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Finding arbitrary circumference/circle on a sphere

  1. Nov 2, 2011 #1
    I need to find the green circle described in the picture below. (go from top left to bottom right)
    DCY5F.png
    The base values are:
    the radius of the ball = d1 = 10
    height down into the ball that forms the circle d2. h = 0.5.
    I don't know if these values are useful in the end, but R on the right is sqrt(19)/2. which is the radius of the smaller circle, and also how far this circle is from the top. a way to visualize that is this picture.
    [URL]http://upload.wikimedia.org/wikipedia/commons/5/56/Small_circle.svg[/URL]
    from the formation of the equilateral triangle, a 90 degree angle is made, which finally forms a line that travels from that point of the ball to the bottom point of the ball, and finally back to where it is from.

    so in the end, i am looking for the circumference of the green line on the ball. This was very hard to describe to, even to professors, which in the end couldn't help me, so I thought i would ALSO make a video of the problem!
    http://www.youtube.com/watch?v=fCHQLQiLYUU"
    The L in the video is wrong, it should be R, which would describe the same R as in the diagram!
    Feel free to ask for more details, since even i don't think there might be enough information initially to figure this one out.

    If you guys figure it out, i'll explain what this is used for! it's not just a purely mathematical exercise!
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
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