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

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10.2 - The extended Drake-Seager-Equation

Red Dwarf The Drake-Seager equation treats only a certain amount of red dwarf stars, ie stars of the spectral class M, namely only stars that can be detected by the JWST telescope.

The Drake-Seager equation can also be extended to all red dwarf stars, in the galaxy.

N* = NRZ = A·FRZ is the number of M stars (Red Dwarfs) present in the galaxy with FRZ = 0.7 and A = 200-300 billion stars.

fQ stands for the proportion of quiet M-stars, which account for about 80 %

fHZ = Fph = Fp·Fh is the proportion of those M stars, which have a planet first and secondly it is in the habitable zone.Fp = 201:14,000 and Fh = 10:603 with Fph = 1:4,200.

fO quantifies the proportion of those planets that are visible at the star for the JWST.(0.01 x 0.1= 0.001)

fL = FL is the fraction of animated planets, 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

This results in:

10.2.1 Equation N = A · FRZ · fQ · Fph · fO · FL · Fi · Fz
N = A · F
RZ · fQ · Fph · fO · FLiz

Substituting the values into equation10.2.1 yields:

N = (100-300)·109 · 0.7 · 0.8 · 0.001 · 1:4200 · 1:1001
N = 14 – 40 technological civilizations

According to Theorem 6.4.1, there are 10 – 290 technological civilizations, in sun-like star systems, in our galaxy.
This results in a much smaller number of civilizations, with red dwarfs as central stars, than in sun-like systems.

10.2.2 Equation NS > NRZ

A biosignature means certain signs in the atmosphere of an exoplanet, such as the existence of certain gases (such as CO2 and CFCs) that indicate the presence of a technological civilization.


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