Constructing a model of the solar system
Part 1: The relative size of planets
Time: approximately 35-45 minutes, depending on student familiarity with ratios.
Materials:
A collection of different sized balls, including one 70 cm diameter exercise ball
A few different sized marbles
Several different sized ball bearings, available at most hardware stores
Other round objects of different sizes, including bead, pebbles, etc.
A few grains of sand, poppy seeds, sugar and/or ground black pepper
Metric rulers (one for each group)
Calculators (one for each group)
Solar system chart from Appendix B
Overview
In this first of two lessons the students will model the different sizes of the
Sun and the nine planets relative to each other, without concern to their distance
from the Sun. Groups of students are assigned a planet. They will use a given
scale, or ratio, to determine what size of object would best represent their planet at
that scale. They will then select an object that most closely approximates the size.
As a class, students will compare the different objects to infer the relative sizes of
the Sun and nine planets.
Purpose
Students will see how much more massive the Sun is compared to the
planets of the solar system. This lesson also involves knowledge of ratios, scale
models and measuring.
Standards
A complete list of the standards covered by this lesson is included in
Appendix A at the end of the lesson.
Procedure
Constructing a model of the solar system to fit into a typical schoolyard is
probably best done as two separate lessons, for reasons that will become obvious
later in this lesson. This first lesson will have students model the relative sizes of
the Sun and the 9 planets. In the second lesson students will model the distances of
the planets from the Sun.
It is important that the students be offered a selection of objects that
comprise a very wide range of sizes, starting with the 70 cm exercise ball as the
largest and going all the way down to grains of dust or ground black pepper.
Objects that aren’t used in this lesson because they are too small will be used in
the second lesson.
It is recommended that the group of objects include a basketball, soccer ball
and/or inflatable rubber playground ball. Even though these objects will not be
used, they should be available as choices so that a smooth size transition from the
largest to the smallest objects is displayed. For this lesson, a baseball or ball
similar in size, must be included.
Step 1: Divide the class into nine groups and assign each group one of the
nine planets so that every planet is represented. Tell the class that they are going to
construct a scale model of the solar system, and that today they are going to
compare the different sizes of the Sun and nine planets.
Hold up the exercise ball and explain that it will be used to represent the
Sun. Point out the other objects that you have gathered and ask each group to
predict which ball or round object will be used to represent the Earth. Allow one
member of each group to select an object and bring it back to their group. The
group members will decide whether that object is a good prediction or if the
selector should get a larger or smaller one. It is recommended that only one
member from each group be allowed to come up to the table containing the balls
to avoid congestion. Ask each group to hold their ball up so their classmates can
see it. After each group has decided and shown their prediction to the class, ask
that all balls and objects be returned.
Step 2: Pass out the solar system charts (Appendix B). The first step is to
decide on a proper scale for constructing the model. Use your own judgment how
much help to give the class at this point. You may need to review the definition of
“diameter,” and you might want to point out the rounding is okay, so the students
can treat the diameter of the Sun as approximately 1,400,000 kilometers. It might
be helpful to put the following formula on the board:
1,400,000 km (diameter of the Sun)
? km
=
70 cm (diameter of the exercise ball)
1 cm
The class should arrive at the conclusion that, if they use the exercise ball
to represent the Sun, they will need to use a scale of 1 cm equal to 20,000 km.
Next they will need to calculate the size of the object they will use to represent
their planet using the same scale. That is, they will need to divide the diameter of
their planet by 20,000 to find out how many centimeters, or what part of a
centimeter, the diameter of their object should be. There are different ways to set
up the equation. Here is one way if students need help:
Diameter of their planet, in km
20,000 km
=
Diameter of object, in cm
1 cm
Once they know the diameter of their object, the person in charge of
materials should get an object they think is the correct size and bring it back to the
group to be checked. The best way to check it is to place it on the ruler and look
down over it. Using this method, students can measure the diameters of different
objects until they find one that everyone agrees is the correct diameter. Students
working with smaller planets may need to be reminded that 1 centimeter equals 10
millimeters, so 0.38 centimeters is about equal to 4 millimeters.
