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From: Frank Reed (no email)
Date: Sun May 09 2004 - 13:30:58 EDT
Kieran K wrote:
" How did they determine what star was crossing their local meridian at the
time of U3? To do this they would have needed an accurate clock and done a
double altitude shot both ante and post meridian."
No, I wouldn't say so. Finding the meridian to a degree or two of accuracy is
one of the easiest things that an observer can do (on land at a fixed site!).
And:
"The author suggested they used a clepsydras (water clock). Would this have
been accurate enough?"
It's not even necessary. If you can describe the point in the heavens that is
on the meridian at the time of some specific event in the eclipse, you're
done. You send your results back home (or to anyone else who watched the eclipse
and performed the same observations). The difference in longitude between the
two points in the heavens is the difference in longitude between the observe
rs.
And wrote:
"As an experiment I went outside with a compass and tried to visually
ascertain true North and which star was crossing my local meridian at a point in
time. Impossible."
Try again. And remember, there's no rush. After the meridian has been found
once, you can draw a line on the ground and you have it forever. Furthermore,
they don't even need the whole meridian. The zenith will do! On land you can
find the zenith with a plumb line. Once that's done, you can easily record the
location of the zenith within a star pattern (e.g. the "center of the keystone
of Hercules", or the "middle of the handle of the teapot in Sagittarius"). A
single zenith observation simultaneously yields latitude and local sidereal
time. If observers scattered around the globe record what they see at their
zenith at the instant of some widely visible astronomical event, they have mapped
the world.
And:
"2) What instrument did they use to make a sufficiently accurate
celestial observation of a star to determine its meridian passage? Certainly not a
sextant! Did they have telescopes to determine the exact moment of U3. I don't
think so."
I don't think either complaint is relevant. They didn't need to measure an
altitude. They needed nothing more than a line drawn on the ground, the ability
to hang a string parallel to that line above it (with plumb lines hanging off
it at convenient points) and their own eyes to observe the eclipse. You don't
need a telescope to see U3!
And:
"3) Could this observation have been made without a very accurate set
of tables such as a Nautical Almanac?"
Absolutely. The motion of the Moon over the course of many decades has been
understood to an accuracy of +/-1.5 degrees in ecliptic longitude and +/-0.25
degrees in ecliptic latitude since the time of Ptolemy. Thirteen centuries
later (really an enormous stretch of time), the Chinese easily could have had
access to Ptolemy's work or components of it from numerous sources. They also
could have developed their own lunar model independently. Either way, pre-modern
computation skill would have been more than satisfactory for predicting lunar
and solar eclipses.
And:
"4) What happened if no star was crossing the meridian at the time of
U3 or was so faint that it could not be observed?"
The meridian is loaded with stars. Assuming we seek an accuracy of, say, +/-1
degree, there is almost certain to be some star brighter than magnitude 3
near the meridian. Even if you limit yourself to first magnitude stars, you can
record something like "the meridian crosses the line between Vega and Deneb
approximately 35% of the way from Vega towards Deneb".
From my perspective, the most difficult part of this observation as a method
for determining longitude is observer bias in defining when U3 has actually
occurred. It's largely a matter of experience. Still, with relatively central
lunar eclipses, this should yield a timing error of no worse than perhaps ten
minutes. That ten minute error corresponds to an error of 2.5 degrees in
longitude. Add to that an independent error of +/-1 degree from our meridian star
observation, and you get an expected error in the longitude of about 2.7 degrees.
Assuming everyone records their observations and returns them to a central
mapping authority, a fairly accurate map of a large portion of one hemisphere
could be produced in only a few years (a "few" because a third to a half of
your observers will be clouded out for any given lunar eclipse).
Frank R
[X] Mystic, Connecticut
[ ] Chicago, Illinois
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