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Drake Equation
Lecture Thirty-Three, April 23,
2003
Project
• Due Friday April 25.
• Discuss as much of the science from class
as possible.
• If your project is in electronic form you
can turn in a disk or email it.
• However, also turn in a hard copy!
• Everyone should turn in a paper copy.
SETI: Message in a Cosmic Bottle
• How to send or receive a radio beacon?
• Want signal to look “unnatural” and stand out
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above background of natural radio noise in
Galaxy.
Broad frequency region around a few GHZ (few
times 109 cycles per second). This is in the
microwave region (high frequency radio) of the
spectrum. Here natural noise is relatively small.
Radio communication over interstellar distances
is feasible with present technology!
Is anyone there?
• Intelligence is ability to use radios.
• Important differences searching for
intelligent compared to primitive life!
• How many civilizations are there in the
galaxy that might try to call us?
• The Drake equation is away to discuss our
ignorance of this fundamental question.
Drake Eq.
• Is there likely to be anyone
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trying to send radio signals? Is
SETI likely to succeed?
Assumes a steady state: rate
of new civilizations is nearly
equal to rate of their death.
“Writes one number, that we
do not know, as the product of
seven numbers, that we do not
know.”
Drake Equation
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Nc=Rs fp n fl fi fc L
Rs=rate of (suitable) star formation
fp=fraction of stars with planets
n=number of “Earthlike” planets per solar
system
fl=fraction of “Earths” with life
fi=fraction that is intelligent
fc=fraction that develops a civilization
L=lifetime of civilization
Drake Equation
Ns = A ¢ B ¢ C
A = Astronomy = Rs¢ fp ¢ n
B = Biology = fl¢ fi
C = Civilization = fc¢ L
Astronomy factors Rs, fp, n
• Rs =# of suitable stars born each year in galaxy.
• If suitable stars mean sun like. Rs¼ 2 (Probably
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want single stars not binary)
fp = fraction of stars with planets. We are
measuring fp as we find planets. fp > 0.1
n=# of earths per solar system. We will start to
measure this with Terrestrial Planet Finder or
similar spacecraft in near future. Now we have
no reason to assume n is small. Note, how
much like earth do we require??
Astronomy Factors
• So far Rs, fp and n are straight forward
factors from astronomy that we either
know or will soon at least partially
measure.
• Therefore these factors are not very
controversial and probably not very small.
• Thus these factors do not dampen
enthusiasm for SETI.
Biology Factors fl, fi
• Fraction of earths that develop life fl.
• Some requirements for life:
– Elements such as H, C, N, O…
– Liquid H_2O
– Energy source (chemical or star light…)
– Primitive organic compounds such as amino
acids.
– Time to allow chemical reactions to increase
the complexity of molecules.
fl may be large
• We assume fl may be large
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because life started relatively
quickly on earth.
Simple organic compounds may be
common. (Remember Miller exp.)
However, there is a lot we don’t
know about the origin of earth life.
Finding life on Mars or elsewhere
would strongly suggest that fl is
large.
Origin of Intelligence
fi= fraction of life that develops
intelligence
• Intelligence may provide evolutionary
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advantage.
However brain needs massive resources.
Evolution will not favor intelligence unless
advantages are very large.
Low level intelligence needed for vision, mobility,
eye-limb coordination…
How large is the leap from this to humans?
How long does intelligence need to evolve?
Fraction that develops Civilization
• What is civilization? Working together?
Using technology? …
• Do army ants or bees have a civilization?
• What role does civilization play in
evolution?
• Here civilization means technology and
radios.
Lifetime of Civilization
• Many civilizations on earth come and go:
Egypt, Greece, Rome,…
• We face many man made and natural
dangers.
• Vast majority of species that every lived
on earth are now extinct.
Total Extinction
• How close have we ever come to the total
extinction of all life on earth?
• A very large impact could kill all life.
– It would have to be so large that the heat
boiled away all the oceans and filled the
atmosphere with molten rock!
– Perhaps this happened very early on and life
had to start more than once.
– We don’t think there has been this large an
impact since.
Snowball Earth
• We have evidence that about 700 million
years ago earth was covered in a global
and very deep ice age.
• Originally it was thought such an ice age
would be disastrous with no way out.
– Snow and ice reflect sun’s heat and this would
keep earth cold with no way to melt the ice.
– Apparently there is a way out.
CO2 Cycle Controls Temp.
• Volcanoes continue to put CO_2 into atmosphere
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even in ice world.
However, ice covers rock. Thus no way to
capture CO2 back into the rock to make new
carbonates.
Greenhouse CO2 continues to build up in
atmosphere. This finally melts ice and converts
earth from frozen to very warm.
With ice gone, eventually high CO2 in
atmosphere recaptured into rocks.
Snowball earth and life
• Ice killed much life. However, some small
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pockets survived perhaps in volcanically heated
pools.
This was before life had evolved hard parts
(such as bones) that left clear fossils.
Great explosion of life with great increase in
complexity and diversity occurred just after the
snowball.
Space colonization and Lifetime
• If we colonize Mars say this might protect
some life against many dangers such as a
single large impact or a disease.
• Still depend on the same sun so the sun
going red giant will kill both earth and
mars.
• Colonizing other stars may prevent total
extinction of humans and increase L.
Number in Galaxy
• Provides an estimate of distance between
civilizations thus how far one must
communicate.
• Represent galaxy as a disk about 50000
Lt-years in radius.
• Area of galaxy= R2 = 7.85e9 (Lt-Y)2.
• Density of civilizations =N/A
Example N=10^6
• =1e6/7.85e9 = 1.3e-4 civilizations per
square Lt-Y.
• Average distance to next civilization L
•  ¼ 1/L2 assume uniform grid of
civilizations each L apart.
• Or L¼ [1/]1/2.
• L¼ 90 Lt-Years.
What makes Earth Special?
Is this a physics/ astronomy question? Or a
biological question? Or a religious
/philosophical question?
What are some of the physics that goes into
Earth having a stable climate for five
billion years?
Are We Alone?
• Yes!
• But how can that be. All those worlds, all those Suns in
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all those Galaxies.
Why only us?
How could the Universe be so big and so so lonely?
What is our destiny? If we kill ourselves, what has it all
been for?
All those worlds we can not detect. What are they for?
“It would be a great waste of space”.
We are not alone!
• The Universe may team with intelligent life!
• Man has been here for only a few million years.
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Less then one one thousandth the age of the
Universe. It is very likely that other intelligences
are much older and wiser then we.
We are but an insignificant new comer in a vast
crowd.
– What do we matter?
– What will the older and wiser races do with us?
Either Way it’s Scary
• How can we be so utterly alone!
• Or
• How can we be so insignificant. Just one
among so many countless millions.
Primitive Life
• Primitive life may be common in the Universe.
– Organic compounds may be easy to make, [Review
Miller Exp.] , and they may be common [Amino acids
found in meteorites, spectral lines from some
compounds found in space and in the atmosphere of
Titan…].
– Life appears to have started quickly on Earth. [What
happened quickly may be highly probable to happen
elsewhere.]
• Life is extraordinarily complicated. We don’t
understand very much about how it got started
on Earth.