You should circulate around the classroom as the groups are working and
check the accuracy of the objects they select to represent their planet. Here is a
rough approximation of the size of the objects that the groups should wind up
with:
Object
Diameter
Approximate
Possible Object of Approximate
Size of Model
Size
Sun
1,390,000 km
69.5 cm
70 cm exercise ball
Mercury
4,880 km
2.5 mm
Small pebble or BB shot
Venus
12,104 km
6 mm
Earth
12,756 km
6.5 mm
Bead or large ball bearing
Bead or large ball bearing (should
be slightly larger than Venus)
Mars
6,794 km
3.5 mm
Small pebble or ball bearing
Jupiter
142,984 km
7.1 cm
Baseball
Saturn
120,526 km
6 cm
Uranus
51,118 km
2.6 cm
Neptune
49, 532 km
2.5 cm
Tennis ball
Large marble “shooter” or super
ball
Same as Uranus, but should not be
larger
2,274 km
1 mm
Poppy seed or small grain of sand
Pluto
Step 3: Once all the groups have chosen an object, have a volunteer hold
the “Sun” up in front of the room. Tell the class that you want to show the relative
size of the planets as they move out from the Sun, and ask which group’s planet
should be brought up first (Mercury). Have someone from the group modeling
Mercury bring up their object and compare it to the Sun. Have them remain up in
front of the class as you ask the class which is the second planet out from the Sun
(Venus). Have a member from the Venus group bring their object to the front to
compare to the Sun and to Mercury and remain up front as you continue in this
fashion for the rest of the planets. Keep the students in the correct order as you
move out from the Sun. Be sure to compare the size of the Earth with the Sun and
with the other planets.
Step 4: Ask the class what they noticed when they compared the planets to
the Sun and to each other. There will probably be many different answers, but
hopefully students will notice that the Sun is much more massive than anything
else in the solar system, and that Jupiter, Saturn, Uranus and Neptune are much
larger than the other planets (hence, the term gas or ice “giants” which is often
used to describe them). Many other correct answers are possible.
Step 5: Have the students return all the objects and go back to their seats.
Then tell them that you want to determine how large an area they would need to
construct a model of the solar system at this scale if they placed their objects at the
correct relative distance from the Sun. Ask the class how they would figure this
out.
Since Pluto is (usually) the farthest from the Sun, its orbit will determine
the size of the model. Using the same scale, Pluto’s distance from the Sun would
be 295676 cm, or just under 3 km about 2 miles) from the Sun. Tell the class that
if they used this scale that the model would be too big to construct on the school
grounds. And ask them to think about how they might construct a model that
would fit on a football field. This lesson should be followed up with Part 2
Appendix A
Standards Addressed
Benchmarks (Grades 3 through 5)
2C – Mathematical Inquiry
Numbers and shapes-and operations on them-help to describe and predict things about
the world around us.
In using mathematics, choices have to be made about what operations will give the best
results. Results should always be judged by whether they make sense and are useful.
3A – Technology and Science
Measuring instruments can be used to gather accurate information for making scientific
comparisons of objects and events and for designing and constructing things that will
work properly.
4A – The Universe
The earth is one of several planets that orbit the sun, and the moon orbits around the
earth.
4B – The Earth
Like all planets and stars, the earth is approximately spherical in shape. The rotation of
the earth on its axis every 24 hours produces the night-and-day cycle. To people on
earth, this turning of the planet makes it seem as though the sun, moon, planets, and stars
are orbiting the earth once a day.
9A – Numbers
When people care about what is being counted or measured, it is important for them to
say what the units are (three degrees Fahrenheit is different from three centimeters, three
miles from three miles per hour).
Measurements are always likely to give slightly different numbers, even if what is being
measured stays the same.
9B – Symbolic Relationship
Tables and graphs can show how values of one quantity are related to values of another.
9C – Shapes
Graphical display of numbers may make it possible to spot patterns that are not
otherwise obvious, such as comparative size and trends.
11B – Models
Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps,
and stories can be used to represent objects, events, and processes in the real world,
although such representations can never be exact in every detail.
11C – Constancy and Change
Things change in steady, repetitive, or irregular ways-or sometimes in more than one
way at the same time. Often the best way to tell which kinds of change are happening is
to make a table or graph of measurements.
12B – Computation and Estimation
Add, subtract, multiply, and divide whole numbers mentally, on paper, and with a
calculator.
