Student Page
Version 1.1 9/28/00
SCALING THE MOON
Background
The Moon is one of the first objects that people name when asked to list the objects that
can be seen in the sky (most people don’t realize that the Moon is frequently visible in
the daytime sky, but that is another lesson).
And yet, very few people have an accurate picture of the Moon’s size and distance from
planet Earth. Modeling the Earth/Moon system allows you to see the relationship in a
way that is easy to manage.
After finishing this activity, you will have created a physical model of the Earth/Moon
system that is true to scale... meaning that both the sizes and distances between the
modeled Earth and Moon are accurate relative to each other. Using this model, you
will find it much easier to accurately describe this fundamental relationship between
the Earth and Moon.
Procedure
1. Begin by calculating the ratio between the Earth’s diameter and that of the Moon.
A. A ratio is like a multiplier, it indicates how many times bigger or smaller
something is compared to another object. For example, the ratio between
your height and width (at the shoulders) can be found by dividing your height
by your width [height/width], which most likely is about a ratio of 5:1. This
simply means that you are five times taller than you are wide OR you are 1/5
as wide as you are tall.
Objective
The objective of this activity is to build a
physical model of the Earth/Moon system
that is accurate for both relative sizes and
distances between the two bodies.
Materials
• Globes
• Balls (Various sizes)
• Meter Sticks and Rulers
• Calculator
B. To calculate a ratio, you simply divide one measurement by the other. In
most cases it is best to divide the measurement for what you want to find by
the measurement for what is known. If that sounds confusing, think about
this example...
If I had a list of how wide people’s shoulders are and I wanted to predict how
tall the person should be I could do the following.
Person
Width
Width Height
Sally
20 cm
You---> 21 cm 105 cm
Johnny
23 cm
Seiichi
18 cm
Velma
19 cm
As an example of an average person you could find the ratio of your height to
your width. You would do this by measuring both and then dividing one by
the other. But which should you divide by?
Remember:
divide the measurement for what you want to find
by the measurement for what is known.
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SCALING THE MOON: Student Page
B.
Continued...
IF...
you divide your height (the thing you want to calculate for everyone)
by your width (the thing you know for everyone)
then you wind up with...
105 cm / 21 cm = 5
And Sally winds up with a predicted height of...
20 cm x 5 = 100 cm ...that sounds pretty reasonable!
Summary: If you want to use your ratio for simple multiplication,
make certain to divide the measurement for what you want
to find by the measurement for what is known.
C.
Challenge!
How good of an example is this problem?
Measure and calculate to find the ratio
between your height and width (at the
shoulders’s) and compare.
Your teacher is going to provide you with a model for the Earth that you can
measure and for which we have a known diameter. What you will be asked
to find is the size of a good model for the Moon given its known diameter.
Earth’s Real Diameter
1,275,600,000 cm
Earth Model’s Diameter
Ratio 1 = ________
Moon’s Real Diameter
________
Moon Model’s Diameter
347,600,000 cm
________
2. Find a ball of suitable size from the box of various size balls provided by your teacher.
Make certain to measure the object to ensure it is a good match to your calculated
size for the Moon in this model.
3. Now all we need to do is put the Moon at the correct distance from the Earth so that
it will look the correct size to our eye when we view it from the model Earth. Once
again, a ratio is the easy way to calculate the needed distance.
Moon’s Real Diameter
347,600,000 cm
Moon Model’s Diameter (From Step 1)
________
Ratio 2 = ________
Moon’s Real Distance from Earth (Ave.)
38,440,000,000 cm
Moon Model’s Distance
________
4. Take the ball that you found to represent the Moon in our model and put it at the
correct distance from our Earth model. Make certain to measure the distance to the
Moon object to ensure it is a good match to your calculated distance in this model.
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SCALING THE MOON: Student Page
Questions and Conclusions
1. If you look at the Moon from the Earth, how large does it look?
Hint: Put your eye down near your model of the Earth and look directly at the Moon. Hold out your hand at arms length and
find a finger nail or fingertip that appears to be the same size as the Moon model as it is seen from the model Earth.
