计算地球表面上任意多边形所包围的区域

Say I have an arbitrary set of latitude and longitude pairs representing points on some simple, closed curve. In Cartesian space I could easily calculate the area enclosed by such a curve using Green's Theorem. What is the analogous approach to calculating the area on the surface of a sphere? I guess what I am after is (even some approximation of) the algorithm behind Say I have an arbitrary set of latitude and lon