Use fractions and decimals, translating when necessary between decimals and commonly
encountered fractions-halves, thirds, fourths, fifths, tenths, and hundredths (but not
sixths, sevenths, etc.).
Judge whether measurements and computations of quantities such as length, area,
volume, weight, or time are reasonable in a familiar context by comparing them to
typical values.
12D – Communication Skills
Use numerical data in describing and comparing objects and events.
Benchmarks (Grades 6 through 8)
2C – Mathematical Inquiry
When mathematicians use logical rules to work with representations of things, the results
may or may not be valid for the things themselves. Using mathematics to solve a problem
requires choosing what mathematics to use; probably making some simplifying
assumptions, estimates, or approximations; doing computations; and then checking to see
whether the answer makes sense. If an answer does not seem to make enough sense for its
intended purpose, then any of these steps might have been inappropriate.
4A – The Universe
Nine planets of very different size, composition, and surface features move around the
sun in nearly circular orbits. Some planets have a great variety of moons and even flat
rings of rock and ice particles orbiting around them. Some of these planets and moons
show evidence of geologic activity. The earth is orbited by one moon, many artificial
satellites, and debris.
4B – The Earth
We live on a relatively small planet, the third from the sun in the only system of planets
definitely known to exist (although other, similar systems may be discovered in the
universe).
9A – Numbers
Computations (as on calculators) can give more digits than make sense or are useful.
9B – Symbolic Relationship
Any mathematical model, graphic or algebraic, is limited in how well it can represent
how the world works. The usefulness of a mathematical model for predicting may be
limited by uncertainties in measurements, by neglect of some important influences, or by
requiring too much computation.
9C – Shapes
The scale chosen for a graph or drawing makes a big difference in how useful it is.
11B – Models
Different models can be used to represent the same thing. What kind of a model to use
and how complex it should be depends on its purpose. The usefulness of a model may be
limited if it is too simple or if it is needlessly complicated. Choosing a useful model is one
of the instances in which intuition and creativity come into play in science, mathematics,
and engineering.
12B – Computation and Estimation
Estimate distances and travel times from maps and the actual size of objects from scale
drawings.
Decide what degree of precision is adequate and round off the result of calculator
operations to enough significant figures to reasonably reflect those of the inputs.
12C – Manipulation and Observation
Use calculators to compare amounts proportionally.
12D – Communication Skills
Read simple tables and graphs produced by others and describe in words what they
show.
Benchmarks (Grades 9 through 12)
2C – Mathematical Inquiry
Much of the work of mathematicians involves a modeling cycle, which consists of three
steps: (1) using abstractions to represent things or ideas, (2) manipulating the
abstractions according to some logical rules, and (3) checking how well the results match
the original things or ideas. If the match is not considered good enough, a new round of
abstraction and manipulation may begin. The actual thinking need not go through these
processes in logical order but may shift from one to another in any order.
4A – The Universe
Mathematical models and computer simulations are used in studying evidence from many
sources in order to form a scientific account of the universe.
4B – The Earth
Life is adapted to conditions on the earth, including the force of gravity that enables the
planet to retain an adequate atmosphere, and an intensity of radiation from the sun that
allows water to cycle between liquid and vapor.
9B – Symbolic Relationship
Any mathematical model, graphic or algebraic, is limited in how well it can represent
how the world works. The usefulness of a mathematical model for predicting may be
limited by uncertainties in measurements, by neglect of some important influences, or by
requiring too much computation.
Tables, graphs, and symbols are alternative ways of representing data and relationships
that can be translated from one to another.
11B – Models
The basic idea of mathematical modeling is to find a mathematical relationship that
behaves in the same ways as the objects or processes under investigation. A
mathematical model may give insight about how something really works or may fit
observations very well without any intuitive meaning.
11C – Constancy and Change
Graphs and equations are useful (and often equivalent) ways for depicting and analyzing
patterns of change.
12B – Computation and Estimation
Use ratios and proportions, including constant rates, in appropriate problems.
National Standards (Grades 5-8)
Understandings about Scientific Inquiry
Different kinds of questions suggest different kinds of scientific investigations. Some
investigations involve observing and describing objects, organisms, or events; some
involve collecting specimens; some involve experiments; some involve seeking more
information; some involve discovery of new objects and phenomena; and some involve
making models.
