On 2009 Jun 9, at 09:08 , Irv Bromberg wrote:
Irv replies: If I'm not mistaken, there is no way to calculate an ecliptic longitude of 0.0° without using 0° solar declination as the reference. According to the IAU, the solstices and other equinox can be calculated as ecliptic solar longitude relative to that zero (known as "the equinox of date"), so as a consequence the other equinox will not occur at a solar declination of exactly 0°.
Irv adds: I tried to find some examples of that, where the solar declination of the southward equinox is not exactly 0° at the time that the ecliptic solar longitude relative to the northward equinox of date is exactly 180°, but my solar declination function always returns 0° at the southward equinox. When I looked at the code, however, I found out why: my solar declination function reckons the solar declination on the basis of the obliquity of the ecliptic and the solar longitude! The source formula is at:
This approach is probably very widely used, thus leading to the illusion that the southward equinox is at the same moment by either method. When the solar declination is independently determined by consideration of all the factors that I listed previously, however, slight differences ought to be found, as exist in the southward equinox moments output generated by SOLEX 10.1 when searched for by ecliptic longitude vs. solar declination.
-- Irv Bromberg, Toronto, Canada
