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

 German Version

## 3.3 - Consequences

Cases 2 and 3 of the case distinction can be used to obtain a minimum-maximum statement.

Inserting all values (Fe = 0.1) into equation 3.1.1:

N
he1 = (100-300)·109 · 1:15,000 · 1,212:3,286 · 51:130 · 1:10
N
he1 = 96,465 – 289,395 habitable „Earth 2“

Inserting all values (Fe = 0.01) into equation 3.1.1:

N
he2 = (100-300)·109 · 1:15,000 · 1,212:3,286 · 51:130 · 1:100
N
he2 = 9,646 – 28,939 habitable „Earth 2“

The two results can then be summarized to the following statement:

 3.3.1 Theorem There are probably 9,600 to 289,000 "Earths 2", in solar-like star systems, in our galaxy.

The probability for a habitable, earth-like planet, in solar-like star systems, in the galaxy, is then:

 3.3.2 Definition Fhe = Fsph · Fg · Fa · Fe Fhe= Fs · Fp · Fh · Fg · Fa · Fe

Fhe = Fs·Fp·Fh·Fg·Fa·Fe
= 1:15,000 · 1,212:3,286 · 51:130 · (1:10-1:100)
= 1:1,036,643 – 1:10,366,433

Only every 1.036 - 10.366 millionth star system has a truly earth-like planet.

If you only look at the habitable planets about the size of the earth, then you can establish a probability for the similarity to an "Earth 2".

 3.3.3 Definition Fgae = Fg · Fa · Fe

Two values can be generated:

F
gae1 = 1,212:3,286 · 51:130 · 1:10 · 1:69

F
gae2 = 1,212:3,286 · 51:130 · 1:100 · 1:691

According to definition 1.7.1:

Fsph = Fs·Fp·Fh

Then equation 3.1.1 for an "earth 2" can also be expressed as follows:

 3.3.4 Equation Nhe = A · Fsph · Fgae Nhe = A · Fs · Fp · Fh · Fg · Fa · Fe

F
sph = 1:15.000 Faktor für eine habitable zone
F
gae = 1:69 bis 1:691 Faktor für Earth similarity

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