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Guy Schwartz asked-

An interesting questions posed on a local bay area sailing group.

I will relay the answer back to Max

Guy

I wonder whether it would be possible to re-use an out-dated nautical
almanac for celnav purpose by determining the "error" through an
accurate measurement.
It appears to me that might work fine for the sun and stars, but
probably not for the moon and the planets.
Has someone maybe even done this?
-Max

=======================================

Yes, there are perfectly valid tricks, for Sun and stars. It depends on the 
precision you are asking for.

Determining the Sun/star timing-error of an almanac, as Max suggested, isn't 
a simple thing to do experimentally (because the sensitivity changes through 
the year), but neither is it necessary. Instead, you can work out how to 
extend the life of an Almanac to the next year by making the following 
adjustments, as in the 2001 or 2005 editions, page261-

====================
"Use of this almanac in 2006. This almanac can be used for the Sun and stars 
in 2006 in the following manner-

For the Sun, take out the GHA and Dec for the same date but for a time 5h 
48m 00s earlier than the UT of observation; at 87� 00' to the GHA so 
obtained. The error, mainly due to planetary perturbations of the Earth, is 
unlikely to exceed 0.4'.

For the stars, calculate the GHA and Dec for the same date and the same 
time, but subtract 15.1' from the GHA so found. The error, due to incomplete 
correction for precession and nutation, is unlikely to exceed 0.4'. If 
preferred, the same result can be obtained by using a time 5h 48m 00s 
earlier than the UT of observation (as for the Sun) and adding 86� 59.2' to 
the GHA (or adding 87� as for the Sun and subtracting 0.8', for precession, 
from the SHA of the star).

The Almanac cannot be so used for the Moon or planets. "
====================
Those instructions apply when neither year for which the prediction is 
needed nor the previous year is a leap-year. If it is so, the business of 
allowing for Feb 29 makes it all quite a lot more complicated. It requires a 
bit of deep thought.

If you take just any-old-year for your previous almanac (within limits, say 
25 years or so), without making any of the adjustments described above, then 
predictions for Sun and stars won't differ from the truth, for the 
corresponding date, by more than about 20' for Sun declination, about 5' for 
Sun GHA, with errors of about 15' for star hour-angles. That isn't too good 
for altitude navigation, but could help in an emergency, perhaps.

But you do can MUCH better than that by choosing an appropriate year, just 
four years previous. That puts it into the corresponding point in the 
calendar's cycle of leap-years. Then, without making any corrections, the 
Sun and star predictions will be within an arc-minute or so, and therefore 
perfectly usable for almost any practical purpose at sea. You can choose 8 
years previous, or 12, and the results will be nearly as good. Indeed, once 
you have collected a set of four such consecutive almanacs, you may never 
have to buy another for the rest of your navigating lifetime, depending on 
how picky you are. Same is true of sunrise and sunset times.

Some early almanacs were sold that way, giving Sun declination for four 
years ahead, so then you could go on reusing them. Really useful to the 
navigator, but not a good business proposition to the seller. But then, they 
would spice them up with nonsensical astrological predictions.

Moon and planets are another quite another matter, however. There's no 
practical method of predicting their position that way.

Motion of Sun and stars is very regular and predictable. The only real 
problem is the awkwardness of our calendar, because a year doesn't 
correspond to a whole number of days. The Sun doesn't return to the same 
point in the sky until about 365 and-a-quarter days have passed. So after 
most calendar years of 365 days, it has lagged by a quarter-day, or so. At 
the fourth year, we put in an extra day, to put it right again.

If it was exactly a quarter-day out, then choosing a four-year gap would do 
the trick rather exactly, but actually a year is more like 365.2422 days, 
not 365.25, which gives rise to the residual error.

George.

contact George Huxtable, at  george@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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