
Analogous to the previous basic
model, equation 6.3 for technological
civilizations on an "Earth 2" in
solarlike systems can be extended to such an
extent that it applies to general star systems
with habitable, earthlike planets that have
produced civilizations:



8.4.1 Equation 
N_{zex}
= A · F_{X }·
F_{ph }·
F_{gae }·
F_{Liz} 
The
number N_{zexGal}
of all star systems, with habitable, earthlike planets,
with technological civilizations, in the galaxy is then
the sum across all spectral classes:
8.4.2 Equation 
N_{zexGal}
= ∑ N_{zex}
= A · ∑ (F_{X
}· F_{ph}
· F_{gae}
· F_{Liz}) 

Equation
8.4.2 is the extension of equation system 6.3.3 and
contains all planetary and biological factors that can
influence the development of a civilization by an
intelligent species, on an "Earth 2" in the
galaxy.
In the further course of this paper, Equation 8.4.2 is
therefore referred to as the "General Basic Model".
Strictly speaking, the probabilities F_{ph}, F_{gae},
F_{Liz} would have to be determined individually
for each spectral class.. Since this is not yet possible
today and in the near future, however, a rough
calculation or maximum estimate can be achieved by
assuming, in an initial approach, the same or similar
distributions.
Assuming that nonsunlike stars also have an equal or
similar distribution for technological civilizations, one
can make a rough estimate of how many systems with
habitable "Earths 2" that carry civilizations
could exist.
8.4.3 Approach 
In star systems that are not
sunlike, there are probably the same or similar
distributions, for earthlike planets, with
civilizations as in sunlike systems. 
The
number N_{zexGal }of
all star systems with habitable, earthlike planets, with
technological civilizations in the galaxy (∑ F_{x}=1),
is then approximated:
8.4.4 Equation 
N_{zexGal}
= ∑ N_{zex}
≈ A · F_{ph}
· F_{gae}
· F_{Liz} 
Inserting all values (F_{e} = 0.1) into equation
8.4.4:
N_{zexGal1} = (100300)·10^{9} · 1:4200
· 1:69 · 1:1001
N_{zexGal1}
= 345 – 1034 technological civilizations
Inserting all values (F_{e} = 0.01) into equation
8.4.4:
N_{zexGal2} = (100300)·10^{9} · 1:4200
· 1:691 · 1:1001
N_{zexGal2}
= 35 – 104 technological civilizations
The two results can then be summarized to the following
statement:
8.4.5 Theorem 
The number of star systems
in the galaxy, with Earthlike planets, in
habitable zones that could carry civilizations,
is most likely between 35 and 1034. 
The
probability of finding an Earthlike planet with a
technological civilization is then:
8.4.6 Definition 
F_{zexGal}
= F_{ph}
· F_{gae }·
F_{Liz} 
F_{zexGal
}= 1:4200 · (1:691:691) · 1:1001
F_{zexGal }= 1:290,0892,800 –
1:2,905,102,200
Only every 290.089 millionth  2.905 billionth
star system then has an Earthlike planet, with a
technological civilization.
