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The Drake Equation is a way to estimate the number of communicating advanced
civilizations (N) inhabiting the Galaxy. It is named after Frank
Drake who first summarized the things we need to know to answer the
question, "how many of them are out there?" The equation breaks this big unknown,
complex question into several smaller (hopefully manageable) parts. Once you know how
to deal with each of the pieces, you can put them together to come up with
a decent guess.
N = R* × fp × nE × fl
× fi × fc × L
- R* =
- average star formation rate (number of stars formed each year).
Roughly 200 billion stars in the Galaxy / 10 billion years of Galaxy's lifetime = 20
- fp =
- average fraction of stars with planets. Astronomers are currently focussing
star systems so planets would more likely have stable orbits. With our current technology it is also easier to find planets around single star systems, though we have found planets in binary and multiple star systems. The recent discovery of planets in stable orbits in binary and multiple star systems was certainly a surprise for planetary dynamicists who model planet orbits and boosts the fp term from what we originally thought. Astronomers are looking at stars where the star is not too hot
(hence, short life) nor too cold (hence, narrow habitable zone and tidal locking of
we should look at stars that have signatures of "metals" (elements heavier than helium)
in their spectra---stars in the galactic disk and bulge. Leftover "metal"
material from the gas/dust cloud that formed the star may have formed
Earth-like planets. The census of stars by the Kepler mission has shown that at least 70% of ordinary stars including those hotter than the Sun and the great majority cooler than the Sun have a planet of some size orbiting them (the percentage will only increase as the Kepler team continues processing the data).
- nE =
- average number of Earth-like planets per suitable star system.
The planet has a solid surface and liquid medium on top to get the chemical
elements together for biochemical reactions. The planet has strong enough gravity to hold
onto an atmosphere. Current statistics from the Kepler mission show that 23% of sun-like stars have a planet less than 3 Earth diameters in size. However, the dividing line of size between a rocky planet and a more gaseous one like Neptune is about 1.5 Earth diameters.
- fl =
- average fraction of Earth-like planets with life. Extrasolar life will
probably be carbon-based because carbon can bond in so many different ways and even
with itself. Therefore, carbon can make the large and complex molecules needed for
any sort of biological processes. Also, carbon is common in the galaxy. Many
complex organic molecules are naturally made in the depths of space and are
molecular clouds throughout
the Galaxy. The rarer element silicon is often quoted as another possible
base, but there are problems with its chemical reactions. When silicon
reacts with oxygen, it forms a solid called silica. Carbon oxidizes to
form a gas. Silicon has a much lesser ability to form the complex
molecules needed to store and release energy. See the previous section and Raymond Dessy's
article at Scientific American's
"Ask the Experts -- Space"
web site for further discussion of the limitations of silicon chemistry. The habitable zone idea would be contained either in this term or put in the nE above.
- fi =
- average fraction of life-bearing planets evolving at least
one intelligent species. Is intelligence necessary for survival? Will
life on a planet naturally develop toward more complexity and intelligence? Those are questions
that must be answered before "reasonable" guesses can be put in for fi.
note that on the Earth, there is only one intelligent (self-aware) species among millions
of other species. (Perhaps, whales, dolphins, and some apes should be considered intelligent
too, but even still, the number of intelligent species is extremely small among the
other inhabitants of our planet.) Sharks have done very well for hundreds of millions of
years and they are stupid enough to eat tires! Bacteria have thrived on the Earth for
billions of years. Being intelligent enough to read an astronomy textbook is very nice
but it is not essential for the mandates of life.
Bacteria and other simple forms of life have been found in some very extreme conditions on the Earth.
Simple forms of life can even survive long passages through space. However, we will not be talking with
such simple forms of life. We are more interested in complex life---multi-cellular animal and
plant life. Complex life is more fragile than simple life, so while new research seems to increase the
fl term, the fi term might be smaller than was initially thought.
If the rise of intelligence is accidental, then the fi term will be nearly zero.
If intelligence is an emergent property of any biological system, then intelligence would be
an expected result of complex life, boosting the fi term. An emergent property
is a property that arises when a simple system with a sufficient number of interacting parts spontaneously becomes more complex. The property cannot be seen in individual members of a system but can be seen only in large assemblages of them---complex behaviors of a collective that are more than just the sum of the individual members.
