Welcome to the NavList Message Boards.


A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Add Images & Files
    Re: Location Center of Responses thus Far
    From: R.H. van Gent
    Date: 2001 Jul 24, 10:10 AM

    George Huxtable wrote:
    > I have been pondering on what would be a meaningful way to define a centre
    > of gravity for individuals members scattered over the surface of a sphere.
    > Somehow, I doubt whether averaging latitudes and then separately averaging
    > longitudes provides the best answer. It should be possible to do the job
    > properly, for anyone with a bit of time on his hands. Here is a suggested
    > mechanical analogy.
    > Take a globe of the world, that will float. For example, I have a beachball
    > printed with the World on its surface, crudely marked with lat and long. If
    > you put it into a pool, it will float any way up, like most spheres.
    > Now glue on to its surface a set of identical coins or weights, one for
    > each member, in the spot where they live, and chuck it into the pool again.
    > Now, the lowest point of this globe represents in some way a centre of
    > concentration of the members.
    > It should be possible to devise a computer analogy to avoid having to do
    > the physical experiment. Would it produce the same answer as Dan Allen's
    > method? I wonder...
    This problem can be solved mathematically in the following way;
    Regard each position on the Earth's surface as a vector and reduce each
    longitude-latitude co-ordinate to its Cartesian co-ordinates (x,y,z):
      x = cos(lat) * cos(long)
      y = cos(lat) * sin(long)
      z = sin(lat)
    Add all the x's, y's and z's to form the sum vector (X,Y,Z), and perform
    the inverse operation:
      mean long = arctan(Y/X)
      mean lat  = arctan(Z/sqrt(X*X+Y*Y))
    When the arithmetical signs of X and Y are properly taken into account,
    there will be no longitude ambiguity (in FORTRAN one could use the
    ATAN2(X,Y) function to circumvent this).
    If I have some time later this evening, I will write a quick program and
    do some calculations.
    My lat-long = +52.086  -5.129
    * Robert H. van Gent * Tel/Fax:  00-31-30-2720269      *
    * Zaagmolenkade 50   *                                 *
    * 3515 AE Utrecht    * E-mail: r.h.vangent@astro.uu.nl *
    * The Netherlands    *                                 *
    * Home page: http://www.phys.uu.nl/~vgent/homepage.htm *

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site