Distracted from the wonders of the universe

Brian Cox couldn't keep my attention for ever (or even for the full hour), but he always makes me think.  So I thought:  if the sun could ever get out from behind his Madchester hairdo, how much of its light might we get here on earth?

Simplifying madly (and probably dropping the odd decimal place here and there), this is how I went about it.

1. Imagine a sphere as big as the earth's orbit round the sun:  the sun at its centre and a radius of 150 million kilometres.
2. Think of the earth as a circle on the surface of that sphere:  a radius of 6370 kilometres.
3. The surface area of the big sphere is 283 quadrillion (282,743,338,823,081,391) km^2.
4. The area of the "earth disc" is 127 million km^2.
5. Which is 0.000000045% of the surface area of the big sphere.
6. OK, that's meaningless, so how do we translate it into terms that people might understand?
7. Start with a standard football and imagine it with a tiny sun at its centre and the earth disc on its surface.
8. But that makes earth really, really tiny, and I couldn't find out the area of a pin point.
9. So move up a bit:  imagine the earth with a tiny sun at its centre and the "earth disc" on its surface.
10. A few sums later, and I determine that the earth disc has an area of 230,000 m².
11. Which is 32 football pitches, and everybody understands that.
12. But the basic truth is that the amount of the sun's light that can ever hit the earth is less than half of one ten-millionth of one per cent.

Does that help?