hey this is straightforward .. solid angle subtended by planet at the source = A/R^2=≈πr2/R2
so fraction of energy reaching the planet = πr2/R2/4π (as 4π is the total sollid angle)
so we have energy reaching the planet in time t= (πr2/R2/4π )*P*t=MCΔT
we get t = 4MCΔTR2/Pr2