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

• Jan 6th 2013, 09:40 AM
Bwts
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?

B
• Jan 6th 2013, 10:17 AM
skeeter
Re: Questions about points on the surface of a sphere & great circles...
Quote:

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
• Jan 6th 2013, 10:56 AM
bjhopper
Re: Questions about points on the surface of a sphere & great circles...
Quote:

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?

B

Of course, any three points form a plane (your two on surface and the center of sphere)
• Jan 6th 2013, 11:11 AM
Bwts
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?
• Jan 6th 2013, 01:18 PM
bjhopper
Re: Questions about points on the surface of a sphere & great circles...
Quote:

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?

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
• Jan 10th 2013, 08:01 AM
Bwts
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.
• Jan 10th 2013, 11:08 AM
bjhopper
Re: Questions about points on the surface of a sphere & great circles...
Quote:

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.

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