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

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9 – The Drake-Equation

9.1 - The classic Drake-Equation

Frank Drake The Drake equation [1] is used to estimate the number of intelligent civilizations in our Milky Way. It was developed by Frank Drake, a US astrophysicist.
In November 1960, for the first time, scientists from various disciplines met at Greenbank to discuss the probability of extraterrestrial intelligence and the search for it Frank Drake was responsible for the scientific content and conceivable topics.
For the conference Drake wrote some important points of discussion and wondered in what sequence the topics should be dealt with. All agenda items had the same importance, but they were not directly related.

DDrake assigned a symbolic factor to every meeting point and drew the individual factors into a simple multiplication formula to determine the number of highly developed and communicative civilizations, in the galaxy.

Frank Drake introduced this equation at the conference, and it is also referred to as the Green Bank formula or the SETI equation. [2] (Frank Drake uses other indices than defined in Definition 2.7.2)

9.1.1 Equation N = R · fp · n · fL · fi · fc · L


R is the average star formation rate per year [3] in our galaxy. Depending on whether one is looking at galaxies, star clusters or stellar nebulae, the value for R varies between 4 and 19. [1] The mean value is then 11.5.

fp is the probability for a star system with planets. Here the value from the previous considerations is taken fp = Fp = 0.014,357 = 201:14,000.

n is the number of planets in the habitable zone. Since probably only one planet in the habitable zone produces a civilization, n is set equal to one. The explanation is given below.

fL is the probability for planets to have lives. Again, the value from the previous considerations is taken, thus fL = FL = 0.111 = 1:9.

fi is the probability for planets with technological civilizations.
The Approach here is: fi = Fi
· Fz
The value from the previous considerations (chapter 5.3) for Fi is taken, thus Fi = 0.071,428 = 1:14
The value from the previous considerations (chapter 6.4) for Fz is also taken here, thus Fz = 0.125,895 = 1:7943

The following applies:: fi = Fi
· Fz = 1:14 · 1:7943 = 1:111.203

fc is the probability of the desire for communication. This value is set equal to 1. The explanation follows later.

L is the life span of a communicable civilization. As defined in Axiom 7.2.1, the lifetime is set to a minimum of 400,000 years.

N is the number of extraterrestrial technological civilizations in the galaxy.


The Drake equation can now be partly expressed as a function of the parameters of the basic model:

9.1.2 Equation N = R · Fp· n · FL · Fiz · fc · L


Applying the values, in the Drake equation 9.1.2, provides:

N = (1,45-19)
· 201:14,000 · 1:· 1:9 · 1:111.203 · 1:· 400,000
N = 9 - 109 extraterrestrial technological civilizations

Equivalent and thus comparable to the Drake equation, is equation 8.4.5 from the General Basic Model, which describes all technological civilizations in the galaxy, on Earth-like planets. According to theorem 8.4.5, the maximum number of star systems in the galaxy with Earth-like planets in habitable zones that could support technological civilizations is probably between 35 - 1,034, and the Drake window is well located in the lower part of the generalized basic model window.

This results in a correspondence of the Drake window with the previous probability considerations from the basic model (chapters 1-7) or the general basic model (chapter 8).

It can be concluded that the value in the basic model for an Earth-like planet is closer to Fe = 0,01

 

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