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

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10.3 - The transformed Drake-Seager-Equation

Sun The Drake-Seager equation treats only the red dwarfs, that is, a certain set of stars, the so-called M-stars. One can extend the consideration here and also refer to other sets of stars, e.g. On the G-stars the sun-like stars.
The Drake-Seager equation is then compatible with Equation System 6.3.3 and can be completely replaced by the relationships found in Chapters 1-7.

N* = Ns = A·Fs according to Equation 1.4.1, for the number of G stars (sun-like stars) present in the galaxy with Fs = 7:25 and A = 100-300 billion stars.

fQ G-stars do not throw gamma rays into space, so all stars are observable, ie fQ =1. The factor can therefore be dispensed with.

fHZ = Fph = Fp·Fh is the proportion of those G stars, which have a planet first, and secondly it is in a habitable zone. Fp = 201:14,000 and Fh = 10:603.

fO = Fk quantifies the proportion of those planets which visibly travel past the star for the Kepler telescope. According to Chapter 1.2, the probability of such a transit is 0.47 % so Fk = 0.004,7.

fL = FL is the fraction of planets with life, with FL = 1:9.

fS stands for an intelligence which leaves a measurable biosignature in the atmosphere, ie a technological civilization, with fS = Fi·Fz = 1:14 · 1:7,943 = 1:111.203

The entire Drake-Seager equation can then be applied to the set of solar-like star systems in the galaxy observed with the Kepler telescope (or equivalent). All the probability factors of the Drake-Seager equation are completely replaceable by the factors from the equation system 6.3.3. The transformed Drake-Seager equation for G stars is then:

10.3.1 Equation N = A · Fs · Fp · Fh · Fk · FL · Fi · Fz

According to definition 1.7.1 is Fsph = Fs · Fp · Fh = 1:15,000

According to definition 6.2.2 is: FLiz = FL · Fi · Fz = 1:987

Equation 10.3.1 can thus also be written as transformed Drake-Seager-Equation:

10.3.2 Equation N = A · Fsph · Fk · FLiz

Substituting all the values into equation 10.3.2:

N = (100-300)·109 · 1:15,000 · 0.004,7 · 1:1001
N = 32 – 94 technological civilizations

Comparison of special basic model
Equivalent and thus comparable to the transformed Drake-Seager equation is equation 6.3.3 from the Special Basic Model. According to theorem 6.4.1 of the Special Basic Model, there are probably 10 - 290 technological civilizations, on "Earth 2" in solar-like systems, in our galaxy.
The Drake Seager window is well located in the lower part of the basic model window. The Drake-corrected Special Basic Model 9.8.2 delivers 22 - 199 "Earths 2" with technological civilizations. The Seager_window is well located in the lower part of the Drake window.

10.3.3 Theorem The special basic model and the transformed Drake-Seager equation represent two mutually equivalent approaches.

In the Drake-Seager approach, earth-similarity plays no role and only technological civilizations, on habitable planets in the galaxy, are asked.

This model can also be transferred to other star sets and observation devices. If you omit the factor Fz, then you can apply equation 10.3.2 to intelligent species. If you omit the factor Fi, then equation 10.3.2 can also be applied to animate planets.


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