Question

What fraction of the energy emitted from the sun is absorbed by the Earth? Treat the sun like a light bulb 93 million miles away. Also, assume the Earth only absorbs the energy associated with an area of approximately 50 million square miles. (This is roughly the area of a disc with the same radius as the Earth.)

Answer 1

Sun is radiating energy in all directions. Consider that the sun is at the center of a sphere of radius 93 million miles. Earth lies as a dot on the surface of this huge sphere.
Fraction of energy = Surface area of the earth / Surface of the huge sphere
Surface area of the sphere = 4r², r = 93 million miles
= 4 x 3.14 x (93 million)² square miles
= 108686.54 million² square miles = 108686.54 x 10⁶ million square miles = 10.87 x 10¹⁰ million square miles
Earth's area = 50 million square miles.
Fraction of energy = [50 million square miles] / [10.87 x 10¹⁰ million square miles]
   = 4.6 x  x 10^-10of the total energy.