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

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8.2 - Habitable Planets

Planets If only the planets are considered, an equation for the probability of a habitable planet can be established in any star system. [2]
   
8.2.1 Definition Fph = Fp · Fh


So you can use the rounded values.

Fph = 201:14,000 · 10:603
Fph = 1:4200

Among 4200 star systems there is probably one that has planets, at least one of which is a habitable planet.

Then applies to the set of all star systems of a spectral class that possess habitable planets:

8.2.2 Equation Nphx = NX · Fph
Nphx = A · FX · Fph

It is important here that all factors can be determined in the long term by appropriate instruments of observation, i.e. empirically. According to theorem 6.1.2, this should be the case in the next two centuries.

The set of all star systems NphxGal in the galaxy, with planets and at least one in the habitable zone, is then the sum of all spectral classes:

  NphxGal = ∑ Nphx = ∑ (A · FX · Fph)



Since A remains the same for all spectral classes, A can be taken from the sum:

8.2.3 Equation NphxGal = ∑ Nphx = A · ∑ (FX · Fph)

Strictly speaking, the probabilities Fp and Fh and thus Fph would have to be determined individually for each spectral class.
However, since this is not yet possible, a rough calculation or maximum estimate can be achieved by assuming the same or similar frequencies of the planetary distributions in the spectral classes in a first approach.
If one assumes, in a first assumption, that other star systems, i.e. not sun-like stars, also have the same or similar planetary distribution, one can calculate how many systems could exist with habitable planets at most.

8.2.4 Approach In star systems that are not sun-like, there are probably the same or similar distributions, for habitable planets, as in sun-like systems.

Provided that Fp and Fh remain the same for all spectral classes (approach 8.2.4), they can also be drawn from the sum (equation 8.2.3):

  NphxGal = ∑ Nphx = A· Fph · ∑ (FX)

The sum of all spectral classes (for the probabilities FX) results in the totality of the stars in the galaxy:

  ∑ (FX) = 1

This results approximately from the approach 8.2.4:

8.2.5 Equation NphxGal ≈ A · Fph

Starting point are 100-300 billion solar systems, in the galaxy, and inserting all values into equation 8.2.5 results:

8.2.6 Theorem The quantity of all star systems in the galaxy with planets and at least one in the habitable zone is probably a maximum of 23.81 to 71.428 million.

 

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