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How to find an angle in spherical geometry.

  1. Jan 18, 2013 #1
    Hi
    I am not familiar with spherical geometry. I am working with elliptical polarization that involves using poincare sphere that present the latitude and longitude angle in spherical geometry. I need to find the great circle angle if given two points that each specified by their longitude angle [itex] 2\tau[/itex] and latitude angle [itex] 2\chi[/itex].

    ie. If I am given the [itex] \chi [/itex] and [itex]\tau[/itex] of [itex]M_{1}(\tau_{1},\chi_{1})[/itex] and [itex]M_{2}(\tau_{2},\chi_{2})[/itex], how can I find the great circle angle between [itex]M_{1}(\tau_{1},\chi_{1})[/itex] and [itex]M_{2}(\tau_{2},\chi_{2})[/itex]?

    I really don't want to learn the details of spherical geometry, just want to learn the way of finding the angle as this is only a small part of antenna design.

    Thanks

    Alan
     
  2. jcsd
  3. Jan 18, 2013 #2

    Simon Bridge

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    google for "great circle distance". eg. http://mathworld.wolfram.com/GreatCircle.html

    If the great circle distance is ##d##, then the angle (in radians) between the points is ##\theta=d/R## where R is the radius of the sphere.
     
  4. Jan 18, 2013 #3
    Thanks for the reply, but what if if I have only the longitude and latitude angle of the two points, how can I find the great circle angle between the two points?
     
  5. Jan 18, 2013 #4

    Simon Bridge

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    Step 1: find the great-circle distance between the two points from the long and lat values.
    Step 2: divide this by the radius of the sphere.

    Anticipating your next question: see link in post #2.
     
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