How much of the total energy that leaves the sun makes it to earth? Why?
We subtend a tiny surface when viewed from the sun, with a small fraction in the line of its energy.
#"area" = 4 * pi * "150,000,000 km"^2 = 2.82743 * 10^17 "km"^2#
#(pi*d^2)/4 = "113,097,335 km"^2 = +- 0.00000004%#
To workout the problem we need to understand the concept of solid angle.
Total solid angle at the centre of sphere is
Considering Sun to be situated at the centre of sphere whose radius is equal to the average distance between sun and earth, which is
Solid angle subtended by the area of earth exposed to sun is
Sun radiates energy in all directions. Therefore fraction of energy reaching earth
Inserting given values we obtain
This is a minuscule fraction of total energy radiated by sun. The reason is a very small solid angle
(the problem could also have been worked out by calculating ratio of area of earth's surface receiving energy from sun to total area of the sphere of radius