Where is the centre of gravity of an allotment?
There is no general formula for the centre of gravity and the surface of a polygon (or set of polygons) on a sphere. However, the centre of gravity of a spherical triangle is known to lie on the intersection of its medians, and there exists a formula to calculate its surface. These properties of spherical triangles are used to obtain the centre of gravity of an allotment as follows: 1. The allotment contour (polygon) is subdivided into spherical triangles. 2. The centre of gravity and the surface area are calculated for each triangle. 3. The (lon, lat) coordinates of the centre of gravity of each spherical triangle are converted into Cartesian coordinates (x,y,z). 4. The centre of gravity of the allotment is the weighted mean of the centres of gravity of its constituent spherical triangles where the surface areas of the triangles are taken as their relative weights. 5. The resulting centre of gravity lies inside the sphere, and needs to be brought back to the surface of the sphere by n
