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    Re: Basic celestial naviagtion using a scientific calculator
    From: Gary LaPook
    Date: 2010 Aug 14, 22:34 +0200

    Too use the standard Sin- Cos formulas for sight reduction you can use the 
    following keystroke sequence which works with a TI-30 which has only three 
    Assumed Lat
    2nd DMS-D.D (changes to decimal degree format)
    STO 1  (stored A. LAT in 1)
    2nd DMS-D.D
    STO 2   (stored DEC in 2)
    2nd DMS-D.D
    Assumed Longitude
    2nd DMS - D.D
    = (computed LHA)
    STO 3   (LHA stored in 3)
    RECALL 2  (recalled declination)
    RECALL 1  (recalled Assumed latitude)
    RECALL 1 (recalled A. LAT)
    RECALL 2  (recalled DEC)
    2nd SIN  (ARCSIN, computed Hc)
    2nd D.D-DMS (changes decimal degree Hc to degree-minute-second so it
    can be written down)
    2nd DMS - D.D  (changes it back to decimal degrees)
    1/x   (converts COS Hc to SEC Hc)
    RECALL 3  (recalled LHA)
    RECALL 2  (recalled DEC)
    2nd SIN  (ARCSIN, computed Z)
    Since the azimuth angle (Z) will be in the range of 0° to 90° there are situations where it will not
    be obvious whether the body's azimuth (Zn) is in the northern or southern semicircle.
    In most situations there is no ambiguity as to which 
    quarter the Zn lies since you know the approximate direction you are 
    looking when you take the sight. The problem arises because the azimuth 
    angle is limited to the range of zero to 90 degrees and when the Zn is near 
    east or west the correct Zn might fall either 
    side of the line so there is an ambiguity in converting from azimuth 
    angle to Zn.
    One easy rule to apply first is that if the declination is greater than 
    the latitude then the azimuth can never be in the opposite semicircle. 
    To generalize this rule, if the declination has 
    the same name as the latitude and the declination is greater than the 
    latitude, then you start with the direction of the elevated pole (the 
    nearer pole) when converting from azimuth angle to azimuth (Zn.)
    The second rule to apply is that if the declination is contrary name then the Zn 
    must be in the opposite semicircle. To generalize this rule, if the 
    declination and the latitude have contrary names then you start with the 
    direction of the depressed pole (the further pole) when converting from 
    azimuth angle to Zn.
    These two rules take care of most of the cases, especially for 
    navigators in low latitudes.
    The remaining ambiguity concerns situations in which the declination is 
    the same name as the latitude but is less than the latitude. In this 
    situation the azimuth of the body will be both north and south of the 
    east - west line during part of each day. There is no simple rule to
    deal with this situation.
    Another set of formulas that are very quick and easy to use are those used in 
    the Bygrave slide rule. Here is a link to a post showing
    the keystrokes to use for this
    For you to understand the Bygrave method look at:
    You may want to make a flat Bygrave for yourself in case your batteries go dead in your calculator.
    David Smith wrote:
    > I would like to speed up the checking of calculations in sight 
    > reduction exercises by using an electronic calculator. I have never 
    > used a scientific calculator before, but they don't look too difficult 
    > to master. However the two Casio calculators that I have, the Casio 
    > fx-82MS and fx-82w appear to only work in DDDMMSS.
    > Is there a way of entering DDDMM.M and getting answers in the same 
    > format? If this is not possible, are there any common calculators or 
    > iPhone/iPad apps which are useful for sight reduction calculations? As 
    > I want to get a good familiarity with the printed Nautical Almanac and 
    > sight redution tables, I am not lookiing for anything more 
    > sophisticated than basic arithmatic in DDDMM.M format.
    > I'd value your advice.
    > Cheers,
    > David.
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