A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2010 Apr 5, 03:30 -0700
Dear Andres and Robin
In further reference to :
[NavList 12664 ] Re: Applications of Complex Analysis to Celestial Navigation
Date: 2 Apr 2010 08:43
First of all, Congratulations again to you Robin for a very clever approach to solve CelNav with complex Numbers.
Andres and Robin you might have noticed that the Lunar example quoted here by Robin probably has some unusual characteristics which immediately caught up my attention when Robin first made his article available to us the earlier time (i.e. by the end of 2009 as I can best remember).
Here are (again) the data published by you Robin :
Absarat, Nubia, Nile Valley, 31st December 1884
Moon-Markab (Star alpha Pegasi) LUNAR
Apparent Lunar Distance d = 103°26'24",
Apparent Lunar Altitude hM = 35°37'28",
Apparent Stellar altitude hs = 40°17'24"
"Upon application of corrections for horizon dip, parallax, augmentation, etc., the geocentric altitudes are determined to be
Geocentric lunar altitude, h'M = 36°26'01"
Geocentric stellar altitude, h's = 40°16'15"
further down the page, Robin you gave your own derived results as follows :
the true geocentric distance of the Moon from alpha Pegasi at the time of measurement,
... [a few words suppressed by me here] ...
d' = 102°39'30.6"
an end-resulst to be compared to the Land-Surveyor published result of 102°39'30"
Your method works extremely well. No doubt on that !!!
Interesting Lunar performed by a Land Surveyor, which falls in the now well known category singled out and described by Frank and in which both bodies are almost in fully opposite directions. Therefore you can very simply solve this one with just a simple Nautical Almanac.
1 - EXACT POSITION OF ABSARAT NUBIA, NILE VALLEY
I am unable to pinpoint this exact ABSARAT, NUBIA, NILE VALLEY place just from the readily available standard Google Earth information.
However, from carefully reading and interpreting the pages 264, 265, and following ones (there is one Absarat village in the Nile Valley, Sudan Dongola Province, which lies some 37 Miles (due) south of Kosheh through the desert road, and 14 miles downstream of Dulgo) ... at the address here-after (sorry for the long characters list)
I was able to best guess that ABSARAT is (most) probably located at N20°26'06" / E030°29'40"
Can anybody, more knowledgeable than me in Sudan Geography, can confirm such ABSARAT location ? Thank you in advance, M. Quitehelpful N. Ybody.
BACK TO THIS LAND SURVEYOR LUNAR
If you process this Lunar with Frank's on Line Computer (and by the way Frank, thank you for your now very clear indications on the Moon/Sun "refractional flattening" and Earth shape "oblateness") with an approximate position as determined here above :
- with "Far Limb", you get a Cleared Distance equal to 102°22'8, and
- with "Near Limb", you get a Cleared Distance equal to 102°56'2
... no way to fall anywhere any closer from the resulting Cleared Distance published as 102°39'30" ... which INTERESTINGLY ENOUGH lies almost exactly halfway between the 2 values found by Frank's OLC.
Therefore, I processed again this example on my own (delta-T = -5.6s) with the "Center of figure" of the Moon ( i.e. a "fictitious Moon" having a semi-diameter equal to zero) and here we are ... Cleared distance this time is 102°39'36", quite close from the one you quoted (102°39'30.6")
CONCLUSION AND OPEN QUESTIONS
Assuming that my interpretation of this Lunar and that the computations herabove are all correct (can someone confirm them please ?), it then looks like Land Surveyors might sometimes have had the habit of publishing topocentric "Center to Center" distances rather than topocentric "Limb to Limb" distances.
- Did they directly observe such "Center to Center" distances ? And if so, with which instrument(s) ? Or
- were such "Center to Center" distances intermediate results, which for some reason (why?) they usually published while their did actually have just earlier observed our most familiar - but nonetheless unpublished - "Limb to Limb" distances ? And if such was the case, which instrument(s) did they use ? And
- which second bodies did they most often use ? The (somewhat restricted) list of our dear and well known Navy Lunars stars, or a more comprehensive list including a greater number of fainter stars ? Or even the Planets ?
Anybody having some knowledge here is most welcome to contribute, as I do not recall having read anything here on this specific subject of the Land Surveyors Lunars.
Best Regards to you all
Antoine M. "Kermit" Couëtte
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