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    Re: Latitude by transits of a circumpolar star both above and below the pole
    From: Gary LaPook
    Date: 2007 Oct 02, 01:34 -0700
    Gary writes:

    Well, that is going to be your problem. Transits are 12 hours apart so this will never work in the spring or summer since one of the transits will always be during daylight. During the fall and winter when your day is substantially shorter than 12 hours (depends on your latitude) you may be able to find a star suitably placed to accomplish this but it will take some luck.

    I would recommend that you take many shots of Polaris when it is near your meridian. This happens about 3 am local time on October first but then it occurs 2 hours earlier each month. When Polaris is crossing your meridian its altitude stays constant for a considerable time allowing many sights to be taken without the need to do any additional calculation. Its altitude doesn't change even 0.1' for the period of 15 minutes before and after transit;  0.5' plus or minus 34 minutes of transit 1.0' for the period of 48 minutes before and after it crosses the meridian.

    If you want to check the accuracy of your sextant simply pre compute what altitude you should measure based on your latitude. At upper transit the altitude of Polaris should equal your latitude plus the distance Polaris is from the pole, 90º - declination.  For lower transit subtract the polar distance from your latitude. Then ADD the refraction correction and you will have pre calculated the altitude you should be measuring with your sextant.

    Andres Ruiz wrote:
    Latitude by transits of a circumpolar star both above and below the pole

    In the book: An Introduction to Practical Astronomy, (Elias Loomis, NY, 1860)

    Chapter VI contains an old method of determining the latitude of a place by observations of a circumpolar star at the time of its upper and lower culminations

    ·       It is independent of the declination of the observed star
    ·       It is as free as possible from the errors of refraction

    If both altitudes being measured from the north horizon:

    Latitude: B = 1/2*(H_up + H_low)

    Where H is the altitude measured by the sextant, corrected for index error, dip and refraction.

    This past weekend I try to use the method, and I have not been able to find a star that had the two transits at the same night.

    Simulating some data, the problem from my latitude at this moment is the difference between the times of the two phenomena: one by day and another at night.

                    UT                      H      
                    h       m       Culmination     º       ´      
    29-sep-2007     Polaris 2       20      Upper   N       44      1.2    
    29-sep-2007     Polaris 14      18      Lower          42      36.8   
    29-sep-2007     Merak   10      39.1    Upper   N       76      59     
    29-sep-2007     Merak   22      37.1    Lower          9       39.8   
    29-sep-2007     Alkaid  13      24.4    Upper   N       84      2.9    
    29-sep-2007     Alkaid  1       26.1    Lower          2       35.9   

    Has anybody used this simple method in order to obtain the latitude, at land or at sea?

    Andrés Ruiz

    Navigational Algorithms


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