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ASTROBIOLOGY IN THE CLASSROOM
NASA – CERES Project –http://btc.montana.edu/ceres
Montana State University
Preliminary Edition
“The Drake Equation – Estimating
the Number of Civilizations in the
Milky Way Galaxy”
Students estimate the number of civilizations in the galaxy by first estimating
the number of craters on the Moon and then by performing estimates of
multiple-variable systems culminating in the use of the Drake Equation. In
this three-part activity, students use estimation techniques to describe
complex situations. First, students are given a close-up photograph of a
small portion of the Moon’s surface. Using the scale provided on the image,
students count the number of large craters in the image and extrapolate to
find the number of such craters on our Moon. In the second part, students
are given a list of variables that describe a particular population of
students. Students estimate the portion of the population that match the
given characteristics and answer questions about how their estimates
change with alternatively defined variables. Finally, students utilize a form
of the Drake Equation to estimate the number of communicating civilizations
that exist in the Milky Way Galaxy.
Students examine the range and
definition of each variable comprising the Drake Equation and evaluate how
changes in the variables influence their result.
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
STUDENT INSTRUCTION AND ANSWER SHEET
Part I – Exploration: How many craters are on the Moon?
Below is a 2.7 square kilometer (2.7 km2) image of the Apollo 14 landing site on the Moon. You can
divide the Moon’s surface up into 14,000,000 such patches. Write a step-by-step plan for estimating the
number of craters on the Moon that are larger than a football field. After you have shown your plan to your
teacher, carry out your plan and compare your results to the class average.
Image Source: http://www.nasm.edu:80/APOLLO/AS14/a14landsite.htm
A. Record your step by step plan in the space below. What was your estimate for the
number of football field sized craters?
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
B. Describe why your estimate might increase or decrease if a different picture of the Moon’s surface
were used.
C. How would your estimate change if you were estimating the number of craters that are smaller than a
football field or larger than your entire school including the parking lot and sports fields?
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
Part II – Concept Introduction: Making Complex Estimates
There are many instances in science where estimation is much more useful and efficient
than counting. In particular, estimation techniques are important when analyzing a
system for which counting is not actually possible. Complete the following estimation
task.
PREDICTION: How many females in the 9th grade with long hair are scheduled to be at
lunch between 12:15 and 12:30 and are eating in the cafeteria and having french-fries
with ketchup? __________________
TASK: To check your prediction, complete the following table by estimating the:
Variable
Estimated Value
n – total number of students in your
school
ff - fraction of females in your school
ff,9 - fraction of those females in 9th
grade
ff,9,L - fraction of those females in 9th
grade with long hair
ff,9,L,t - fraction of those females in 9th
grade with long hair at lunch between
12:15 and 12:30
ff,9,L,t,c - fraction of those females in 9th
grade with long hair at lunch between
12:15 and 12:30 in the cafeteria
ff,9,L,t,c,FF - fraction of those females in
9th grade with long hair at lunch
between 12:15 and 12:30 in the cafeteria
eating french-fries
ff,9,L,t,c,FF,k - fraction of those females in
9th grade with long hair at lunch
between 12:15 and 12:30 in the cafeteria
eating french-fries with ketchup
F - Fraction Of Total Population
(the product of all the fractions)
T - Number of People at Your School
Meeting The Criteria (product of
fraction of total population F, and the
total school population, n)
CLASS AVERAGE, Tavg
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
Notes
Reflection Questions about the Lunchroom Equation
T = n x ( ff x ff,9 x ff,9,L x ff,9,L,t x ff,9,L,t,c x ff,9,L,t,c,FF x ff,9,L,t,c,FF,k ) = n x (F)
A. What value of T did you determine and how did it compare with the class average?
B. Give specific reasons why your value was different than the class average?
C. Predict how the calculation will change if you observe males instead of females.
Check your prediction by performing the necessary calculation.
D. Explain how the value of T would be different if you changed your definition of long
hair? Provide an example calculation with your written explanation.
E. Suppose that you were making this estimate for an all-female school where lunch is
served from 12 to 1 pm. How would your estimate change? Why?
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
Part III – Concept Application: Using The Drake Equation
N = R* x fp x ne x f1 x fi x fc x L
In part II we estimated the number of students that had particular characteristics. In this
activity we will use the same estimate techniques to discover the number of existing
extraterrestrial civilizations that possess the technology to communicate beyond their
home planet. Your task is to complete the table below and use those values to solve the
Drake Equation in order to estimate the number of intelligent civilizations in the Milky
Way. You might wish to review the Drake Equation Background Information Sheet
before making your estimation. After you make the calculation, answer the reflection
questions.
R - Number of target stars in the galaxy that:
 are second generation stars with heavy elements
 are hot enough to have a large habitable zone
 have a long enough lifetimes for life to develop
fp - Fraction (percentage) of those stars with planets or planet
systems.
ne -Number of "earth-like planets" in a planetary system that are
at the right temperature for liquid water to exist (in the habitable
zone).
fl - Fraction (percentage) of earth-like planets where life actually
develops
fi - Fraction (percentage) of earth-like planets with at least one
species of intelligent life
fc - Fraction (percentage) of earth-like planets where the
technology to communicate beyond their planet develops
L - "Lifetime" of communicating civilizations (years) - Note:
This number must be divided by the age of the galaxy, 10 billion
years when you make your final calculation.
