Calculating Minimum Distance Between Two Co-ordinates on Earth

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The shortest distance between two coordinates on Earth is calculated using the concept of great circles, which are circles that share the Earth's center. To find this distance, one must determine the central angle θ between the two points based on their latitude and longitude. The formula for the arc length is Rθ, where R is the Earth's radius and θ is in radians. If θ is given in degrees, it should be converted using the factor π/180. This method provides an accurate calculation for the minimum distance between any two geographic locations.
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Could somebody please please explain how to work out the minimum distance between two co-ordinates on the earth, eg hobart(43 S,147 E) to Beijing (39 N, 117 E). Apparently there is a method incorporating great circles which finds min distant. If anyone knows the formula and could give me a quick explanation, would be much appreciated.
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Yes, the shortest distance between two points on the surface of a sphere is along a "great circle" which is a circle having the center of the sphere as its center. The length of an arc of radius R and subtending central angle \theta, in radians, is R/theta. If \theta is in degrees that is R\theta (\pi/180). Here R is the radius of the Earth and you will need to work out the angle \theta from the latitude and longitude.
 

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