Re: How much of the sun's energy reaches the Earth?

The sun radiates its energy outwards. The flow of energy is fairly uniform in all directions, on 
average. This means that if you imagine a huge sphere, the size of the Earth's orbit, then all of the 
sun's energy will pass through the surface of that sphere. The Earth itself is a small part of that 
sphere. The amount of area on the surface of the sphere that the earth takes up is that area of a 
circle with the earth's radius.

The formula for the surface area of a sphere is 4 * pi * radius ^ 2. In this case, "radius" is the 
radius of the Earth's orbit (assuming it to be circular). It comes to about 150 million kilometres 
(1.5E8).
The surface area of the sphere that all the sun's energy passes through at the earth's radius is 280 
thousand trillion square kilometres (2.8E17).

The area of the earth's disk is given by pi * radius ^2. This time "radius" means the radius of the 
earth itself - about 6400 km. So the total size of the earth's disk is about 130 million square 
kilometres (1.3E8). The Earth's disk therefore occupies roughly half a part in 1 billion of the sphere 
at the earth's distance from the sun (1.3E8/2.8E17 = 0.5E-9), and that is the proportion of the 
sun's energy output that the earth receives.

Incidentally, that is not quite enough energy to stop us from freezing. The average temperature on 
the earth's surface would be about -20 deg C (as it is on the moon) if it were not for the 
greenhouse gases in our atmosphere -- mainly water and carbon dioxide -- keeping us a bit 
warmer. The average surface temperature on earth is about +15 deg C.