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

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3.2 - Case Distinctions

A first estimate for the probability factor Fe can be developed.

CASE 1

The probability of encountering an approximately earth-great planet in the habitable zone is Fg = 0.368,837 = 1,212:3,286.
The probability of finding an approximately earth-like planet is Fa = 0.392,3 = 51:130. The probability for a second earth could be in the same order of magnitude.
The probability of a second earth is therefore set at a maximum of 30 %. The probability factor is therefore Fe1 = 0.3 = 3:10. The probability of finding an "Earth 2" among habitable planets is therefore:

Fgae1 = FgFaFe1
Fgae1 = 1,212:3,286 51:130 3:10
Fgae1 = 0.043,409 = 1:23

That means: Among 23 habitable planets there should be an "Earth 2". So we should have found a second Earth by now. Since this has not yet happened (so far 53 habitable planets are known) the probability Fe1 = 0.3 is too high and can therefore be omitted in the further considerations.


CASE 2

The probability of finding an approximately earth-like planet in the habitable zone can be formulated as follows:

Fe2 = FgFa
Fe2 = 1,212:3,286 51:130
Fe2 = 0.144,697 = 1:7

The probability of an approximately earth-like planet is 14.46%. The probability for a second earth is therefore chosen at a maximum of 10%. The probability factor is Fe2 = 0.1 = 1:10.

Fgae2 = FgFaFe2
Fgae2 = 1,212:3,286 51:130 1:10
Fgae2 = 0.014,469 = 1:69

That means: Among 69 habitable planets an "Earth 2" should be found. Since 53 habitable planets are known, we should therefore be on the verge of finding a second Earth in the next few years.


CASE 3

The number of solar-like systems with planets determined by the Kepler telescope is 1.4357 %. The number of suns, with planets, in habitable zones is 1.658 %.
The probability of a second earth is therefore chosen at a minimum of 1 %. The probability factor is Fe3 = 0.01 = 1:100.

Fgae3 = FgFaFe3
Fgae3 = 1,212:3,286 51:130 1:100
Fgae3 = 0.001,446 = 1:684

Among 684 habitable planets an "Earth 2" should be found.

 

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