2. Compare your model of the Earth/Moon system to that of your classmates, are they all the same? Why is this true?
3. Is the size of the model Moon larger than, equal to, or smaller than what you expected based on your prior knowledge of the
Earth/Moon system?
4. Was the Moon closer to, equal to, or farther away from the Earth than you expected it to be based on your prior knowledge of
the Earth/Moon system?
5. If we wanted to model the orbit of the Moon around the Earth, how could we accomplish this task? Describe step-by-step how
to do this accurately using your Earth/Moon system model!
6. The next time you see the Moon in the sky, use the same technique described in question 1 to measure the apparent size of the
Moon in the real sky. Is it the same as, smaller than, or larger than the Moon from your scale model?
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Intentionally left blank...
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School District
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SCALING THE MOON
Name
Pre-Activity Procedure
In the diagram provided below, there is a circle which represents the planet Earth as it
might appear from outer space. To complete this activity, simply place marks on the
line at the correct distance from the Earth to represent how far away the objects listed
are from the planet.
Make the following mark for each of the objects listed...
*
O
M
SS
Stars
Clouds
Moon
Space Shuttle
Objective
The objective of this activity is to have
you record your understanding of the
Earth/Moon system prior to completing
a knowledge building activity.
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Planetarium
and Observatory
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SCALING THE MOON: Student Page
Intentionally left blank...
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Version 1.0 8/05/00
What is happening?
The most difficult thing for students to do is translate numbers into a visual impression of what something looks like or how large or far away an object appears to be.
This exercise is designed to take the dimensions of the astronomical objects closest to
home, namely those of the Earth and the Moon, and use them to learn a little astronomy
while simulataneously practicing multiplication, division, and the use of ratios to solve
problems. Specifically, this activity will ask students to:
Calculate to find the correct size for a model of the Moon.
Calculate to find the correct distance from Earth for the model of the Moon.
Compare the scale model observations to reality... prove that scale means
scale!
Important Points for
Students to Understand
• The Moon is a relatively large object in space. It is much farther away from Earth
than most people think when they consider the Earth/Moon system..
• Students should understand that the Moon’s motion is not simple by any stretch of
the imagination. We as educators frequently simplify our explanations of natural
phenomena (other things as well) so as to make a subject understandable at a given
age level. The modey created in this activity is simply an “average” situation. The
Moon is hardly ever in this position, spending most of its time slightly farther or
closer to the Earth. The Moon has additional motions which are not modelled at
all.
• Scale models accurately represent the appearance of their contents as viewed from
outside or inside of the model. This point is proven by the observation of the Moon
“from Earth” in the model and from the real Earth to the real Moon in the sky.
The two Moons appear identical in size if the model has been accurately made to
scale.
Time Management
Materials: total for the class
• Copies of the student pages.
• Globes or “Earth Balls”
• Box of assorted balls, must include balls
that are ~1/4 the size of your Earths. Include some that are larger and smaller.
• Meter Sticks and Rulers
• Calculators
Vocabulary
The Moon: The large natural satellite
of Earth gets the official “The Moon” or
“Moon” title. All of the satellites of the
other planets are described as “The Moons
of (Planet Name Here) or by their proper
name such as Io, Europa, Titan, etc.
Ratio: The multiplier which represents
the relative size of two measurements or
values.
Diameter: The measure, or length of a
line which extends from the periphery of
a circle or sphere and passing through the
center of the object.
Distance: The measure of the separation of two objects as measured in a
straight line that connects the center of
the objects.
Scale Model: A representation of an
object or process in which all dimensions
have been enlarged or reduced by the
same ratio.
1. Gather materials.
2. Decide on a starting date for the project. Although this is not critical to the success
of this activity, it is pretty cool to make a connection to the real sky. See the box on
the following page for more information on selecting a starting phase of the Moon.
Reference almost any calander to determine what date the next major phases of the
Moon will occur.
3. Complete the Activity. This will take anywhere from 50-90 minutes depending on
how in depth you want to get into talking about the Moon in general and the concepts
of scale prior to completing the model construction and how in depth the discussion
of the questions are taken.
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SCALING THE MOON: Teacher Page
Preparation:
• An introduction to the concept of scale models is very beneficial. Using models such
as those of miniature railroad cars, architectural blueprints, diagrams of parts from an
instruction manual, etc. are all excellent representations of scale models.
