  There is something about inverse-square laws that makes them fail at
extremities. The inverse-square law, which is used commonly in studying the
irradiance on exoplanets fails at the extreme case of planets closer than 0.01
AU. Therefore, in order to correctly predict possible climate states of such
systems, we need a new model which accurately calculates angles subtended by
various surface elements and integrate the generalized equation. A direct
consequence of such a model is the shift of the terminator about 20 degrees
beyond the poles. The irradiance at the poles is about 100-200 kW/m2 higher
than what is predicted by the inverse-square law. This work therefore becomes
crucial because it underscores the need to modify the current GCM models. The
error in the numerical integration values of irradiance is less than one
percent making our estimate very reliable.
