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Michael, you wrote:

"In reference to the almanac page posted by Walden that shows the lunar
distance for Antares on 8/1/773 at noon to be 48-18-36.
I have some questions.
1) What delta T would be appropriate for that date?"

My online lunar distance tools use dT=15 for 1770, dT=16 for 1780, and
simple linear interpolation for dates in between. So roughly dT=15.4 for
this date. Not significantly different from dT=15.0.

And you wrote:
"2) Would that distance be based on topo position or apparent position or
something else? And what location would be assummed?"

The distance in the Nautical Almanac from any year before 1834 is the
geocentric distance at a particular moment of Greenwich Apparent Time. From
a modern perspective, this is the LD at a given value of Sun GHA. In
calculational terms, you do a little loop for GMT around the time in
question, until the Sun's GHA has the required value. For example, if I want
some astronomical quantity for 1500 GAT, I need to find the exact GMT when
the Sun's GHA is 45 degrees (three hours past noon). Through 1833, the
Nautical Almanac listed the LDs in GAT. After that, they were listed in
terms of GMT, which is more appropriate for comparisons with chronometers.

And you wrote:
"3) What distance is given by current almanac programs for that date?"

Matching the value you've listed as "apparent", 48-14-56 would be the
geocentric LD for 1200 GMT.

To compare with the published almanac, we need the LD for 1200 GAT. My
online tools at www.HistoricalAtlas.com/lunars have provided this
information for about three years. You can select GAT for the data output.
When you do this for the date in question, you find 48-18-16 at 1200 GAT,
which differs 20 arcseconds from the published value. So for a navigator "at
sea", no matter how well the observation was made, the resulting longitude
would be in error by about 10 minutes of arc. It is possible to correct this
error later when the expedition returns to England... if the astronomers at
Greenwich were observing frequently and if they had good weather. In fact,
even without a published Nautical Almanac or any theory of the Moon's motion
at all, observations from different observers could be cleared and compared
to yield an accurate difference in longitude. I know of only one case where
this was certainly done, but there may have been a few others, especially
for longitudes as important as these. It was a lot of computational labor
and probably not worth the effort since chronometers were improving so
rapidly.

One other issue you have to worry about with old almanac data and
navigational observations is the choice of date accounting. There's the
common, modern dating system where the day starts at midnight. There's the
sea account system where the day starts at noon. And then there's the
astronomical day which also starts at noon --but not on the same day as the
sea account. :-) Luckily, in published tables and logbooks, it's not hard at
all to figure out which one is used. They often say so explicitly and if
not, it's clear from the measured distances and altitudes. The tools on my
web site incidentally assume that the entered or selected date is the
standard modern date.

 -FER


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