Calculation of solar eclipse light curves

The light intensity observed by someone on Earth for a total solar eclipse from first contact to last contact is calculated using random sampling (essentially Monte Carlo integration of the unblocked portion of the Sun's disk). While analytic expressions are not difficult for uniform disks, the Monte Carlo method is easily extendable to include models of limb darkening and has a more transparent relationship to the acutal mechanism determining how much light gets from the Sun's disk to an observers location. It is therefore a natural problem to use to introduce such computational techniques to students--even those with minimal physics background.