The intensity of sunlight falling on the earth is about 1.4 kw/m2 (before any gets absorbed by our atmosphere). at what rate does the sun emit light energy? (the earth-sun distance = 1.5 * 108 km and the earth's radius = 6.4 * 103 km.)

The area of the Earth (Ae) that is irradiated by is given by:

Ae = 4πRe^2, where Re = Distance from Sun to Earth

Substituting;

Ae = 4π * (1.5*10^8*1000) ^2 = 2.827*10^23 m^2

On the Earth, insolation (We) = Psun/Ae

Therefore,

Psun (Rate at which sun emits energy) = We*Ae = 1.4*2.827*10^23 = 3.958*10^23 kW = 3.958*10^26 W