NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: 1491 The year China discovered longitude
From: Frank Reed CT
Date: 2004 May 9, 13:30 EDT
From: Frank Reed CT
Date: 2004 May 9, 13:30 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 observers.
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
" 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 observers.
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
