Astrobiology in the Classroom
NASA – CERES Project –http://btc.montana.edu/ceres
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 multiplevariable systems culminating in the use of the Drake Equation. In this threepart activity, students use estimation techniques to describe complex situations. First, students are given a closeup 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.
Below is a 2.7 square kilometer (2.7 km^{2}) 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 stepbystep 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?
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?
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 9^{th} grade with long hair are scheduled to be
at lunch between 12:15 and 12:30 and are eating in the cafeteria and having
frenchfries with ketchup?
__________________
TASK: To check your prediction, complete the
following table by estimating the:
Variable 
Estimated Value 
Notes 
n – total number of students in your
school 


f_{f}  fraction of females
in your school 


f_{f,9}  fraction of those
females in 9^{th} grade 


f_{f,9,L}  fraction of those
females in 9^{th} grade with long hair 


f_{f,9,L,t}  fraction of those
females in 9^{th} grade with long hair at lunch between 12:15 and
12:30 


f_{f,9,L,t,c}  fraction of those
females in 9^{th} grade with long hair at lunch between 12:15 and
12:30 in the cafeteria 


f_{f,9,L,t,c,FF}  fraction of those
females in 9^{th} grade with long hair at lunch between 12:15 and
12:30 in the cafeteria eating frenchfries 


f_{f,9,L,t,c,FF,k}  fraction of those
females in 9^{th} grade with long hair at lunch between 12:15 and
12:30 in the cafeteria eating frenchfries 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, T_{avg} 


Reflection Questions
about the Lunchroom Equation
T = n x ( f_{f}
x f_{f,9 } x f_{f,9,L } x f_{f,9,L,t } x f_{f,9,L,t,c } x f_{f,9,L,t,c,FF }x f_{f,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 allfemale school where lunch is served from 12 to 1 pm. How would your estimate change? Why?
Part III – Concept Application: Using
The Drake Equation
N = R_{*} x f_{p} x n_{e}
x f_{1} x f_{i} x f_{c} 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 
R = 

f_{p}  Fraction (percentage) of those stars with planets or planet systems. 
F_{p} = 

n_{e} Number of "earthlike planets" in a planetary system that are at the right temperature for liquid water to exist (in the habitable zone). 
N_{e} = 

f_{l}  Fraction (percentage) of earthlike planets where life actually develops 
F_{l} = 

f_{i}  Fraction (percentage) of earthlike planets with at least one species of intelligent life 
F_{i} = 

f_{c}  Fraction (percentage) of earthlike planets where the technology to communicate beyond their planet develops 
F_{c} = 

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. 
L = 




N  Number of communicative civilizations 
N = 

Reflection
Questions about the Drake Equation
N = R_{*} x f_{p} x
n_{e} x f_{1} x f_{i} x
f_{c} 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 Sunlike 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 f_{p},
n_{e}, f_{1}, f_{i}, and
f_{c }could
have. Record your values for each
term below.
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 f_{p} = 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 n_{e} =1. Since Earth is the only planet in our
solar system that we know to have developed life, it seems reasonable to set f_{l}
= 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 conservative estimate for f_{i}
and f_{c} 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.
Drake Equation Background Information
Sheet
N = R_{*} x f_{p} x n_{e} x f_{1} x f_{i} x f_{c} 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, supermassive 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 Sunlike
stars. A reasonable estimate for
the number of target stars is
400e9 * 10% * 75% = 30 billion stars.
f_{p} – 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.
n_{e} –This number
represents how many "earthlike 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.
f_{l} – This
number represents the fraction of earthlike 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.
f_{i} – This
number represents the fraction of earthlike 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.
f_{c}  This number
represents the fraction of earthlike 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.