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    Re: Longitude from Local Apparent Noon Altitudes
    From: John Huth
    Date: 2012 Aug 19, 11:04 -0400
    Bruce - 

    I use Mathematica to fit that kind of data to a parabola.   Then with the parameters of a parabolic fit, you can determine the mid-point with good accuracy.    You can also get the max. altitude reasonably well with a parabolic fit.    

    If you really want to 'go to town', you can calculate the chi-square per degree of freedom just to convince yourself that a parabola is a reasonable approximation.

    The only think I note in your data is that you should include points much further away from the actual meridian passage.   Most of the precision in a longitude measurement in the equal altitude method comes from readings when the altitude is changing rapidly.  Obviously this only works for a stationary observer.   But, I like to take a series of readings when the altitude is maybe 15 degrees both rising and setting.   That gives you a much better handle on longitude than a short time bracketing the meridian passage.    

    John H. 


    On Sun, Aug 19, 2012 at 9:41 AM, Bruce J. Pennino <bpennino.ce@charter.net> wrote:

    Hello:

    I'm still working to improve CN skill and my data has improved (especially since I finally learned to keep object centered when I "swing the arc").

    I took the altitudes below and tried to determine longitude by "folding the curve" and taking mid point between rising and falling limbs. Decided to post data because it is useful for discussion and teaching students. Further, I'm curious that there must be a way to do a "best fit" regression analysis to determine high point Hs and line of symmetry (essentially longitude). Would love to hear others' conclusions about latitude and longitude.

    I'll eventually post exactly where I was , but for now the data was taken from the northern tip of Cape Cod very near the Pilgrim Monument in Provincetown,MA.

    The raw altitudes Hs are shown below. Index correction is zero. Eye height 14 ft. Date August 17, 2012. All times are eastern DAYLIGHT time. Watch is 26 seconds SLOW. Time on watch hour:min:sec altitude xx deg yy.y minutes

    Altitudes (measured with Astra iii B)
    12:21:39 60d 28.0 m ; 12:22:52 60d 34.8 m ; 12:24:26 60d 36.8 m;
    12:26:05 60d 38.6 m ; 12:26:59 60d 40.8 m ; 12:28:23 60d 41.8 m;
    12:29:35 60d 44.8 m ; 12:30:39 60d 44.6 m ; 12:31:50 60d 46.8 m;
    12:33:07 60d 47.8 m ; 12:35:13 60d 51.5 m ; 12:36:13 60d 51.5 m;
    12:37:03 60d 50.8 m ; 12:38:23 60d 53.6 m ; 12:39:36 60d 52.4 m;
    12:40:36 60d 52.2 m ; 12:41:44 60d 54.0 m ; 12:42:45 60d 52.8 m;
    12:43:52 60d 55.0 m ; 12:44:55 60d 54.2 m ; 12:45:52 60d 53.8 m;
    12:47:48 60d 53.0 m ; 12:49:27 60d 52.0 m ; 12:50:16 60d 51.0 m;
    12:51:04 60d 49.6 m ; 12:52:31 60d 50.2 m ; 12:53:43 60d 48.6 m;
    12:55:53 60d 47.2 m ; 12:58:14 60d 44.0 m ; 1:00:29 60d 40.0 m;
    1:01:55 60d 37.8 m ; 1:03 30 60d 34.4 m

    Again,,,,watch is 26 seconds SLOW. Please calculate latitude and longitude.Hope you enjoy interesting data.

    Best regards and thanks,
    Bruce Pennino
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