The Alien-Hypothesis
A probability analysis
Copyright © Klaus Piontzik Claude Brtels

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Chapter 7.2 – Non sun-like starsystems

 

If one assumes that other star systems, with non sun-like stars, have the same or similar planetary frequency, then equation 7.1.1 can be modified in such a way that it applies to any star quantity NX:

7.2.1 Equation NX = AFX


FX is the probability for the occurrence of a set of stars that have a certain property, namely the spectral class.
A = 200 – 300 billion is the number of stars in the galaxy.
This concept can be applied to all stars for which observational data are available
.


Looking at the planets, an equation for the probability of a habitable planet, in any system, can be set up:

7.2.2 Definition Fph = FpFh


Fph = 201:14,000 10:603 = 1:4,200

Among 4,200 star systems is one that possesses planets and among them at least one habitable planet exists.


Then for the set of all systems
Nphx of a spectral class with planets and at least one in the habitable zone:

7.2.3 Equation Nphx = AFXFph = AFXFpFh


For the set of all solar systems
NphxGal in the galaxy, with planets and at least one in the habitable zone:

7.2.4 Equation NphxGal = ∑ Nphx


The following applies:

NphxGal = ∑ Nphx = ∑ (AFXFpFh)

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

NphxGal = ∑ Nphx = A∑ (FXFpFh)

Under a first assumption that Fp and Fh remain the same for all spectral classes, they can also be drawn from the sum:

NphxGal = ∑ Nphx ≈ AFpFh∑ (FX)

The sum over all spectral classes (for the probabilities FX) yields the entirety of the stars in the galaxy, so:

∑ (FX) = 1

It is thus a total of:

7.2.5 Equation NphxGal = ∑ Nphx ≈ AFph


7.2.6 Theorem The amount of all star systems, in the galaxy, with planets and at least one in the habitable zone, is 47.619 to 71.428 million.


It is important here that all factors can be determined empirically by appropriate instruments of observation.



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