Sunlight Intercepted by Planets

The vast majority of the sun's light will never encounter matter again. What fraction reaches the major and dwarf planets?

Given the diameter in km D, and the average distance from the sun in AU, the fraction intercepted by a round object object is:

• (pi*D²/4)/(4*pi*(149598000*AU)²) = ( 1 / (16 * 149598000²)) * ( D / AU )² = 2.793E-18 * ( D / AU )²

So, 99.99999958% of the Sun's light leaves the solar system. Half of the tiny fraction intercepted is by Jupiter, 19% by Venus, 11% by Saturn, 10% by Mercury, and 8% by Earth, with a small fraction of the tiny fraction intercepted by the other planets, dwarf planets, moons, asteroids, and Kuiper belt objects.

A hypothetical giant telescope mirror 100 meters across and 100 light years away might intercept 1.1E-32 of the Sun's output, about 4 microwatts. At that distance, the Sun would be magnitue 7.6, not quite visible to an unaided human eye. If intelligent life is rare and widely spaced, then chances are nobody would notice if we captured all the light.

On the other hand, a 50AU diameter infrared Dyson shell, with an average black body temperature of 56K and a peak infrared wavelength of 52 microns by Wein's Law. That would be quite visible (and anomalous!) to a very distant astronomer with a very large, orbiting infrared telescope. An orbiting 1000 meter collector would see a round object (rather than a diffuse cloud) at 10,000 light years; such a collector ( beyond a triple layer reflector and outside our own Dyson shell ) might weigh a few tons, an infinitesimal fraction of our own shell weight. Large, sharp-edged infrared spheres may prove to be the most reliable sign of well behaved shell civilizations elsewhere.