- fc =
- average fraction of intelligent-bearing planets capable of
interstellar communication. The intelligent life we will be able to talk to will
have to use some sort of symbolic language. Will intelligent
life want to communicate to beings of a different species? The anthropologists,
psychologists, philosophers, and
theologians will have a lot of input on this term in the Drake Equation.
- L =
- average lifetime (in years) that a civilization remains technologically
active. How long will the civilization use radio communication? Will they
be around long enough to send messages and get a reply? Even if we manage to
take better care of the Earth and each other, our technology is changing so
we may not use radio communication.
It used to be that our television and music/talk broadcasts were "over the air"
using radio and microwaves. Some of that radio/microwave energy leaked out into
interstellar space (that may be why all of the extraterrestrials are staying
away). Those broadcasts are now happening mostly via cable. Now the voice communication
that used to be via cable is now happening mostly with radio/microwaves (land
lines vs. cellular phones). There is also the fact (yes, I use "fact") that
individual species have changed and died out as their environment changed. Humans
will be very different in a million years from now (if we survive that long).
Because of the huge interstellar distances in the Galaxy, the L term is the
most significant constraint on communicating with an extraterrestrial.
Another version of the Drake Equation (used by Carl Sagan, for example)
replaces R* with N*---the number of stars in the Milky
Way Galaxy and L with fL---the fraction of a planetary lifetime
graced by a technological civilization. Once you have found N, the average distance
d between each civilization can be found from Nd3 = volume of Galaxy =
5.65 × 1012 light years3. Solve for the average
distance between each civilization = (volume of the Galaxy/N)1/3
The certainty we have of the values of the terms in the Drake Equation decreases
substantially as you go from R* to
L. Astronomical observations will enable
us to get a handle on R*,
and fl. Our knowledge of biology
and biochemistry will enable us to make some decent estimates for
fl and some rough estimates for
fi. Our studies in anthropology, social
sciences, economics, politics, philosophy, and religion will enable us to make
some rough guesses for fi,
fc, and L but those terms involve sociological factors (behaviors of alien civilizations) and we have a hard enough time trying to understand how our own human societies interact (our predictions often fail miserably). Furthermore, numerical analysis is not used in philosophy and religion.
Some astronomy authors are so bold as to publish their guesses for all of the
terms in the Drake equation even though estimates of nE
and fl are only
rough and values quoted for the last three, fi,
are just wild guesses. I will not publish my values for the last few terms because I do not
want to bias your efforts in trying come up with a value for N.
We do know enough
astronomy to make some good estimates for the first two terms. The current star
formation rate is about 2 to 3 stars/year, but in the past it was much larger so I
average value of 20 stars/year. The fraction of stars that are sun-like medium temperature stars that are single and that would have any chance of life-filled
planets orbiting them is about 1/50 = 2%. Proto-planetary
disks have been detected around some stars and astronomers are now just beginning
to detect planets around solar-type stars, including those in binary or multiple-star systems as well as planets in the habitable zones of the very common cooler stars (so the 2% figure is probably too small for fp). See the end of the Solar System Fluff
chapter for a discussion of finding exoplanets and web links to
up-to-date information about them.
A nice interactive to try out your values in the Drake Equation is The
Drake Equation interactive from NOVA's Origins series that was
broadcast on PBS (selecting the link will bring it up in a new window either
in front of or behind this window).
For a sample of the scientific debates over the values in the Drake Equation
(and perhaps the need to add more terms!), see the Complex
Life Elsewhere in the Universe? debate that includes the "Rare Earth" authors,
Don Brownlee and Peter Ward (selecting the link will bring it up in another
window). Ward and Brownlee got the astrobiology/SETI community to re-examine
its assumptions about extra-terrestrial
life when they
out their case for why complex life (life beyond the microbial level) may be
very rare in the universe in their book "Rare Earth". Needless to say there
is disagreement, but it is a healthy debate in the determination of what it
to make a
planet that can support complex, intelligent (self-aware) life.
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January 24, 2014
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