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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.
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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. 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.
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On the other hand, consider a 50AU diameter Dyson shell surrounding our sun, with an average black body temperature of 56K and a peak infrared wavelength of 50 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 ( including a triple layer reflector and outside a similar Dyson shell ) might weigh a few tons, an infinitesimal fraction of total shell weight. Large, sharp-edged infrared spheres may prove to be the most reliable sign of well behaved shell civilizations elsewhere.
Once such civilizations are discovered, narrow beam optical wavelength interstellar communication becomes possible.
== 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 5.4e-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 5.4e-6/1.2e8 or 4.5e-14 of the sky (probably much less, given the domination of the bright ones). Clouds of cold gas may intercept a great deal more light. Overall, though, the amount of light intercepted by objects outside the solar system is probably less than 1e-12, a tiny fraction of the light intercepted by the planets. The universe is an empty place; when light leaves the sun, it effectively disappears.
 

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

Planet

Diameter km

Distance AU

Intercepted Fraction

Mercury

4878

0.39

4.37e-10

Venus

12104

0.72

7.89e-10

Earth

12756

1.00

3.15e-10

Mars

6787

1.52

5.57e-11

Jupiter

142800

5.20

2.11e-09

Saturn

120000

9.54

4.42e-10

Uranus

51118

19.18

1.98e-11

Neptune

49528

30.06

7.58e-12

Dwarf Planet

Ceres

975

2.77

3.46e-13

Pluto

2300

39.44

9.50e-15

Eris

~2700

67.67

4.45e-15

Total

4.17e-09

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.

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 5.4e-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 5.4e-6/1.2e8 or 4.5e-14 of the sky (probably much less, given the domination of the bright ones). Clouds of cold gas may intercept a great deal more light. Overall, though, the amount of light intercepted by objects outside the solar system is probably less than 1e-12, a tiny fraction of the light intercepted by the planets. The universe is an empty place; when light leaves the sun, it effectively disappears.

SunlightPlanets (last edited 2024-02-18 09:54:00 by KeithLofstrom)