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    Re: When is the Autumnal Equinox?
    From: Paul Hirose
    Date: 2011 Sep 09, 17:25 -0700

    Geoffrey Kolbe wrote:
    > The definition of the 
    > equinoctal points on the celestial sphere are those points where the 
    > ecliptic intersects the celestial equator.
    > Thus the origin of the 
    > celestial sphere, the first point of Aries, zero degrees of celestial 
    > longitude, is the position of the sun on the celestial sphere as it 
    > crosses the equator from North to South and has zero declination.
    Not *strictly* correct, because at high precision it's inconsistent with 
    the first sentence. The notion of the ecliptic as the apparent path of 
    the Sun must be abandoned in faver of the mean plane of the orbit of the 
    Earth - Moon barycenter (center of gravity) about the solar system 
    Earth and the Moon also orbit each other about their barycenter, in an 
    orbit inclined with respect to the ecliptic. It follows that Earth's 
    center is on the ecliptic only twice in each monthly orbit. Due to 
    parallax, an imaginary observer at the geocenter therefore sees the Sun 
    travel a sinuous path north and south of the ecliptic.
    The wobble is less than 1", so at Nautical Almanac precision the
    geocentric apparent Sun passes through 12 hours RA and zero declination. 
    But at .1" precision it doesn't happen unless you're lucky enough to 
    catch the right point in the wobble cycle.
    > But, after a little digging, it would appear that the continuously 
    > moving feast that is the "dynamical equinox", as defined above, is not 
    > convenient for astronomical catalogues, so they fix an equinox at some 
    > epoch to create a "catalogue equinox" as the point of reference for the 
    > catalogue.
    That used to be the practice for star catalogs. However, nowadays they
    use the ICRS, which is independent of any motion of a solar system body. 
    Its equator and prime meridian are implicitly defined by adopting a set 
    of quasar coordinates.
    > I suspect that the definition which Paul quoted was a reference to a 
    > catalogue equinox for the Astronomical Almanac, whereas the dynamical 
    > equinox would be what you would lift out of the pages Nautical Almanac.
    If "the definition" is "the point on the celestial sphere where the
    ecliptic and the celestial equator intersect, and which the Sun is near
    at the time of the vernal equinox," that's true for all reference
    systems with an origin based on the equinox.
    There are differences in exactly which equator is used. Star catalogs 
    formerly had coordinates with respect to the equinox and mean (nutation 
    removed) equator at some standard epoch.
    For solar system bodies, geocentric coordinates with respect to the
    equinox and true (affected by nutation) equator of date are usually
    tabulated in almanacs. In recent years a new paradigm has appeared, 
    though. Instead of the equinox, the "celestial intermediate origin" 
    marks the zero point on the equator. See any Astronomical Almanac from 
    the past few years.
    But I'm drifting away from the original subject. The question was asked 
    if there's a site to get equinox times to one second. Not directly, as 
    far as I know. But an online calculator can do the hard work.
    For example, the equinox on the 23rd of this month is at 09:05 UT 
    according to the USNO. Find the time to one second. It should be between 
    09:04:30 and 09:05:30.
    To identify the correct second, send an email to horizons@ssd.jpl.nasa.gov
    Compose it in plain text (UTF-8 is OK). If you send HTML the JPL machine 
    will return an error message. For the subject, use the single word: job
    In the message body, put:
      COMMAND    = 'sun'
      START_TIME = '2011-sep-23 09:04:30ut'
      STOP_TIME  = '2011-sep-23 09:05:30'
      STEP_SIZE  = '60'
      QUANTITIES = '2,31'
      TIME_DIGITS = 'sec'
    About a minute after sending you'll receive a table of geocentric 
    apparent right ascension, declination, ecliptic longitude, and latitude. 
    The numbers tend to confirm most of what I've said.
    1. At 09:04:30 the declination is already -.2". If the equinox is the 
    moment of zero declination, the USNO's time is not correct to the 
    nearest minute.
    2. On the other hand, if the equinox is the moment of longitude 180°, it 
    occurs at 09:04:39. That's consistent with the USNO.
    3. The Sun does not pass exactly through right ascension 12 h, 
    declination 0. When RA is 12h 00m 00.00s, dec. is -.4".
    4. Ecliptical latitude is -.4" throughout the minute.
    I filter out messages with attachments or HTML.

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