The following is a post I did in a usenet group about how Hipparchus used eclipses to measure the ecliptic longitude of stars. Thought is might make some interesting reading - Canopus56(Kurt) ========================= mack wrote:
If I put a bit of time into it, I can by looking at the fuzzy terminator against blue sky just after sunset, differentiate a full moon from a moon 24 hours away from a full moon, but that's about as good as I can get. Presumably the Greeks had much better accuracy than that. How did they do it? <snip> Presumably any of these measurements would be confounded by parallax?
Evan's _The History and Practice of Ancient Astronomy_ also contains an example of how Hipparchus might have used eclipses to measure the solar (ecliptic) longitude of Spica. Evans at 256-259. Once the solar longitude is found, transformation into right ascension is a straight-forward application of a spherical right triangle. The technique Evans used to demonstrate how the ancients estimated the solar longitude of Spica might be applied to the partial lunar eclipse set for Monday morning - Oct. 17 at 12:03 UTC to determine the solar longitude and right ascension of alf Psc. The following are some instructions. Materials: Graph paper, protractor with weight on a string to measure angles (or a sextant), a drafting compass and a metric ruler (to measure scales). 1) On the graph paper, draw a degree grid for your western horizon about 20 deg by 20 deg. 2) As the maximum eclipse approaches, with the protractor or sextant, measure and mark the relative alt and az of: a) sigma Aries b) omicron Psc You can use any fixed point on the horizon or due west. Hipparchus would have had his catalogue noting the ecliptic latitudes of some bright stars along the ecliptic. The ecliptic latitudes for the two stars above are: Obj Ecliptic latitude sigma Aries -01d17m39.1s or about -1.294167 decimal degrees omicron Psc -01d37m12.9 or about -1.62 decimal degrees and for checking purposes (not used in computations) - Obj Ecliptic longitude sigma Aries 44d 56m 38.6s omicron Psc 27d 44m 35.3s c) To define the ecliptic, draw a circle around sigma Aries and omi Psc with a radius equal to the absolute value of their ecliptic latitudes. A tangent line along the top of the two circles will define the ecliptic. The Moon will be about 0.7 degrees above this line at the maximum eclipse. You can confirm the obliquity of the ecliptic at your geographic position by downloading an Excel spreadsheet from: http://www.jqjacobs.net/astro/arc_form.html For example, at my op the angle between the horizon and the ecliptic at the time of maximum eclipse will be about 42.3 degrees. d) At the point of maximum eclipse - 1) measure the alt and az of the Moon and plot it on the graph paper. 2) the zenithal distance of the Moon. 3) for reference purposes, also measure the angular distance between the Moon and omi Psc, the Moon and alp Psc, and omi Psc and alp Psc. e) Now adjust the plotted position of the Moon for geocentric parallax using the equation: P = arcsin ( ( r * sin z ) / d ) where: r = radius of the Earth d = geocentric earth moon distance (center of earth to Moon) where - r/d = approx. 1/57 z = Moon's zenithal distance f) Apply the parallax in azimuth on your chart and replot the Moon higher. g) On the chart, construct a perpendicular line through the center of the Moon to the ecliptic (using the drafting compass). For geometric construction hints see - http://whistleralley.com/construction/c3.htm in http://whistleralley.com/construction/reference.htm h) On the chart, construct a perpendicular line through the center of alpha Psc to the ecliptic (using the drafting compass). i) Measure the degrees of longitude between the Moon and alpha Psc on the ecliptic line. Hipparchus was believed to have constructed a table of solar ecliptic longitudes although his tables have not been passed down. That is he knew how to compute the mean and apparent solar longitude based on his prior estimation of the tropical year at 365 1/4 days. See Evans _History_ at 226-231 re: solar longitude tables. j) At the moment of maximum eclipse on 10/17/2005, the Sun's position - which is 180 degrees from the Moon will be - JD Ecliptic long RA/Dec 2453661.062315 +204º16'33" +13h29m55s -09º24'47" per http://www.gcstudio.com/cgi-bin/sunpage and the RA and Dec per the Minor Planet Center will be - Date__(UT)__HR:MN R.A._(ICRF/J2000.0)_DEC R.A.__(a-apparent)__DEC 2005-Oct-17 12:03 m 13 29 25.49 -09 21 51.6 13 29 42.07 -09 23 33.0 Note that if the Sun is 180 degrees away, the ecliptic longitude of the Moon should be about - 24d 16m 33s = +204d 16m 33s - 180d 0m 0s and that's about 3 degrees away from the ecliptic longitude of omi Psc at - 27d 44m 35.3s which looks about right on the chart I plotted for the eclipse from Cartes du Ciel. k) On your graph paper-chart, measure the ecliptic longitude between alpha Psc and the Moon along the ecliptic line. Add this to the ecliptic longitude of the Moon. This gives the result, the ecliptic longitude of alpha Psc. In conclusion, this is one probable method by which an ancient like Hipparchus would have used the Moon and eclipses to determine a low precision ecliptic longitude position of a star. In this example, I have not adjusted for precession from 2000 or for atmospheric refraction. Hipparchus discovered precession, but atmospheric refraction was first published by Ptolemy in the second century C.E. and after Hipparchus. Regards - Canopus56 __________________________________ Yahoo! Music Unlimited Access over 1 million songs. Try it free. http://music.yahoo.com/unlimited/