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    Re: A noon sight conundrum
    From: Kieran Kelly
    Date: 2003 Nov 29, 19:41 +1100

    To Paul Hirose and others,
    Thank you for your input but I am now completely lost. If I take the USNO
    figures they suggest to me, on an equal altitudes basis, that noon occurs at
    3h 15m 39s. However you appear to demonstrate that this is not correct.
    So I went back to first principles and posed the question: If an observer is
    standing at longitude 132d 40'E on July 20, 2002 what time will the sun
    cross his meridian if Meridian  Passage quoted in the Nautical Almanac that
    day is 12h 06s? Converting the arc of 132dd 40' to time I derive longitude
    of 8h 50m 40s E.  Subtract his from GMT of Meridian Passage as we are east
    and I derive a mer passage on that day at Long 132dd 40' of 3h 15m 20s GMT.
    This is 19s different than the figure provided by an equal altitudes
    computation from the USNO site.
    My questions are:
    1) Where is my error and why is there such a big discrepancy between the mer
    passage as indicated from first principles in the Almanac and what the USNO
    site says?
    2) Is the USNO site not accurate enough to perform this type of observation
    i.e. test and verify field observations by comparing to USNO data? This is
    in fact what I was doing.
    3) In your learned opinion what was the time of meridian passage on that day
    at long 132d 40' E.
    4) Am I getting confused between meridian passage i.e. when the sun crosses
    the meridian and noon i.e. when the sun culminates and reaches its highest
    point. I thought both were the same. Apparently not.
    Many thanks
    Kieran Kelly
    -----Original Message-----
    From: Navigation Mailing List
    [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Herbert Prinz
    Sent: Thursday, 27 November 2003 10:09 AM
    Subject: Re: FW: A noon sight conundrum
    Paul Hirose wrote:
    > By switching the MICA time scale to TT
    > and applying the actual offset between TT and UT1 on the date of
    > Kieran's observation, I got these values for zenith distance and
    > azimuth:
    > 2002 Jul 20 03:16:43.4      42 30 54.3       0 00 02.6
    > 2002 Jul 20 03:16:44.4      42 30 54.3     359 59 41.9
    Paul and All,
    Unless you have a new magic version of MICA, things are not as simple as
    they look on the surface.
    There is some more processing under the hood, which Paul has been hiding
    from us. When one switches the time scale in MICA to TT, longitudes are
    referenced to the ephemeris meridian. That is a line east of Greenwich
    where the zero meridian would be, if the Earth would rotate at uniform
    speed. In order to obtain the above results, one has to adjust Kieran's
    longitude by the angle corresponding to the rotation during the time
    interval deltaT, i.e. to 132deg 23' 57" or thereabouts.
    In the following way it's easier to see without much calculation that
    inaccurate deltaT cannot have much impact on transit times: UT is, by
    definition, the time scale that leaves the time of sun transit invariant.
    Ephemeris time (TT) governs the position of the sun w.r.t. the equinox.
    Each time we introduce a leap second into UTC, TT gets a second ahead.
    But how much do the sun's celestial coordinate, i.e. the RA or SHA and
    its declination change in a second?
    And Paul concluded...
    > Those times correspond to the UT1 times that I previously posted:
    > 2002 Jul 20 03:15:39.0      42 30 54.3       0 00 02.3
    > 2002 Jul 20 03:15:40.0      42 30 54.3     359 59 41.6
    > So it looks like meridian passage occurred at 03:15:39 UT1, which
    > agrees with what Kieran estimated.
    But the agreement is a mere fluke. First, Kieran says that he estimates
    meridian transit from the two "equal" altitudes at 3:07:42 and 3:23:36,
    given as 47deg 26.6'.  In fact, these altitudes differ by 7.5" from each
    other when computed with higher precision. And they remain within a +/-
    0.05' bandwith for a duration of ca. 8 seconds. This is enough to throw
    the result off by 5 seconds. One simply cannot compute the time of
    meridian transit from two altitudes taken within such a short time span
    or so close to noon.
    Second, your own data obtained from MICA that you posted in an earlier
    message shows beautifully that meridian passage preceeds culmination by
    5.5 seconds, in perfect agreement with the correction formula posted in
    various forms by Zorbec Legras and George Huxtable.
    The two errors seem to cancel each other in Kieran's analysis.
    Herbert Prinz

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