AAWSAP DIRD, An Introduction to the Statistical Drake Equation, March 2010

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We know Ns, the number of stars in the Milky Way galaxy, fairly well, by careful counts
of stars in a small but representative region of the sky. It is a few hundred billion; some
recent estimates place it at 4 x 1011 . Very few of these stars are of the massive short­
lived variety that squander their reserves of thermonuclear fuel. The great majority
have lifetimes of billions or more years in which they are shining stably, providing a
suitable energy source for the energy and evolution of life on nearby planets.
There is evidence that planets are a frequent accompaniment of star formation: in the
satellite systems of Jupiter, Saturn and Uranus, which are like miniature solar systems;
in theories of the origin of the planets; in studies of double stars; in observations of
accretion disks around stars; and is some preliminary investigations of gravitational
perturbations of nearby stars. 1 Many, perhaps even most, stars may have planets. We
take the fraction of stars that have planets, fp, as roughly equal to 1/3. Then the total
number of planetary systems in the galaxy would be Ns fp ~1.3 x 1011 (the symbol ~
means "approximately equal to"). If each system were to have about ten planets, as
ours does, the total number of worlds in the galaxy would be more than a trillion, a vast
arena for the cosmic drama.
In our own solar system there are several bodies that may be suitable for life of some
sort: the Earth certainly, and perhaps Mars, Titan and Jupiter. Once life originates, it
tends to be very adaptable and tenacious. There must be many different environments
suitable for life in a given planetary system. But conservatively we choose ne=2. Then
the number of planets in the galaxy suitable for life becomes Ns fp ne ~3 x 1011 .
Experiments show that under the most common cosmic conditions the molecular basis
of life is readily made, the building blocks of molecules able to make copies of
themselves. We are now on less certain grounds; there may, for example, be
impediments in the evolution of the genetic code, although I think this is unlikely over
billions of years of primeval chemistry. We choose fl~ 1/3, implying a total number of
planets in the Milky Way on which life has arisen at least once as Ns fp ne fl~ 1 x 1011 ,
a hundred billion inhabited worlds. That in itself is a remarkable conclusion. But we are
not yet finished.
The choices of fi and fc are more difficult. On the one hand, many individually unlikely
steps had to occur in biological evolution and human history for our present intelligence
and technology to develop. On the other hand, there must be quite different pathways
to an advanced civilization of specified capabilities. Considering the apparent difficulty
in the evolution of large organisms, represented by the Cambrian explosion, let us
choose fix fc = 1/100, meaning that only 1 per cent of planets on wh ich life arises
actually produce a technical civilization. This estimate represents some middle ground
among the varying scientific options. Some think that the equivalent of the step from
the emergence of trilobites to the domestication of fire goes like a shot in all planetary
systems; others think that, even given ten or fifteen billion years, the evolution of a
technical civilization is unlikely. This is not a subject on which we can do much
experimentation as long as our investigations are limited to a single planet. Multiplying
1 Carl Sagan was writings these lines back in the 1970's, when no extrasolar planets had been discovered yet. The
first such discovery occurred in 1995, when Michel Mayor and Didier Queloz, working at the "Observatoire de Haute
Provence" in France, discovered the first extrasolar planet orbiting the nearby star 51 Peg. This first extrasolar
planet was hence named 51 Peg B. Many more extrasolar planets were discovered around nearby stars ever since.
As of April 2009, 347 extrasolar planets (exoplanets) are listed in the Extrasolar Planets Encyclopaedia.
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