Project Cyclops, A Design... - Department of Earth and Planetary ...

if the longevity of that life is typically less than one or
two billion years, advanced life was more common in the
past than it is now. Of course, if G + L is greater than
the present age of the Galaxy then the density of life in
the Galaxy is still increasing. R, = 20/year
If we assume that L is small, say on the order of one
billion years, then G + L is less than the present age of fp = 1/2
expression identifies the important factors and allows us
to assess them independently. Let us enter some very
approximate and probably optimistic values into (13).
(= N,/T = average rate)
(excludes multiple star systems)
the Galaxy and the third form of (9) applies. In this case ne = 1
we have
L = 1/5
g(t) _- f' (t - G - -- ) L (10)
2
The number of sites in the Galaxy can be expressed as jr/ = 1
the product of the number of stars N, and several fc = 1/2
"selectivity factors":
(correct
for solar system)
(only certain F, G, K main sequence
stars suitable
(Darwin-Wallace evolution inevitable)
(only land-based life develops technology)
where
N s = N,F = N,fpnef£f i
(11) With these values
N L (14)
and
F = Ns/N, : fpnef_f t.
fp = fraction of stars having planets
ne = number of suitable planets per ecosphere
f£ = fraction of suitable planets on which life starts
fi = fraction of life starts that evolve into intelligence
Multiplying (10) and (11) we get for the number N of
intelligent civilizations in the Galaxy:
where
N = R, FL (12)
L
R, = N,f" (t-G---
2
)
L
= rate of star formation G + --
2
years ago
If we wish N to represent the number of "communicative"
civilizations we must interpret L as the longevity of
the communicative phase and include an additional
selectivity factor in F:
fc = fraction of intelligent civilizations that attempt
communication.
This yields Drake's expression
N = R,fpnjd/J, (13)
which has been described as a way of compressing a large
amount of ignorance into small space. Nevertheless, this
which says that the number of communicative races in
the Galaxy is roughly equal to the average number of
years spent in the communicative phase. This turns out
to be the most uncertain factor of all!
The substitution of N,/T for R, made above does
not assume a constant rate of star formation, but only
that the rate G + (L]2) years ago was about the average
rate. This may be slightly optimistic; in Figure 2-10 the
slope of .f(t) at t = 5 billion years is about 3]4 rather
than 1, but this is a small error compared with all our
other uncertainties. If we make this same substitution in
(12) we find
L
N = N, F--
T
(15)
and if we now divide both sides by N, we obtain the a
priori probability p = N/N, that a given star selected at
random is in the communicative phase
L
p = F--
T
(16)
If we confine our attention to what we consider
particularly likely stars, say single main sequence F, G,
and K stars, p is increased because the selectivity factors
contained in F are presumably greater for this subset of
stars. If our knowledge about planetary system statistics,
atmospheric evolution, genesis times, etc., were complete,
we might be able to be so selective in choosing
target stars as to make F-_ 1. At our present state of
knowledge, all we can say is that probably
10-2 < F< 1, but we cannot guarantee the lower limit.
The probability p is used in Chapter 6 to estimate the
probability Pc of achieving contact as a function of the
range to which we carry the search.
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