Mathematics is important in all aspects of scientific inquiry.
Earth in the Solar System
The earth is the third planet from the sun in a system that includes the moon, the sun,
eight other planets and their moons, and smaller objects, such as asteroids and comets.
The sun, an average star, is the central and largest body in the solar system.
National Standards (Grades 9-12)
Understandings about Scientific Inquiry
Mathematics is essential in scientific inquiry. Mathematical tools and models guide and
improve the posing of questions, gathering data, constructing explanations and
communicating results.
Indiana Standards
Grade 5
Mathematics – Problem Solving
5.2.6 – Use estimation to decide whether answers are reasonable in addition,
subtraction, multiplication, and division problems.
5.7.1 – Analyze problems by identifying relationships, telling relevant from irrelevant
information, sequencing and prioritizing information, and observing patterns.
Science – Computation and Estimation
5.2.1 – Multiply and divide whole numbers mentally, on paper, and with a calculator.
Earth and the Processes That Shape It
5.3.7 – Describe that, like all planets and stars, Earth is approximately spherical in
shape.
Numbers
5.5.1 – Make precise and varied measurements and specify the appropriate units.
Systems
5.6.1 – Recognize and describe that systems contain objects as well as processes that
interact with each other.
Grade 6
Mathematics – Number Sense
6.1.6 – Use models to represent ratios.
Computation
6.2.5 – Solve problems involving addition, subtraction, multiplication, and division of
positive fractions and explain why a particular operation was used for a given situation.
6.2.6 – Interpret and use ratios to show the relative sizes of two quantities. Use the
notations: a/b, a to b, a:b.
6.2.9 – Use estimation to decide whether answers are reasonable in decimal problems.
Science – Communication Skills
6.2.6 – Read simple tables and graphs produced by others and describe in words what
they show.
The Universe
6.3.1 - Compare and contrast the size, composition, and surface features of the planets
that comprise the solar system, as well as the objects orbiting them. Explain that the
planets, except Pluto, move around the sun in nearly circular orbits.
6.3.3 – Explain that Earth is one of several planets that orbit the sun, and that the moon,
as well as many artificial satellites and debris, orbit around Earth.
Models and Scale
6.7.2 – Use models to illustrate processes that happen too slowly, too quickly, or on too
small a scale to observe directly, or are too vast to be changed deliberately, or are
potentially dangerous.
Grade 7
Mathematics – Measurement
7.5.2 – Use experimentation and modeling to visualize similarity problems. Solve
problems using similarity.
Problem Solving
7.7.1 – Analyze problems by identifying relationships, telling relevant from irrelevant
information, identifying missing information, sequencing and prioritizing information,
and observing patterns.
7.7.11 – Decide whether a solution is reasonable in the context of the original situation.
Science – Models and Scale
7.7.2 – Use different models to represent the same thing, noting that the kind of model
and its complexity should depend on its purpose.
Grade 8
Mathematics – Measurement
8.5.3 – Solve problems involving scale factors, area, and volume using ratio and
proportion.
Problem Solving
8.7.11 – Decide whether a solution is reasonable in the context of the original situation.
Science – Manipulation and Observation
8.2.3 – Use proportional reasoning to solve problems.
8.2.4 – Use technological devices, such as calculators and computers, to perform
calculations.
Earth and Space Science
The Universe
ES.1.7 – Describe the characteristics and motions of the various kinds of objects in our
solar system, including planets, satellites, comets, and asteroids. Explain that Kepler’s
laws determine the orbits of the planets.
Appendix B: Solar System Chart
Object
Sun
Diameter
Distance from Sun
1,390,000 km
Mercury
4,880 km
57,910,000 km
Venus
12,104 km
108,200,000 km
Earth
12,756 km
149,600,000 km
Mars
6,794 km
227,940,000 km
Jupiter
142,984 km
778,330,000 km
Saturn
120,526 km
1,429,400,000 km
Uranus
51,118 km
2,870,990,000 km
Neptune
49, 532 km
4,504,000,000 km
Pluto
2,274 km
5,913,520,000 km
Earth’s Moon
Diameter
3,475 km
Distance from Earth
384,400