Hi Sam,
You can actually calculate how much dimmer the light from the Sun, or any other bright light source, is as you get further away from it. The light from the Sun radiates out in all directions, so you can think of it as being spread out over a spherical shell of radius R. The surface area of a sphere is proportional to R2, so the intensity, or brightness, of the light from the Sun falls off as 1/R2. This basically means that if you double your distance away from a light source like the Sun, the light appears 1/(2x2)=1/4 as bright as it did at the source. If you triple your distance away, it appears 1/(3x3)=1/9 as bright.
Kris