## Extension Activity

### Distance between any two places on the earth's surface

It is possible to find the great circle distance between any two points on the surface of the Earth. As long as the two points are NOT directly opposite each other on the Earth's surface (antipodes), then there is a unique great circle that can be drawn through these two points. The length of the shorter arc between these two points is the great circle distance we are after.

There are three formulations that are commonly used for calculating these great circle distances.

The simplest method is based on the "Spherical Law of Cosines" which is a method for finding distances on the surface of a sphere. It can have difficulties calculating distances between two places that are very close together (less than 10 metres), but this is not really a practical calculation.

A more complex method, based on the "haversine" calculation method, forms the basis of a number of web-based processes for performing these calculations. It is accurate for most distances on a sphere, but has difficulties with "antipodal points" which are points at each end of a diameter .

A more complicated formula that is accurate for all distances is a special case of the Vincenty formula, which is generally used to calculate distances on ellipsoids. In this case, the sphere is an ellipsoid with equal major and minor axes.

In light of the fact that the "cosine" based method is easier to use, and is the preferred method of many geoscientists, it will be the method demonstrated here.

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