- Let's look at the solar light flux as a starting place: The Solar Output is the rate of energy release by the Sun 3.83E+33 erg/sec
- From spherical geometry, the energy density at the earth's orbit is the Solar Constant 1.37E+06 erg/cm2*sec
- 40% of the Sun's energy is visible light 5.48E+05 erg/cm2*sec
- The energy of typical visible light photon is determined from E=hv (1) 4.00E-12 erg/photon
- So the visible solar flux is 1.37E+17 photon/cm2*sec
- 70% of visible light gets through the atmosphere when viewed at the zenith (2) 9.59E+16 photon/cm2*sec
- Therefore 100 thousand million million photons blast away at every square centimeter of the surface of the earth. This partially explains sunburn.
- Now let's apply these facts to the observation of a more remote star. Tau Ceti is dimmer than the sun (0.45 as bright)
- The light flux of Tau Ceti on an earth-like planet 1 AU from the star 4.32E+16 photon/cm2*sec
- The distance of Tau Ceti from the earth is 10.8 light years
(or to relate to Solar distance 6.80E+05 AU)
- Since light diminishes in intensity as the square of distance, viewing Tau Ceti from our earth gives Tau Ceti's flux as 9.32E+04 photon/cm2*sec
- This is one millionth of a millionth of the Sun's light. And yet, we can see Tau Ceti with our naked eyes.
- The amount of light from an earthlike planet as a fraction of it's star's output (3) 1.00E-09 (This is the shakiest assumption)
- IF Tau Ceti had a planet, it's light flux is 9.32E-05 photon/cm2*sec
- We would have to wait a long time for one of these photons to hit a square centimeter: 10727 seconds or 3.0 hours
- Our eyes are 0.5 cm in aperture so naked eye observing would wait 7.6 hours
- This is not much light so let's use some astronomical equipment to help
- 50 mm binoculars capture a bunch more light - 39.3 cm2
- So light headed for both eyes is 3.66E-03 photon/sec
- 75% of light makes it through binoculars (4) 2.75E-03 photon/sec
- 1% of photons entering the eye fire a neuron (this is the quantum efficiency of the eye) so the rate of "photon seeing" is (5) 2.75E-05 photon/sec
- To reliabily assume that you have seen a photon from Tau Ceti's planet, you have to look for 36423 seconds or 10 hours
- This would be pretty boring so let's try a bigger telescope.
- 10 inch newtonian reflector receives more light (517 cm2)
- The secondary blocks some of the light (486 cm2)
- So the light headed for one eye is 4.53E-02 photon/sec
- 70% of the light bounces through the mirrors so the amount that gets to the eye is 3.17E-02 photon/sec
due to relectivity losses (6)
- 1% of photons entering the eye fire a neuron (3.17E-04 photon/sec)
- To reliabily assume that you have seen a photon from Tau Ceti's planet, you have to look for 3154 seconds or 53 minutes
- If Tau Ceti had 5 planets, you only have to look for 11 minutes
- Now this is only one possibly likely star. Let's look at lots of stars
- M31, The Great Galaxy in Andromeda is 2.20E+06 light year away or 1.39E+11 AU
- M31 glows with the light of 1.1E+10 suns
- Its light flux on the surface of the earth is 5.49E+04 photon/cm2*sec
- Peeking through our 10 inch telescope, we "see" 1.87E+05 photon/sec
- IF every visible star had a planet like the earth or every fifth star had 5 planets the light from M31's planets would be 1.87E-04 photon/sec
- To reliabily assume that you have seen a photon from M31's planets, you have to look for 5354 seconds or 89 minutes
- This is a long time. How about we try a philosophical telescope with is only naked flesh?
Wearing only shorts, my exposed skin area is 600 sq inches or 3871 cm2
- This is the same area as a telescope of aperture 27.6 inches
- The visible light from M31 hitting this body is 2.13E+08 photons/sec
- Since we are talking contact, not vision, we can assume more of the radiation is recieived than just visible - 80%
- So the photon flux from M31 is 4.25E+08 photons/sec and from the planets: 2.35 sec/photon
Relative to the eye and 10" telescope, it is 2276 times as efficient
- Adapting the Frank Drake Equation to our case:
Number of stars visible in M31 1.1E+10 stars
Fraction of stars which live long enough 0.500
Average number of planets per star 10 planets
Fraction of planets suitable for life 0.025
Fraction of suitable planets where life rises 0.500
Fraction of suitable planets w/ intelligence 0.500
Avg life of visible evidence of intelligence 1.0E+07 years
Estimated galaxy lifetime 1E+10 years
- Visible number of planets with civilizations: 343750 planets
- The light of M31's civilized planets hitting me is: 1.33E-05 photons/sec
- Or my body receives 75269 sec/photon or 21 hours/photon
- What if we add persons?
If we had 10 people 125 minutes/photon
100 13 minutes/photon
1,000 75 seconds/photon
10,000 8 seconds/photon
- Can photons have bounced off creations of intelligence? From a planet like ours, most light is clouds (99%), therefore, 1% is surface.
- The fraction of light from the surface which touched intelligent creations (roads buildings beings etc) is 1%
- Therefore, of the light coming off an inhabited planet, only a fraction has contacted intelligent life 0.0001
- What if we add persons?
If we had 10 people 871 days/photon
100 87 days/photon
1,000 209 hours/photon
10,000 21 hours/photon
100,000 125 minutes/photon