# How much of the total energy that leaves the sun makes it to earth? Why?

##### 2 Answers

We intercept

#### Explanation:

We're

We subtend a tiny surface when viewed from the sun, with a small fraction in the line of its energy.

At

#"area" = 4 * pi * "150,000,000 km"^2 = 2.82743 * 10^17 "km"^2#

We intercept

#(pi*d^2)/4 = "113,097,335 km"^2 = +- 0.00000004%#

To workout the problem we need to understand the concept of solid angle.

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

where

Sun radiates energy in all directions. Therefore fraction of energy reaching earth

Using (1)

Inserting given values we obtain

This is a minuscule fraction of total energy radiated by sun. The reason is a very small solid angle

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(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