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

 German Version

## 12.2 - Civilizations in the Galaxy

NX therefore represents the number of civilizations related to a particular type of sun. In order to determine the number of all civilizations in the galaxy, the sum of all partial results, i.e. across all spectral classes, must then be formed:

 12.2.1 Equation Nziv = ∑ NX = ∑ (A·FX·Fph·Fk·FLiz)

The number A of stars in the galaxy is the same for all star types and can therefore be drawn from the sum:

 12.2.2 Equation Nziv = ∑ NX = A·∑ (FX·Fph·Fk·FLiz)

The probabilities FX, Fph, FLiz depend on the spectral class of the respective star set and Fk on the observation instrument used. All factors can be empirically determined in the long run, according to sentence 6.1.2 within 2 centuries.

Based on the Seager approach, Equation 12.2.2 represents the most general form in which the subject of intelligent life or technological civilizations, on a habitable planet, in the galaxy, can be mathematically represented.

Equation 12.2.2 is therefore referred to as the "
General Approach". Equation 12.2.2 can be used to estimate the number of civilizations in the galaxy.

According to previous observations, the frequency for G stars, i.e. sun-like stars, is about 28% of the total stars.
The red dwarfs, i.e. the M stars, represent the major part, with about 70 % of the total stars, of which only 80 % are observable. Therefore:: N* = A · FRZ · fQ.
The remaining 2 % of the total stars belong to the remaining 11 spectral classes and are not taken into account in this estimation without impairing the observation.

The probabilities for sun-like stars are known according to chapters 1 to 7. The data for the red dwarfs are only partly taken from the data of Sara Seager, because some of her assumptions (life and biosphere) are too optimistic. Then the following values are used for equation 12.2.2:

Nziv = A·Fs·Fph·Fk·FLiz
+
A·FRZ·FQ·Fph·FO·FLiz

Nziv = (100-300)·109 · 1:15,000 · 0.004,7 · 1:1001
+ (100-300)·109 · 0.7 · 0.8 · 1:4200 · 0.001 · 1:1001

Nziv = 32 - 94
+ 14 - 40

N = 46 – 134 technological civilizations

Comparison General Basic Model
According to sentence 8.4.5 of the General Basic Model, the number of star systems, with Earth-like planets, in habitable zones that could support civilizations is probably between 35 - maximum 1,034.
The Drake-corrected General Basic Model 9.8.2 provides 22 - 199 "Earths 2" with technological civilizations.
The Seager-corrected General Basic Model 11.4.2 provides 35 - 334 "Earths 2" with technological civilizations.
The calculated window of the General Approach corresponds well with the window for the General Basic Model and thus results in a good match between the two approaches. This results in a good agreement between the general approach and the previous probability considerations from the corrected general basic model.
This confirms that the General Approach and the General Basic Model are two equivalent approaches.

Comparison Drake Equation
The Drake equation 9.1.2 provides 9 - 109 extraterrestrial technological civilizations and is thus well within the range of the calculated window of the General Approach.
The corrected Drake equation 9.5.3 lets expect 11 - 146 extraterrestrial technological civilizations and is thus well within the range of the calculated window of the General Approach.
This results in a good agreement of the general approach with the Drake equation.
This confirms that the General Approach and the Drake equation represent two equivalent approaches.

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