VERY bad examples of scale diagrams can be found in many places, especially related
to astronomy where the distance between objects is tremendously larger than the
size of the actual objects. Save these for after this activity or the Solar System scale
modeling activity. They make great, “What’s wrong with this picture” material.
• Have students complete the pre-activity provided.
• Teach students techniques for measuring the diameter of a ball. The two simplest
methods are as follows...
Method 1:
Stretch a string around the ball, measure it and divide by π.
Method 2:
Place a bookend or box on either side of the ball, remove the ball and
measure the gap between the two boxes. (see diagram).
Measure this gap
Going Deeper:
The use of ratios as a multiplier for conversion is a powerful and easy method for moving from one measurement to another related measurement. If you want to discuss the
use of ratios in greater detail, here is what happens if you reverse the process.
IF...
you divide your shoulder width by your height you wind up with
21 cm / 105 cm = 0.2
we know each person’s width so if we multiplied by this ratio
we would find for Sally that she is...
20 cm x 0.2 = 4 cm tall ??? I don’t think so!
It is important to reinforce the use of estimation and confirmation of mathematical solutions. In this case, it is fairly obvious that something is incorrect with our solution.
But was the problem simply a “typo” into the calculator or is this really the solution?
Doing the math again or having a friend duplicate the solution shows that this is not
simply a typo. How can we fix the problem?
Ratios are simply multipliers... and that means that they can be used to convert answers
in either direction. In this case, our ratio of 0.2 can be applied (using multiplication)
to the height of an individual to find their width. But if we want to go the opposite
direction (as we do in this problem) then we have two options. The first is to use the
math process that is opposite of multiplication... division! The second solution is to
calculate the ratio by dividing in the opposite order.
Timing the Project
Observing the Moon during
the daytime (Question 6):
This question asks the student
to look at the real Moon and
compare it to the Moon in the
model. To make it easy to
observe the Moon in the afternoon, start with a First Quarter
Moon. To make it easy to observe in the morning, start with
a Third Quarter Moon.
First Quarter Moon
An excellent starting point
with easy observation anytime after about 1 P.M. and
until about 6 hours after
sunset.
Third Quarter Moon
An excellent starting point
for morning observing projects with easy visibility
anytime from an hour after
midnight until about 1 hour
before Noon.
Warning!
Although it is tempting, don’t try
to use this model to demonstrate
solar or lunar eclipses! This is
challenging to do correctly without
reinforcing common misconceptions and increasing confusion. If
you want to model eclipses, see the
“Modeling Eclipses” activity.
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SCALING THE MOON: Teacher Page
The First Option: Using Division
IF...
you divide your width (the thing you know for everyone)
by your height (the thing you want to calculate for everyone)
then you wind up with...
21 cm / 105 cm = 0.2
This time we DIVIDE everyone’s width by the ratio and
Sally winds up with a predicted height of...
20 cm ÷ 0.2 = 100 cm ...that sounds pretty reasonable!
The Second Option: Dividing in the opposite order to calculate the ratio:
IF...
you divide your height (the thing you want to calculate for everyone)
by your width (the thing you know for everyone)
then you wind up with...
105 cm / 21 cm = 5
we still use the original method of multiplying by the ratio and
Sally winds up with a predicted height of...
20 cm x 5 = 100 cm ...that sounds pretty reasonable and is the same as the result of the first method!
Summary: If you want to use your ratio so that you can finish the problem using simple multiplication, make certain to
divide the measurement for what you want to find by the measurement for what is known. If your answer seems
unreasonable; double check the calculation for typos, try dividing by the ratio rather than multiplying by it, or
calculate the ratio by dividing in the opposite order.
Variations:
• For smaller children, the activity can be completed without any math! Simply take the students outside to “measure” the moon
using the technique described in question 1 of the activity. Now put your eye next to the Earth model (globe or ball) and using
the same measuring technique have a partner move the correct size Moon closer or farther away until it measures the same as the
actual Moon in the sky. You have just put your model “into scale” by taking two objects scaled for size and making it “look right”
based on real world experience.
