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    Re: Mecca
    From: R.H. van Gent
    Date: 2000 Aug 27, 6:12 AM

    Lu Abel wrote:
    
    > I'm not sure what is meant by the "geodesic," but as a curiosity question,
    > does anyone know if when a Muslim determines the direction to Mecca is it
    > the rhumb line or the great circle??  I asked while on a tour of a mosque,
    > but the guide didn't understand the difference.
    
    As was pointed out earlier by Tony, the geodesic line is the shortest
    line connecting two points on a given surface. It has the property that
    at each point along the line, the radius of curvature (i.e. the radius
    of a circle that locally best fits an infinitesimal segment of the line)
    is perpendicular to the surface.
    
    On a sphere the geodesic line becomes a great circle and Islamic
    astronomers and geographers have always calculated the direction to
    Mecca (this is known as the qibla) by determining the great circle
    connecting a given locality with Mecca.
    
    Unlike the rhumb line therefore, the azimuths or compass bearings at the
    begin and end points can be quite different. I.e. a North-American
    Muslim generally prays to the North-East while his prayer actually
    'arrives' at Mecca in a South-Easterly direction.
    
    On a axially-symmetric spheroid, which closely approximates the actual
    Earth,
    the calculation of the Qibla direction becomes more complicated but is
    still possible with the help of the so-called Bessel-Helmert equations
    which I will not try to reproduce here, but which can be found in the
    standard literature on geodesy (i.e. G. Bomford, Geodesy, etc.).
    According to the TEX article mentioned in Dan Allen's message, the
    difference in qibla direction as measured along a great circle or a
    geodesic line can amount up to a few tenths of a degree which does not
    seem to be of a magnitude that modern Muslims should worry about to
    much.
    
    In a recent personal message, George Huxtable sketched to me the
    intriguing image of a Muslim society centred on the anti-Meacca point
    (which my not too recent and not too detailed World Atlas places just
    North of the island of Mururoa in French Society Islands), where its
    inhabitants all correctly direct their daily prayers to different
    directions of the compass.
    
    Yesterday I found a Windows program called QiblaCalc that calculates the
    qibla direction for any place on Earth, with respect to true North or
    magnetic North, at:
    
      http://www.ummah.net/software/qibla10.zip
    
    The author of this program assumes the Ka'ba of Mecca to be located at:
    
      Lat = 21� 25.3' North, long. = 39� 49.5' East
    
    List members interested in how Islamic astronomers and geographers
    solved the problem of determining the qibla direction in the past with
    the aid of tables and instruments (all of course assuming a spherical
    Earth) can find all that they ever wanted to know on this subject in:
    
      King, D.A., World-Maps for Finding the Direction and
      Distance to Mecca: Innovation and Tradition in Islamic
      Science (E.J. Brill, Leiden, 1999).
    
    ========================================================
    * Robert H. van Gent * Tel/Fax:  00-31-30-2720269      *
    * Zaagmolenkade 50   *                                 *
    * 3515 AE Utrecht    * E-mail: r.h.vangent{at}astro.uu.nl *
    * The Netherlands    *                                 *
    ********************************************************
    * Home page: http://www.phys.uu.nl/~vgent/homepage.htm *
    ========================================================
    

       
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