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

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source ...

Great Circle -- from Wolfram MathWorld

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Originally Posted by Bwts

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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Of course, any three points form a plane (your two on surface and the center of sphere)

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?

Quote:

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Originally Posted by Bwts

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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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

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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Originally Posted by Bwts

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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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