of arc,
15 miles in the tropics. Dyson's estimate of 20 miles wasn't far out, in my
view. Dyson was careful to state (from his 1920s perspective)
"Unfortunately, even with perfect tables, , it is found that the most
skilful mariner cannot obtain avery accurate position of his ship in this
manner. With great pains and elaborate calculations he can be correct to
within 20 miles."

And so, Frank's qualification to that statement is irrelevant "And don't
forget that an error of 20 miles included the error from the lunar distance
tables in the Nautical Almanac. Since those were about 0.3' for the latter
half of the period when lunars were commonly used, the implied error in the
observations is even a little less.". It wasn't. Dyson was assuming perfect
tables, and said so.

Frank denigrates the Astronomer Royal as "not knowledgeable on lunars". I
have asked Frank before now, on several occasions, to explain to us his own
qualifications and experience in determining lunars fron a vessel AT SEA. He
has never responded.

George.

contact George Huxtable, at  george{at}hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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```
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