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    Re: Winter solstice this weekend
    From: Bill B
    Date: 2014 Dec 20, 04:22 -0500

    On 12/20/2014 3:11 AM, Paul Hirose wrote:
    Thanks Paul. This is something I've curious about since Herbert's
    posting, but has not come up in OCD detail ;-)
    > 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.
    > View and reply to this message

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