What is a Great Circle ?

The concept of the 'Great Circle' is a difficult one for newcomers to grasp. Possibly this is because most people are used to looking at the world on a two dimensional flat map. If you are trying to understand this concept I'd encourage you to have a Globe, or at least some spherical object ( e.g. Ball or round fruit ) to hand when reading this.

Question;

From Chris;
Could you please help me. What does the great circle distance mean? Is it related to a straight line or curve distance.

Answer;

Very simply put, the Great Circle Distance is the shortest distance between two points along the surface of the Earth.

The Earth is essentially a sphere, so the line that connects two points on it is not straight but curves along it's surface. In mathematical jargon this line is an arc of a circle.
Diagram of a circle with arc & radii highlighted

Picture if you will a sphere and a disc (like a CD) of exactly the same size. The disc would fit snuggly inside the sphere in any of an infinite number of ways. The whole edge of the disc would touch the inside of the sphere and would trace a circle on the inside of it. Crucially the center of the disc and that of the sphere would be in the same position. Scale this up to a disc & sphere ~13000 km (~8000 miles) across and hey presto you have a Great Circle around the Earth.

It's relatively straightforward to compute the length of an arc of a circle. Given that the circumference is 2*PI*Radius, the length of the arc is simply a function of the number of degrees it subtends from the center. The magic of the Great Circle calculation is converting two lat/longs into that degree value. Unfortunately my Spherical Geometry is not up to explaining this and I can only point you to the formula used in my program. If there are any Mathematician's out there I'd welcome your input... References The Geometry of the Sphere - Dept. of Mathematics, Rice University, Texas Spherical co-ordinates and the GPS, Montana university

Great Circle Schematic

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