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

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12.2.3 - Total Number of technological Civilizations

Related to all star systems A in our galaxy, the number NX of a set of star systems belonging to a certain spectral class is given:

12.2.3.1 Equation Nx = A · FX


A = (100 – 300)·10
9 = Number of Suns in the Galaxy

F
X is the probability of the occurrence of a set of stars belonging to a certain spectral class. There are 13 spectral classes (chapter 12.1)

There is the set of sun-like G stars, with a yellow spectral color and the probability of Fs = 0,28 = 7:25.
There is the set of red dwarfs, i.e. M stars with a red-orange spectral color and a probability of FRZ = 0,7 = 7:10.
The two spectral classes G and M make up 98% of the total stars in the galaxy.
The spectral types O, B, A, F, K, i.e. the blue, blue-white, white, white-yellow and orange spectral colours make up about 1% of the total stars.
The brown dwarfs and the red giants, i.e. the spectral classes L, T, Y, R, N, S, also make up 1% of the total stars.



According to equation 12.1.1, the set of civilizations of a set of stars, each caused by a spectral class, applies.

  Nzx = Nx · Fph · Fk · FLiz = A · Fx · Fph · Fk · FLiz


Equation 12.2.2 gives the total number of civilizations in the galaxy in sum across all spectral classes:

  NzivGal = ∑ Nzx = A·∑ (Fx · Fph · Fk · FLiz)
   
12.2.3.2 Equation


F
p
= 0,014.4 = 201:14.000 star systems with planets
Fh = 0,016.6 = 10:603 planets in habitable zones

By definition 8.2.1: Fph = Fp · Fh

Fph = 201:14.000 · 10:603
Fph = 1:4.200

By equation 12.5.1 applies:; Fk = Fgae
with
0,001 < Fk < 0,004.7 and 0,000.927 < Fgae < 0,004.672
The probability Fgae for the similarity of the Earth is of the same order of magnitude as the observation probabilitiesFk.with which all models are equivalent.


By definition 6.3.2: FLiz = FL · Fi · Fz

Then equation 12.2.3.2 can also be written like this:

12.2.3.3 Equation




According to equation 4.1.4.5, the probability of life applies:

 


In particular:
There are n = 8 components called for life to become possible.
It applies to the single probability: fj = 1:72

This can also cause 8 failures.

For weighting factors, approach 4.1.4.6 applies.: aj = 1
Thus, the chance of life arises FL= 1:(n+1) = 1:9.



According to equation 5.2.2.5, the probability of intelligence applies:

 


In particular:
There are k = 13 causes listed that can destroy life on earth globally.
It applies to the single probability:: fj = 1:182

Only every 14th planet on which there is life could produce a conscious species.

For the weighting factors, the approach 5.2.2.6 applies: bj = 1
Thus, the chance of intelligence arises Fi= 1:(n+1) = 1:14.



This results in the number of civilizations, of one civilization level, in the galaxy:

12.2.3.4 Equation




According to equation 6.2.4, the following probability can be established for one civilization level:

 

Technological civilizations form the levels 6,7 and 8. Therefore the total probability for a technological civilization is:

 

Fz = 14.400/7.301 · (1:36+1:49+1:64)
F
z= 405.225/3.218.741 = 1:7,943 ¤ 1:8

This results in the number of technological civilizations in the galaxy:

12.2.3.5 Equation


Adapted to the model used so far:

 


A,
Fx, Fph, Fk are empirically determined factors that are expected to increase in the future.

For the factors FL and Fi there is enough leeway to capture any set of prerequisites and therefore try different models.

There are n components so that life can be made weighted with the aj.
There are k components that can prevent the intelligence weighted with the bj.

The probability of Fz can be applied to a level of civilization as well as a number of stages of civilization. m is the stage of civilization and
&sum m is a set of civilization levels.


Equations 12.2.3.4 and 12.2.3.5 include all the cosmic, planetary, and evolutionary influences that a species is exposed to until it has developed a technological civilization.

Equations 12.2.3.4 and 12.2.3.5 build a matrix of variables into which all impacts, from development to civilization, can be assessed and estimated.

 

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