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    Re: Winter solstice this weekend
    From: Paul Hirose
    Date: 2014 Dec 19, 23:56 -0800

    According to the formal definition, solstice occurs when the Sun's
    apparent ecliptic longitude is 90° or 270°.
    
    http://asa.usno.navy.mil/SecM/Glossary.html#_S
    
    Longitude increases at a nearly constant rate of 1° per day, or 1
    arcsecond per 24 seconds of time. Thus it yields a more definite time
    than you'd get from declination stand-still.
    
    Similarly, an equinox is when the Sun's longitude is exactly 0° or 180°.
    Its declination would be zero at these times if the Sun were exactly on
    the ecliptic. But in general it's not, so normally the Sun is slightly
    displaced from the equator at an equinox.
    
    For example, I calculate the winter solstice at December 21 23:04:09
    Terrestrial Time, or 23:03:02 UTC. JPL HORIZONS agrees within about 36
    milliseconds of arc. Possibly the discrepancy is due to different
    ephemerides or precession / nutation models. Or I blundered a little
    with the JPL DE422 ephemeris and IAU 2006/00A model.
    
    At that time, longitude and R.A. are equal. I believe this is always the
    case at a solstice, because the applicable longitude and R.A. meridians
    coincide.
    
    It's not the case at the equinoxes, where the meridians are skewed by
    the obliquity of the ecliptic (ca. 23.5°). This would make no difference
    if the Sun were exactly on the ecliptic, but as I said above, generally
    it's not. For instance, I put the autumnal equinox at Sep 23 02:30:12
    TT. At that time, Sun geocentric apparent R.A. was a couple tenths of an
    arcsecond short of 180°, and declination about .4 arcsecond south of the
    equator.
    
    The reason the Sun doesn't exactly follow the ecliptic is suggested by
    definition #1 of "ecliptic" in the glossary above: "1. The mean plane of
    the orbit of the Earth-Moon barycenter [center of gravity] around the
    solar system barycenter." Since Earth and Moon orbit once per month
    about their barycenter, in a plane not parallel to the ecliptic, an
    imaginary observer at the geocenter travels north and south of the
    ecliptic on a monthly cycle. Due to parallax he sees a corresponding
    wobble in the Sun's declination. It's a few tenths of an arcsecond.
    
    

       
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