That's exactly how it's done, for what it worth (though you use 3D cartesian coordinates instead of spherical coordinates). Treat each point on the sphere as a

That's exactly how it's done, for what it worth (though you use 3D cartesian coordinates instead of spherical coordinates). Treat each point on the sphere as a 3D unit vector, weight as appropriate, and the center of mass is the sum of all of the vectors.