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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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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