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    Datums in CN; WAS: Plumb-line horizon vs. geocentric horizon
    From: Jim Thompson
    Date: 2005 Feb 6, 10:04 -0400
    That's a nifty analogy, Frank.  This URL shows a more complex visual depiction of the "deflections of the vertical at the surface of the Earth... The deflection of the vertical is the departure of a plumb bob's true pointing from the ellipsoidal normal direction..These quantities are typically a few arc seconds, but can reach an arc minute of departure.":
    http://www.ngs.noaa.gov/GEOID/DEFLEC99/  That webpage makes this statement: "Deflections are used to relate the orientation of a locally-leveled instrument, such as a theodolite, to a spatial reference system. Important uses are corrections to zenith distance (vertical angle) measurements, and the conversion between astronomic and ellipsoidal azimuths (the Laplace correction)." which got me thinking that I have not spent near enough time trying to understand geodesy. 
     
    Trevor's question about Table 15 in Bowditch definitely triggered a run of very useful education for me. I realized that I was completely blanked on the value of the plumb line to celestial navigation, and I have been bugged by why we do not think about datums much in celestial navigation. After re-reading Bowditch Chapter 2 on Geodesy (thanks, Trevor), which does not explain things well for a beginner, the Nav-L archives (good discussion in 2002 but did not resolve the question), and googling, I finally came up with this introduction to geodesy for beginner CN'ers:
    http://jimthompson.net/boating/CelestialNav/CelestNotes/Coordinates.htm#Geodesy
     
    For completeness, the most illuminating Nav -L posts on datums in CN in 2002 were these:
    Trevor Ketchington
    http://www.i-DEADLINK-com/lists/navigation/0201/0086.html
    Mike Wescott
    http://www.i-DEADLINK-com/lists/navigation/0201/0100.html.
    John Kabel
    http://www.i-DEADLINK-com/lists/navigation/0201/0098.html
    Steve Tripp
    http://www.i-DEADLINK-com/lists/navigation/0201/0090.html
    dkruger
    http://www.i-DEADLINK-com/lists/navigation/0201/0102.html
    Hal Mueller
    http://www.i-DEADLINK-com/lists/navigation/0201/0103.html
    Bill Noyce
    http://www.i-DEADLINK-com/lists/navigation/0201/0105.html
    Paul Hirose, with a summary that almost satisfies my curiosity:
    http://www.i-DEADLINK-com/lists/navigation/0201/0121.html
    Herbert Prinz:
    http://www.i-DEADLINK-com/lists/navigation/0201/0123.html
     
    Glad I saved Frank's aspirin.

    Jim Thompson
    jim2@jimthompson.net
    www.jimthompson.net
    --------------------
    Outgoing email scanned by Norton Antivirus

    -----Original Message-----
    From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Frank Reed
    Sent: Thursday, February 03, 2005 8:38 PM
    To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
    Subject: Plumb-line horizon vs. geocentric horizon

    I don't know if this was mentioned this time around, but it's worth repeating. Local horizontal coordinates, as already discussed, are defined by the plumb-line. The zenith is opposite the direction of local gravity and therefore the horizon of the coordinate system is essentially parallel with the sea horizon. How much difference would it make if we did it differently? If we defined the zenith to be opposite the direction to the Earth's exact center, where would the horizon be? If you work it out, the difference is just about (12')*sin(2*Lat). At 45 degrees latitude, the direction to the zenith would be fully 12 minutes of arc shifted if we defined the coordinates in terms of the Earth's center. That's a substantial difference from the point of view of sextant observations.
     
    Another way to think about this: when you look straight down at the ground, you're not quite looking in the direction of the Earth's center. The local plumb-line points slightly south of there in the northern hemisphere. If you want to look "straight at" the Earth's geometric center, place an ordinary aspirin tablet on the floor. That's about 12' minutes of arc in apparent diameter (use half an aspirin if you're at 15 or 60 degrees latitude<g>). Aim your gaze about that much to the north from the plumb-line direction and your line of sight will be passing through the very center of the Earth.
       
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