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    Re: A noon sight conundrum
    From: Fred Hebard
    Date: 2003 Nov 24, 10:23 -0500

    Jay has covered the rounding errors associated with Kieran's conundrum.
      I might add that 360 degrees is equivalent to 0 degrees.  In February,
    George Huxtable presented an additional reason for the mean time of
    maximum apparent solar altitude being offset from real local noon, that
    being the northward and southward progress of the sun during the
    seasons.  Perhaps he or Herbert Prinz will chime in here and
    re-enlighten us regarding this.  This may be an alternative explanation
    to Jay Borseth's for the discrepancy Jay pointed out.
    Being a Philadelphia sports fan, I can share Kieran's pain regarding
    the loss of the Rugby Cup, although perhaps with more satisfaction than
    if I were a New York Yankees fan!
    On Nov 24, 2003, at 5:25 AM, Jay Borseth wrote:
    > I believe you're just seeing a rounding artifact due to lack of
    > displayed precision in the results from the USNO webbsite.
    > Pocket Stars (www.nomadelectronics.com) uses the same fundamental Novas
    > routines which are used to create the Nautical Almanac and presumably
    > also to create the tables on the USNO website.  It provides the
    > following output, showing Az to an additional digit of precision:
    > UTC            Hc             Az
    > 3h 15m 51s     47d 27.29'     359.90d
    > ...
    > 3h 15m 36s     47d 27.29'     359.98d
    > 3h 15m 35s     47d 27.29'     359.99d
    > 3h 15m 34s     47d 27.29'     360.00d
    > 3h 15m 33s     47d 27.29'     000.00d
    > 3h 15m 32s     47d 27.29'     000.01d
    > 3h 15m 31s     47d 27.29'     000.01d
    > 3h 15m 30s     47d 27.29'     000.02d
    > 3h 15m 29s     47d 27.29'     000.03d
    > 3h 15m 28s     47d 27.29'     000.03d
    > ...
    > 3h 15m 16s     47d 27.28'     000.10d
    > So the sun does in fact continue to move smoothly during the 9 seconds
    > on either side of the meridian time.
    > Hijacking this thread for a moment...
    > Note that the meridian time of 3h 15m 33s is offset from your result by
    > approximately 5 seconds.  I assume that the discrepancy in local noon
    > between various NOVAS implementations is due to differing values of
    > DeltaT (the difference between "Terrestrial Time" and "Universal Time"
    > which can be expressed as Delta T = 32.184 s + (TAI - UTC) - (UT1 -
    > UTC)).  Pocket Stars estimates the value of DeltaT based on
    > interpolating the Julian Day from the following table:
    > Julian Day Number                  DeltaT
    >  2447892.5000000, /*1990.0000,*/   56.8550,
    >  2449718.5000000, /*1995.0000,*/   60.7850,
    >  2451544.5000000, /*2000.0000,*/   63.86,
    >  2453371.5000000, /*2005.0000,*/   69.0,  // I've also seen an
    > alternate
    > estimate of 66
    >  2455197.5000000, /*2010.0000,*/   74.0,  // I've also seen an
    > alternate
    > estimate of 70
    > Does anyone know what value of DeltaT is used for 2005 and 2010 on the
    > USNO website?  I'm guessing it's just using the 2000 value of 63.86 for
    > dates beyond 2000 as this roughly accounts for the local noon
    > difference.
    > - Jay
    >> -----Original Message-----
    >> From: Navigation Mailing List
    >> [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM] On Behalf Of Kieran Kelly
    >> Sent: Sunday, November 23, 2003 11:59 PM
    >> Subject: FW: A noon sight conundrum
    >> On a recent trip to Central Australia I performed an
    >> observation of the sun to determine local noon and thus
    >> longitude. This was done by performing a series of
    >> observations about an hour before and an hour after what I
    >> thought would be the time of meridian passage. On returning
    >> to Sydney I was able to locate my exact position on a map and
    >> was curious to see how close to local noon my calculation was.
    >> My definition of local noon is:
    >> (1) When the centre of the sun crosses the observers meridian and
    >> (2) When the centre of the sun is due north of the observer
    >> i.e. its Zn is 360d true and
    >> (3) When the centre of the sun reaches its highest altitude
    >> To test my results I went to the USNO site and plugged in the
    >> following
    >> data:
    >> Position        :       S 21d 48.3'     E 132d 40.0'
    >> Date:            July 20, 2002
    >> The USNO computer gave me the following results:
    >> GMT             Hc              Zn
    >> 3h 23m 36s      47d 26.6'       357.3d
    >> 3h 15m 48s      47d 29.2'       359.9d
    >> 3h 15m 47s      47d 29.2        360.0d
    >> 3h 15m 40s      47d 29.2'       360.0d
    >> 3h 15m 38s      47d 29.2'           0.0d
    >> 3h 15m 35s      47d 29.2'           0.0d
    >> 3h 15m 34s      47d 29.2'           0.0d
    >> 3h 15m 29s      47d 29.2'           0.0d
    >> 3h 15m 28s      47d 29.2'           0.1d
    >> 3h 07m 42s      47d 26.6'           2.7d
    >> Based on this analysis local noon was at 3h 15m 39s i.e. the
    >> mid point between the equal altitudes of 47d 26.6'. I have
    >> several problems with this answer.
    >> Firstly how can the Azimuth of the sun move from 0d to 360d
    >> as it passes the local meridian. I have checked my two
    >> compasses - a Francis  Barker prismatic and a modern Silva
    >> baseplate and neither exhibits 0d. Isn't zero degrees the
    >> absence of degrees? And aren't there 360d in a circle
    >> therefore the sun bears 360d at local noon. By definition it
    >> doesn't move from 0d to 360d. Further the USNO site shows the
    >> centre of the sun maintaining a constant Zn of due north (0d
    >> or 360d) from 3h 15m 29s to 3h 15m 47s - a period of 18s.
    >> While the sun's altitude does not change at culmination its
    >> progress across the sky certainly does. I do not believe it
    >> is stationary for 18s.
    >> I may have made a mistake and would appreciate input (or
    >> possibly the sun behaves differently down here). We have just
    >> lost the Rugby World Cup so the sun may never shine in
    >> Australia again.
    >> Kieran Kelly

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