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Re: A noon sight conundrum
From: Kieran Kelly
Date: 2003 Nov 29, 19:41 +1100
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 To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM 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