The document discusses factors involved in estimating the number of technological civilizations that may exist among stars using the Drake Equation. It examines each variable in the equation - R* (rate of formation of suitable stars), fp (fraction with planets), ne (number of planets suitable for life), fl (fraction where life appears), fi (fraction where intelligent life emerges), fc (fraction emitting detectable signals), and L (length of time signals emitted). It provides estimates and considerations for each variable based on current astronomical and biological understandings.

1. Life
LACC: §29.1, 29.2, 29.3
• The Drake Equation: How many communicating
civilizations are in our galaxy? Could be just about
any number, but 10 to 10,000 isn’t unreasonable.
• The Fermi Paradox: Where is everybody? Since we
don’t see anybody, we’re probably alone.
• SETI: The Search for Extraterrestrial Intelligence--is it
worth it? Even if they are out there, it could take
millennia for signals to be passed back and forth.
An attempt to answer the “big questions”: What is out
there? How did we get here? Are we alone?
Thursday, May 27, 2010 1

2. The Drake Equation
How can we estimate the number of technological
civilizations that might exist among the stars? The
Drake Equation, as it has become known, was first
presented by Dr. Frank Drake (now Chairman of the
Board of the SETI Institute) in 1961 and identifies
specific factors thought to play a role in the
development of such civilizations.
The equation is usually written:
N = R* • fp • ne • fl • fi • fc • L
http://www.seti.org/Page.aspx?pid=336
Thursday, May 27, 2010 2

3. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
Where,
N = The number of civilizations in The Milky Way Galaxy whose
electromagnetic emissions are detectable.
R* =The rate of formation of stars suitable for the development of
intelligent life.
fp = The fraction of those stars with planetary systems.
ne = The number of planets, per solar system, with an environment
suitable for life.
fl = The fraction of suitable planets on which life actually appears.
fi = The fraction of life bearing planets on which intelligent life emerges.
fc = The fraction of civilizations that develop a technology that releases
detectable signs of their existence into space.
L = The length of time such civilizations release detectable signals into
space. http://www.seti.org/Page.aspx?pid=336
Thursday, May 27, 2010 3

4. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
R* = The rate of formation of Suitable Stars in the Milky Way Galaxy
Estimates for the number of stars in the Milky Way vary from a low of
100 billion to a high of 400 billion. Estimates for the age of the Milky Way
also vary from a low of 800 million years [!!!] to a high of 13 billion
years. [200 billion stars / 10 billion years = 15 stars/year]
An important caveat to the above values is that the rate of star
formation in the galaxy is not constant over time. In the galaxy's younger
days, stars were being formed at a much higher rate. Today, estimates for
the overall star formation rate range from 5 to 20.
[But, which stars are “suitable”? O? B? A? F? G? K? M?]
http://www.astrodigital.org/astronomy/drake_equation.html
Thursday, May 27, 2010 4

5. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
R* = The rate of formation of Suitable Stars in the Milky Way Galaxy
However, the criteria that these stars be suitable means that they must
be F, G or K stars, and these stars account for about 10% of the stars in
the Galaxy. [15 stars/year x 10% F, G, or K = 1 suitable star per year]
http://www.airynothing.com/smackerels/DrakeEquation.html
...astronomers have recently determined that stars
formed at a higher rate several billion years ago, when
the stars that might now bear intelligent life were
being born. So a value of R = 3 is more realistic.
http://www.skyandtelescope.com/resources/seti/3304541.html?page=2&c=y
Thursday, May 27, 2010 5

6. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
fp = the fraction of stars that have planetary systems
Reasonable guesses might be 20 to nearly 100 percent. (A September
2003 paper by Charles Lineweaver and Daniel Grether delves into this.)
At least half of the young stars seen in [the
Orion Nebula] are surrounded by thick,
dusty disks — excellent planet-forming
material.
The planet is thought to be one to two times as
massive as Jupiter, according to the scientists
who imaged it. It orbits a star similar to a young
version of our Sun.
http://www.skyandtelescope.com/resources/seti/ http://www.space.com/scienceastronomy/
3304541.html?page=2&c=y 050401_first_extrasolarplanet_pic.html
Thursday, May 27, 2010 6

7. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
ne = is the average number of planets in a star's habitable zone.
The terrestrial example suggests complex life requires water in the liquid
state and its planet must therefore be at an appropriate distance. This is
the core of the notion of the habitable zone or Goldilocks Principle . The
habitable zone forms a ring around the central star. If a planet orbits its
sun too closely or too far away, the surface temperature is incompatible
with water being liquid (though sub-surface water, as suggested for
Europa, Enceladus, and Ceres, may be possible at varying locations).
http://www.absoluteastronomy.com/ http://physics.uoregon.edu/~jimbrau/
topics/Rare_Earth_hypothesis astr123/Notes/Chapter28.html
Thursday, May 27, 2010 7

8. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
fl= The fraction of life bearing planets on which life emerges.
A deep ocean
hydrothermal vent belching
sulfide-rich hot water. A
variety of life forms
comprise a food web
based on bacteria that live
off of the energy provided
by the sulfide-rich vent
waters. It is possible that
the Earth's earliest life
forms evolved in an
environment like this.
Photo: NOAA/WHOI.
http://www.nss.org/adastra/volume14/rothschild.html
Thursday, May 27, 2010 8

9. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
fl= The fraction of life bearing planets on which life emerges.
The first ecosystem ever found having only a single biological species has
been discovered 2.8 kilometers (1.74 miles) beneath the surface of the
earth in the Mponeng gold mine near Johannesburg, South Africa. There
the rod-shaped bacterium Desulforudis audaxviator exists in complete
isolation, total darkness, a lack of oxygen, and 60°C
heat (140°F). D. audaxviator survives in a habitat
where it gets its energy not from the sun but from
hydrogen and sulfate produced by the radioactive
decay of uranium. Living alone, D. audaxviator must
build its organic molecules by itself out of water,
inorganic carbon, and nitrogen from ammonia in
the surrounding rocks and fluid.
http://esciencenews.com/articles/2008/10/09/
bold.travelers.journey.toward.center.earth#
Thursday, May 27, 2010 9

10. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
fi= The fraction of life bearing planets on which intelligent life emerges.
It is also true that, although simple forms of life on Earth arose quickly, it
took billions of years before complex life forms appeared and longer still
before intelligent life arose. Thus even if evolution will eventually bring
about intelligent life, it could well require a stable environment for a
significant fraction of the lifetime of a suitable star.
http://www.lifeinuniverse.org/noflash/Drakefi-07-02-06.html
Top Six Most Intelligent Animals in the World
6. Pigs 3. Smaller Toothed Whales
5. Elephants 2. Octopus
4. Dolphins 1. Chimpanzees*
*: including other monkeys that are related...
http://www.scienceray.com/Biology/Zoology/Top-Six-Most-Intelligent-Animals-in-the-
World.623017
Thursday, May 27, 2010 10

11. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
fc = The fraction of communicative planets
Though not a SETI League "hit," no
discussion of SETI results would be
complete without this one. The most
famous of all SETI candidate signals (it was
even mentioned on The X-Files), the Ohio State University "Wow!" signal
was detected on 15 August 1977. Twenty years later, after more than
100 follow-on studies, it remains an intriguing unexplained phenomenon.
These articles discuss the signal and its implications to The SETI League's
present search.
http://www.setileague.org/photos/hits.htm
Thursday, May 27, 2010 11

