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Math Help - Questions about points on the surface of a sphere & great circles...

  1. #1
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    Questions about points on the surface of a sphere & great circles...

    Hi,

    Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points?

    I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture

    B
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  2. #2
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    Re: Questions about points on the surface of a sphere & great circles...

    The shortest path between two points on a sphere, also known as an orthodrome, is a segment of a great circle.
    source ...

    Great Circle -- from Wolfram MathWorld
    Thanks from MarkFL and Bwts
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    Re: Questions about points on the surface of a sphere & great circles...

    Quote Originally Posted by Bwts View Post
    Hi,

    Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points?

    I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture

    B

    Of course, any three points form a plane (your two on surface and the center of sphere)
    Thanks from Bwts
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    Re: Questions about points on the surface of a sphere & great circles...

    Thanks my follow up question is this, if using the same 2 points I construct a another circle on the sphere's surface (not a great circle this time) how would I prove that the segment of this new circle is greater then the great circle segment between the same points?

    I think it must have something to do with the curvature of the circles but am having trouble visualising it?
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    Re: Questions about points on the surface of a sphere & great circles...

    Quote Originally Posted by Bwts View Post
    Thanks my follow up question is this, if using the same 2 points I construct a another circle on the sphere's surface (not a great circle this time) how would I prove that the segment of this new circle is greater then the great circle segment between the same points?

    I think it must have something to do with the curvature of the circles but am having trouble visualising it?

    the shortist distance between points on the earths surface is along a great circle.Navigators have to change course regularlyto follow such a route.Points are places like New york and London and are not changable
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    Re: Questions about points on the surface of a sphere & great circles...

    Yes but how do I prove this is the case?

    There are many arcs on the surface of a sphere that will pass through the same two points.
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    Re: Questions about points on the surface of a sphere & great circles...

    Quote Originally Posted by Bwts View Post
    Yes but how do I prove this is the case?

    There are many arcs on the surface of a sphere that will pass through the same two points.


    Look up the definition of great circle and remember that 3 points create a plane. Two surface points and center of sphere.Take a ball and mark two points less than a diameter apart.Measure the distance by using a string. Try to find a route shorter than the string
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