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

Only 4.2 parts per billion of the Sun's light hits planets. 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.

Note in particular that small, cold Mars intercepts 18% as much light as the Earth. More light than one continent on Earth intercepts, but not nearly as much as currently-lifeless areas of the Earth's oceans. Mars is an unlikely "Earth replacement", but could be an essential test lab for "Earth remediation" and perhaps even "Earth enhancement".

Designing controllable artificial life for Earth's dead ocean areas could greatly increase terrestrial net primary biological productivity, far more than we could ever hope to create on Mars. For safety's sake, pressurized robotic biolabs on Mars, illuminated by 2.3x light concentrators, could mimic those Earth ocean conditions, with a vanishingly small chance of an accidental lab escape contaminating the Earth.

Book Fraction

Earth's "Sun intercepted fraction" is a very small number, 3.15e-10, difficult to imagine in isolation, but we can compare it to other everyday light intercepting objects, such as a period in a book. Here is a very small sample of page 62 of the 2018 hardbound edition of "The Future of Humanity" by Michio Kaku.

Interstellar Interception

With a diameter of 1,390,000 kilometers, the Sun's disk comprises 98% of the cross section of all the area of solar system bodies. Light from other stars has no detectable effect on the Sun, and vice versa, but at least that light gets intercepted. What percentage of the sun's light will hit other stars, rather than continue into empty intergalactic space?

We can work the problem backwards. All the light from all the stars are equivalent to about 1000 stars with a visual magnitude of 1. (Roach, F. E. & Megill, L. R., "Integrated Starlight Over the Sky", Astrophysical Journal, vol. 133, p.228 ). To an observer on the Earth, the Sun has a visual magnitude of -26.74, so it is 10^(27.74/2.5) or 1.2e11 brighter than one of those stars, or 1.2e8 times brighter than all of them. Since we are getting 1366 watts per square meter from the sun, we are getting 11 microwatts per square meter illumination from all the stars.

The sun occupies 4.8e-6 of the sky. If we assume those other stars have similar light outputs per steradian, (dodgy assumption, a few bright ones dominate!) then those stars occupy 4.8e-6/1.2e8 or 4e-14 of the sky. Clouds of cold interstellar gas may intercept more light, but if that was significant, we would expect to see more reflected light from those clouds. Overall, the amount of light intercepted by matter outside the solar system is probably less than 1e-13, a tiny fraction of the light intercepted by the planets. The universe is an empty place; when light leaves the sun, it effectively disappears.