The Great Circle Distance

The Great Circle Distance

Since the Earth is a sphere, the shortest path between two points is expressed by the great circle distance, which corresponds to an arc linking two points on a sphere. The circumference inferred out of these two points divides the earth into two equal parts, thus the great circle. The great circle distance is useful to evaluate the shortest path when intercontinental distances are concerned. It follows the sphericity of the globe, any shortest route is the one following the curve of the planet, along the parallels.

Because of the distortions caused by projections on a flat surface, a straight line on a map is not necessarily the shortest distance. Ships and aircraft usually follow the great circle geometry to minimize distance and save time and money. For instance, the above map shows the shortest path between New York and Moscow (about 7,540 km). This path corresponds to an air transportation corridor. Air travel over the North Atlantic between North America and Europe follows a similar path. To calculate the great circle distance (D) between two coordinates the following formula is used:

Cos (D) = (Sin a Sin b) + (Cos a Cos b Cos |c|)

Where a and b are the latitudes (in degrees) of the respective coordinates and |c| is the absolute value of the difference of longitude between the respective coordinates. The results of this equation are in degrees. Each degree on the earth’s surface equals about 111.32 km, so the result must be multiplied by this number.