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Re: Longitude by calculator -theodolite
From: Bruce J. Pennino
Date: 2013 Jun 29, 00:24 -0400
From: Bruce J. Pennino
Date: 2013 Jun 29, 00:24 -0400
Hello All :
Thank you for looking over the theodolite data. I did use the traditional CN equation for calculating the LHA. That was incorrect for a number of reasons. Mostly, the moon was too far south. FER's suggestion is best: Calculate HC and compare to Ho. Actually, for my next set of sights I'm going to use some early rising stars at twilight. Should work ok. Someone asked about my using the moon. I used the moon because I can't put any shades on the theodolite, and there would be optical distortion (maybe) as suggested.
I am measuring time to nearest whole second. So I'm probably accurate to plus or minus 1/2 second for a single measurement, at very best . Wistful dreaming? But by recording 5 points and plotting a graph, hopefully a selected point from the "best fit" graph is good to 1/2 to 1 second. My goal has been to determine my total precision and accuracy. I now believe the calculation of (Hc - Ho) will indicate error of my total measuring scheme. The theodolite is a "6 second gun", which means I can directly read to 3 seconds, and maybe estimate to the nearest second or so. With my theodolite ,I now believe, on the average, I can measure a zenith angle on a celestial body to plus or minus 6 seconds of arc, at best. Maybe overall accuracy is plus or minus 12 seconds of arc? I'm measuring in normal viewing mode. If I flipped the scope and resighted every other sight I might improve this by a 1.5 seconds. Collimation error is about 1.5 seconds, but there is scatter in this data.
Very roughly then, I can locate myself to about plus or minus 1000 ft ?. I'm just astounded that this is possibly using standard NA tables and techniques via the zenith angle! Almost mystical!
Thanks again and best regards.
Bruce
On Sun, Jun 23, 2013 at 2:45 PM, =?utf-8?Q?Antoine Cou=C3=ABtte?= wrote:
___________________________________
re : http://fer3.com/arc/m2.aspx/Longitude-calculator-theodolite-Pennino-jun-2013-g24454
Hello Bruce,
Thanks for publishing your theodolite data which I first decided to "number-crunch" them as standard LOP's.
Here are the starting data I have used under our " CelNav classical form", as "best-guess processed/derived/translated" from the ones you published :
UT Date of observations : June 20th, 2013 around 00h30m00.0s UT1
TT-UT = +68.3s
Observer's Position at N42°2°'3 W071°48'5 and Altitude : 241m above WGS84 Ellipsoid (as per Google Earth)
HOE = Oft *** P = 990mb = 29.23"Hg *** T = 20°C = 68°F
UT = 00h27m02.0s Zenith Distance = 59°53'44" Height = 30°06'16" i=+0.1 NM Z = 163.6°
UT = 00h28m36.0s Zenith Distance = 59°48'51" Height = 30°11'09" i=+0.5 NM Z = 164.0°
UT = 00h30m23.0s Zenith Distance = 59°43'54" Height = 30°16'06" i=+0.5 NM Z = 164.5°
UT = 00h31m35.0s Zenith Distance = 59°40'30" Height = 30°19'30" i=+0.6 NM Z = 164.8°
UT = 00h32m26.0s Zenith Distance = 59°38'27" Height = 30°21'33" i=+0.4 NM Z = 165.0°
I am using own internal Moon Ephemeris believed to be accurate to +/- 4".
I am not absolutely sure that I have correctly "translated" your data into our usual CelNav form. Please be so kind as to confirm this point, and if not please indicate which such "translated data" should be, and how you derive them from the ones you did publish.
Anyway, from what I can see all your intercepts are below 1 NM, which already fully confirms Frank's predictions.
And assuming that my "data transcription" is correct, these intercepts would tend to indicate suspecting an instrument zero offset.
I fail to see the interest of deriving your Longitude from your known Latitude, with such observations so close from the south. Would they be much closer to West or East they would be definitely better in this regard.
If you do want to compute Longitude from Latitude from these "rather south" observations, which exact Formula are you using ?
I am asking simply because our standard CelNav Formula "sin(Height)=sin(Lat)*sin(Dec) + cos(Lat)*cos(Dec)*cos(Body Local Hour Angle)"
is not best suited to determine "Body Local Hour Angle" as its cosine starts becoming close from 1, as is the case here.
Any comments will be highly appreciated, from yourself or from somebody else well familiar with theodolite observations.
Standing by, and many thanks in advance
:-)
Best Regards from
Kermit
PS : Many moons back - in the early 90's - , I performed theodolite observations to determine our Home position through standard brute force LOP's , and - from some 100 observations from SUN, Polaris, and some selected stars - I was able to eventually narrow it down with an error a little less than 2", i.e just within 50 meters from the coordinates currently indicated by Google Earth. I happen to be lucky at times.
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