12. The Drake Equation
N = R* • fp • ne • fl • fi • fc • L
L = Average lifetime of a technological civilization
Among the cosmic phenomena that astronomers have identified as being of potential biological
importance are:
1.
Large-scale stellar flares http://www.daviddarling.info/
2.
Nearby supernova explosions encyclopedia/C/coscatasbio.html
3.
Gamma-ray bursters
4.
Impacts by asteroids or comets
Among these are the very hazards which humanity presently faces:
1.
Large-scale nuclear or biological war
http://www.daviddarling.info/
2.
Global epidemics of lethal disease resulting from
encyclopedia/E/etcivhaz.html
◦
the emergence of antibiotic-resistant pathogens
◦
back-contamination
3.
Environmental disasters stemming from a combination of industrial pollution, over-
population, and destruction of natural habit, including
◦
global warming due to a gradual elevation in the level of greenhouse gases
◦
disintegration of the ozone layer
4.
Unforeseen side-effects of new technologies, such as genetic engineering
Thursday, May 27, 2010 12

13. The Drake Equation
Taking the historical values given by Drake
and his colleagues in 1961: Drakes current values:
R* = 10 suitable stars per year R* = 5 suitable stars per year
fp = 50% of the stars have planets fp = 50% of the stars have planets
ne = 2 planets on average are habitable ne = 2 planets on average are habitable
fl = 100% of habitable planets produce life fl = 100% of habitable planets produce life
fi = 1% of life bearing planets produce fi = 20% of life bearing planets produce
intelligence intelligence
fc = 1% of intelligences can communicate fc = 100% of intelligences can communicate
L = 10,000 average lifetime of a civilization L = 10,000 average lifetime of a civilization
N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000 N = 5 × 0.5 × 2 × 1 × 0.2 × 1 × 10,000 =
= 10 civilizations in our galaxy. 10,000 civilizations in our galaxy.
http://www.fermisparadox.com/Fermi- http://www.pbs.org/wgbh/nova/
paradox.htm origins/drake.html
Thursday, May 27, 2010 13

14. The Fermi Paradox
Fermi realized that any civilization with a
modest amount of rocket technology and an
immodest amount of imperial incentive could
rapidly colonize the entire Galaxy.
Growth of the number of probes would
occur exponentially and the Galaxy
could be explored in 4 million years.
While this time span seems long compared
to the age of human civilization, remember
the Galaxy is over 10 billion years old and
any past extraterrestrial civilization could
have explored the Galaxy 250 times over.
Within a few million years, every star system
could be brought under the wing of empire.
http://abyss.uoregon.edu/~js/cosmo/lectures/lec28.html
Thursday, May 27, 2010 14

15. SETI: Should we bother?
Let’s consider our Milky Way Galaxy as a flat disk about 30 kpc in
diameter, 0.5 kpc thick, and containing about 100 billions stars. The
volume of our galaxy would then be πr2•h= 350 kpc3
100,000,000 stars / NDrake =
about how many stars you could expect to search before finding one
with a communicating civilization
350kpc3 / NDrake =
typical volume surrounding each communicating civilization in kpc3
3√(typicalvolume surrounding each communicating civilization) =
estimation of distance between communicating civilizations in kpc
distance between communicating civilizations in kpc • 3260 ly/kpc • 2
= typical time between sending a signal and receiving a reply
Thursday, May 27, 2010 15

16. SETI: Should we bother?
Let’s consider our Milky Way Galaxy as a flat disk about 15 kpc in
radius, 0.5 kpc thick, and containing about 100 billions stars. The
volume of our galaxy would then be πr2•h= 350 kpc3
100,000,000 stars / 10,000 = 10,000 stars
about how many stars you could expect to search before finding one
with a communicating civilization
350 kpc3 / 10,000 = 0.035 kpc3
typical volume surrounding each communicating civilization in kpc3
3√(0.035kpc3) = 0.33 kpc = 330 pc
estimation of distance between communicating civilizations in kpc
0.33 kpc • 3260 ly/kpc • 2 = 2100 years
typical time between sending a signal and receiving a reply
Thursday, May 27, 2010 16

17. LACC Ch 29: Franknoi, Morrison, and
Wolff, Voyages Through the Universe,
3rd ed.
Study for you Final.
Thursday, May 27, 2010 17