• For high school student, white out the numbers provided and put them into scientific notation. Do not allow the use of calculators
and use estimation techniques and the rules for multiplying and dividing in scientific notation to complete the activity. You will
be amazed how close to the “correct” mathematical solution these techniques will come.
• Use beads of various sizes rather than globes and balls if this is more convenient. You can find “Earth” marbles and beads that
would reduce the full size of the model to table top dimensions rather than the large sizes involved with globes and balls. However,
there is nothing like the impression made by the size of the model when made with a 10” or 12” globe.
• Modify the ratio calculation to involve metric conversion if you desire.
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SCALING THE MOON: Teacher Page
Variations (continued):
• For step 1C, it can be instructive to point out that for most ratios, more than one possible solution method is possible. In this case,
the “Ratio =____” has been placed into the center of the four numbers so it is equally implied that the ratio calculated could be
between the Earth and the Moon’s real diameters, or between the Earth’s real and model diameters. Both solutions work equally
well mathematically but in this case the easier ratio is probably dividing the Moons real size by the Earth’s real size and then applying the ratio to the measured dimension of the Earth model to calculate the predicted necessary size of the Moon model.
• Step 2 of Procedures:
As an alternative, you may ask your students to make a circle of the correct size out of paper and cut it out rather than using a
box of various size balls.
• Student Question 5:
You can have students exchange directions and make them follow them to the letter to see if they actually work. The best descriptions will have some mechanism for maintaining the distance (although in reality this varies a little... such as a length of
string and a second mechanism for motion... such as “move the Moon model counter-clockwise around the Earth model (as seen
from above)”. Please remind students that this activity ONLY models the average distance and diameter of the Moon with any
accuracy. The Moon exhibits complex motions which are beyond the scope of this activity.
Suggestions for Further Study
Activites:
• “It’s only a Phase”
• “Observing the Moon”
• “Modeling Eclipses”
Readings and Reference:
• “Papa, Please get the Moon for Me?”, by Eric Carle [Little Simon, ISBN 0-6898-2959-0]
• “New Astronomer”, by Carole Stott [Dorling Kindersley, ISBN 0-7894-4175-6]
• “Astronomy for All Ages”, by Philip Harrington & Edward Pascuzzi [Globe Pequot, ISBN 1-56440-388-2]
Activity Books for Teachers and Classroom Use:
• “Project Earth Science: Astronomy” [National Science Teacher’s Association(NSTA), ISBN 0-87355-1087]
• “Craters: A Multi-Science Approach to Cratering and Impacts” [NSTA, ISBN 0-87355-132-X]
• “Seeing the Sky” by Fred Schaaf [John Wiley & Sons, ISBN 0-471-52093-4]
Madison Metropolitan School District Planetarium and Observatory
SCALING THE MOON: Teacher Page
SCALING THE MOON
Name
Pre-Activity Procedure
In the diagram provided below, there is a circle which represents the planet Earth as
it might appear from in outer space. To complete this activity, simply place marks on
the line at the correct distance from the Earth to represent how far away the objects
are from the planet.
Make the following mark for each of the objects listed...
*
O
M
SS
SS
Stars
Clouds
Moon
Space Shuttle
O
Objective
Clouds are found in Earth’s
atmosphere. So your circle can be
anywhere on the image of the Earth.
At this size, the thickness of the
Earth’s atmosphere would be thinner
than the piece of thread.
TheSpace Shuttle orbits only
a few hundred miles above the
Earth’s surface and NEVER
travels into “outer space”.
!
y
e
K
r
e
sw
n
A
The objective of this activity is to have
you record your understanding of the
Earth/Moon system prior to completing
a knowledge building activity.
The Stars are so far away from
Earth that to put them on this
scale, the closest star to Earth
(alpha centauri) would have to
be 24,333 Km away!
The Moon is approximately 30
Earth diameters away from the
Earth. This puts it at the end of
this line and about the size of the
circle around the letter “M”!
The Answer Key:
Please save this for after the activity has been completed...
Most people do not realize that the Space Shuttle never leaves Earth orbit...
The last time humans went as far as the Moon was in December of 1972!
Madison Metropolitan School District Planetarium and Observatory
M