## Probabilities in the Galaxy A Distribution Model for habitable Planets Copyright © Klaus Piontzik

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## 8.4 - Technological Civilizations

 Analogous to the previous basic model, equation 6.3.3 for technological civilizations on an "Earth 2" in solar-like systems can be extended to such an extent that it applies to general star systems with habitable, earth-like planets that have produced civilizations:
 8.4.1 Equation Nzex = A · FX · Fph · Fgae · FLiz

The number NzexGal of all star systems, with habitable, earth-like planets, with technological civilizations, in the galaxy is then the sum across all spectral classes:

 8.4.2 Equation NzexGal = ∑ Nzex = A · ∑ (FX · Fph · Fgae · FLiz)

Equation 8.4.2 is the extension of equation system 6.3.3 and contains all planetary and biological factors that can influence the development of a civilization by an intelligent species, on an "Earth 2" in the galaxy.

In the further course of this paper, Equation 8.4.2 is therefore referred to as the "
General Basic Model".

Strictly speaking, the probabilities Fph, Fgae, FLiz would have to be determined individually for each spectral class.. Since this is not yet possible today and in the near future, however, a rough calculation or maximum estimate can be achieved by assuming, in an initial approach, the same or similar distributions.

Assuming that non-sunlike stars also have an equal or similar distribution for technological civilizations, one can make a rough estimate of how many systems with habitable "Earths 2" that carry civilizations could exist.

 8.4.3 Approach In star systems that are not sun-like, there are probably the same or similar distributions, for earth-like planets, with civilizations as in sun-like systems.

The number NzexGal of all star systems with habitable, earth-like planets, with technological civilizations in the galaxy (∑ Fx=1), is then approximated:

 8.4.4 Equation NzexGal = ∑ Nzex ≈ A · Fph · Fgae · FLiz

Inserting all values (Fe = 0.1) into equation 8.4.4:

NzexGal1 = (100-300)·109 · 1:4200 · 1:69 · 1:1001
NzexGal1 = 345 – 1034 technological civilizations

Inserting all values (Fe = 0.01) into equation 8.4.4:

NzexGal2 = (100-300)·109 · 1:4200 · 1:691 · 1:1001
NzexGal2 = 35 – 104 technological civilizations

The two results can then be summarized to the following statement:

 8.4.5 Theorem The number of star systems in the galaxy, with Earth-like planets, in habitable zones that could carry civilizations, is most likely between 35 and 1034.

The probability of finding an Earth-like planet with a technological civilization is then:

 8.4.6 Definition FzexGal = Fph · Fgae · FLiz

FzexGal = 1:4200 · (1:69-1:691) · 1:1001
FzexGal = 1:290,0892,800 – 1:2,905,102,200

Only every 290.089 millionth - 2.905 billionth star system then has an Earth-like planet, with a technological civilization.

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