N - Number of communicative civilizations
R=
Fp =
Ne =
Fl =
Fi =
Fc =
L=
N=
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
Reflection Questions about the Drake Equation
N = R* x fp x ne x f1 x fi x fc x L
A. What value did you get for the number of civilizations?
B. How does the value change if you double the lifetime of communicating
civilizations?
C. How does the estimate change if we discover that only 1/3 of Sun-like target stars
have planets?
D. How would you change your estimate if we discovered that early life developed
on both Venus and Mars?
E. Determine the most reasonable maximum and minimum values that your group
believes the terms fp, ne, f1, fi, and fc could have. Record your values for each
term below.
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
F. Calculate the range of values for “N” that result from using the maximum and
minimum values that your group recorded in the previous question.
G. Do the maximum and minimum values that you calculated make sense to your
group? Explain why you think they might be too large or too small or just right.
H. How many intelligent, communicating species in the galaxy do we actually know
about? What then is the actual minimum value for “N.” Hint it is not zero.
Explain your reasoning.
In this paragraph we will offer some values for several of the terms in the Drake
equation that are often used by scientists when making these estimates. If we think that
all stars that are like are sun have planets than we could estimate fp = 1 to represent
100%. If we use our solar system as a model then there is only one planet in the
habitable zone that we know has liquid water on its surface (Earth) so we could imagine
setting ne =1. Since Earth is the only planet in our solar system that we know to have
developed life, it seems reasonable to set fl = 0.1 to represent that about one out of every
10 planets has life. It is essentially impossible to know the fraction of species that
develop on a planet that turn out to be intelligent and able to communicate so a
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
conservative estimate for fi and fc that we might use is 0.1 for each term. As a rough
guess we might imagine that across the galaxy intelligent communicating civilizations
last for about 20,000 years out of the 10 billion year existence of the galaxy, which sets L
= 2 x 10-6.
I. What value do you get if you use the estimates provided in the preceding
paragraph? How does this value compare to your original estimate, your estimate
for a maximum value, or your estimate for a minimum value?
CHALLENGE PROBLEM: Scientists recently discovered a massive gas giant planet
orbiting the star 51 Peg. This planet orbits in the star’s habitable zone (where liquid
water can exist). Describe how might this finding change your estimate.
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
Drake Equation Background Information Sheet
N = R* x fp x ne x f1 x fi x fc x L
R – This number represents how many billions of stars in the galaxy meet the following
two criteria:
(1) The star must be a second or third generation star formed from an interstellar
cloud that included the necessary heavy elements for life (e.g., carbon,
oxygen, etc.). The elements are created during the evolution of first
generation, super-massive stars and supernova events that occurred early in
the history of our galaxy. A reasonable estimate for this number is 400 billion
stars.
(2) The star must release enough energy to have a sizeable habitable zone. A
habitable zone is the region around a star where liquid water could exist on an
orbiting planet. 90% of the stars in our galaxy are too cool to have a sizable
habitable zone. This eliminates stars with spectral type K5 and cooler. Of the
remaining 10%, nearly a quarter of those have lifetimes too short for life to
develop. This eliminates stars warmer with spectral type F8 and warmer as
they have lifetimes shorter than 4 billion years.
Our Sun, a G2 star, fits both of these categories and thus is one of the target stars.
Such target stars are often referred to as Sun-like stars. A reasonable estimate for the
number of target stars is
400e9 * 10% * 75% = 30 billion stars.
fp – This number represents the fraction of those stars meeting the above criteria that also
have planets or planet systems around them. Recent discoveries of numerous extrasolar planets suggest that most stars like our Sun probably have planets.
ne –This number represents how many "earth-like planets" there are at the right
temperature for liquid water to exist (i.e. in the habitable zone). Recent discoveries
suggest that we should also consider including moons around gas giant planets that
are orbiting their central star in the habitable zone. A reasonable estimate for this
number is difficult to imagine. In our solar system, the number ranges from one to
three depending on if you include Venus or Mars. If Saturn were to migrate into the
habitable zone, its 22 moons would make this number much larger.
fl – This number represents the fraction of earth-like planets where life actually develops.
Some scientists believe that the evolution of life is inevitable when the conditions are
right. Alternatively, we only know of one instance where life has successfully
developed (Earth), therefore it is difficult to estimate this fraction.
fi – This number represents the fraction of earth-like planets where at least one species of
intelligent life evolves. Intelligent life could develop early on some planets and later
on others and therefore again it is difficult to estimate this fraction.
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition
fc - This number represents the fraction of earth-like planets where the technology to
communicate beyond the planet exists. In our own civilization, we have been using
television and radio signals for nearly a century. These signals have leaked into outer
space and might be detectable by extraterrestrial civilizations. As before, it is
extremely difficult to estimate this number.
L – This number represents the number of years that communicating civilizations have
existed out of the total lifetime that the galaxy has existed. We call this fraction of
years "Lifetime." This number depends both on social issues and technological
issues. It is possible that intelligent civilizations elsewhere in the galaxy have existed
for millions of years and may or may not choose to communicate beyond their own
planet. Alternatively, when civilizations develop the technology to communicate they
might simultaneously develop technology capable of making their environment
uninhabitable (e.g., weapons of mass destruction). These factors make this number
extremely difficult to estimate. L could range from only 100 years to many millions
of years.
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Montana State University
NASA CERES Project – http://btc.montana.edu/ceres
Preliminary Edition