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

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7.4 - Temporal Distribution of Civilizations

With the probabilities determined so far, it is possible to make a recalculation of how many civilizations could have existed since the formation of the galaxy. From this, a hypothetical rate of civilization emergence can be determined, which can provide information about the frequency of intelligent life in the galaxy.

R is the mean star formation rate per year in our galaxy. Depending on whether you are looking at galaxies, star clusters, or stellar nebulae, the value of R varies between 4 and 19. The mean is then 11,5. [9]
Tg is the age of our galaxy, at 13.2 billion years.[10]

First, S is the number of stars that have formed since the galaxy was formed.

7.4.1 Equation S = R· Tg

The next step is to determine the maximum number of civilizations that could have been possible since the galaxy was born. In doing so, the distant earth-like planets are taken as a measure.
Fia is the probability of distant earth-like planets, with intelligent life, in this galaxy. According to the previous definitions and according to the rules of this model, the probability is:

  Fia = Fsph · Fg · Fa · FL · Fi

Then the number M of intelligent species formed in the time span Tg can be determined as follows

7.4.2 Equation M = S · Fia
M = R · T
g · Fs · Fp· Fh· Fg · Fa · FL · Fi

Equation 7.4.2 can still be converted to:

  M = R · Tg · Fsph · Fga · FLi

The values determined so far are used for the factors:

R = 11.5 mean star formation rate
Tg = 13.2 billion years, Age of our galaxy

Fs = 0.28 = 7:25 Sun-like star systems
Fp = 0.014,4 = 201:14,000 Star Systems with Planets
Fh = 0.016,6 = 10:603 Planets in habitable zones
Fg = 0.368,8 = 1,212:3,286 approximately earth-great planets
Fa = 0.392,3 = 51:130 approximately earth-like planets
FL = 0.111... = 1:9 planets with life
Fi = 0.071,4 = 1:14 Planets with intelligent species

Fsph = 0.28 = 1:15,000
Fga = 0.142,8 = 1:7
FLi = 0.007,9 = 1:126

The following result is obtained by inserting the values in equation 7.4.2. Since the formation of the galaxy, M = 11,474 intelligent species have probably emerged. This allows the average rate of civilization development to be determined:

7.4.3 Equation rate of civilization development
  rate of civilization development

This results in an average rate of civilization development of Z = 1.15 million years per civilization.

The rate of civilization formation is the mean cycle time between the appearance of two civilizations. This allows for a general definition of old civilizations.

7.4.4 Definition A cycle of civilization is the period of time defined by the rate of civilization development.
7.4.5 Axiom An old civilization is a culture that has survived at least one cycle of civilization.
7.4.6 Theorem An old civilization is a culture that is at least 1.15 million years old.


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