Constructing a model of the solar system
Part 2: The relative distances of the planets from the Sun
Time: approximately 45-50 minutes
Materials:
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
Index cards (one for each group)
Metric rulers (one for each group)
Calculators (one for each group)
Marker pen (one for each group)
Cellophane tape
Measuring wheel or 100 m measuring tape
Solar system chart from Appendix B
Overview
This lesson continues from Part 1: The relative size of the planets. In this lesson,
students will “shrink” the distance from the Sun to Pluto down to about the size of a
football or soccer field. They will place their planet in the field at its relative distance
from the Sun. Students will need to use a new scale to determine a new diameter for their
planet and the distance of their planet from the Sun. In most cases this lesson will need to
be performed outdoors.
Purpose
Students will gain an appreciation for how far away the planets of the solar system
are from each other. 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
A good way to begin this lesson is to remind the class of the question that you
posed at the end of Part 1 – how can you construct a model of the solar system that can fit
into an area about the size of a football field? Ask for ideas from the your students. The
amount of coaching they will need to arrive at a workable scale will depend on the
particular class. You may need to remind them of the following:
 The area required must accommodate the greatest distance that you plan to
represent – the distance between Pluto and the Sun.
 Since a football field is around 100 meters, you want the distance from the Sun to
Pluto to be around 100 m. The average distance from the Sun to Pluto is
5,913,520,000 km. If we round this up to 6 billion km, then we can set our scale at
100 m = 6 billion kilometers.
 For flexibility, we can convert our scale to meters, centimeters or millimeters.
Dividing each side of our scale by 100 gives us 1 m = 60 million km. Dividing this
by 100 on each side gives 1 cm = 600,000 cm, and then dividing each side of this
equation by 10 gives 1 mm = 60,000 mm. Students will probably find 100 m = 6
billion km most helpful when calculating relative distance, and either 1 cm =
600,000 cm or 1 mm = 60,000 km most useful when calculating diameter.
You should inform the class that the solar system model that you will be
constructing is going to show all the planets lined up on the same side of the Sun. In
reality, it is extremely rare for all the planets to be on the same side of the Sun at the
same time. A more accurate model would have the planets randomly distributed in their
orbits around the Sun, but to do this would require twice as much area. Also, it would be
more difficult to see how far away different planets are from each other. So, although you
are showing the Sun and all 9 planets, the model you are constructing is actually showing
only half the area that the planets move through as they orbit the Sun.
The first step is to have the class determine the size of the object you will use to
represent the Sun. They can calculate this with the following equation:
1,400,000 km (diameter of the Sun)
600,000 km
=
? cm (diameter of object representing the Sun)
1 cm
The object used for the Sun will be a little under 2.5 cm, or roughly the size of a
small rubber “super” ball. Select an object of the appropriate size and hold it up in front
of the class. Remind the class of what they found out in Part 1 of this lesson. Ask the
students who modeled Mercury, Mars or Pluto what they learned about their planet’s size
compared to the Sun, and ask them how big they think their planet will be at this new
scale. Remind the class that they will want to lay this model out on the lawn or field
outside, and ask them how easy it will be to see their planet at this new size if they lay it
down directly on the dirt or grass. Since most planets might be very hard to see in this
model, tell the class that you want them to tape their planet onto an index card using clear
cellophane tape. They will need to write the name of their planet, it diameter and its
average distance from the Sun on the index card that they tape their planet to. For
convenience, its is also a good idea to have them write the distance their object will be
from the object representing the Sun in the model on the card. This will speed things up
when they lay out the model outside.
Tell the students that they will need to calculate the diameter of their planet and its
distance from the Sun using the new scale. Distribute index cards, solar system charts,
rulers and calculators. If needed, you can put the following 2 formulae on the board:
Diameter of planet:
? km (diameter of their planet)
60,000 km
=
? mm (diameter of object representing their planet)
1 mm
Distance from Sun:
? km (distance from the Sun)
60,000,000 km
=
? m (distance of object from model Sun)
1m
At these scales, Jupiter will be a little over 2 mm, Saturn about 2 mm, Uranus and
Neptune a little under 1 mm, and the rest of the planets the size of grains of ground
pepper or dust from soil or sand. Mercury, Mars and Pluto will actually be fractions of a
dust grains, so students modeling these planets may have to say the grain of pepper they
are using to represent their planet is actually 10x larger (or whatever number is
appropriate) than what their planet should be.
The students modeling Earth should also calculate the diameter of the Moon and
its distance from Earth (not its distance from the Sun). At this scale, the Moon would be
about 6.5 mm away from the Earth, so they should show both the Earth and the Moon,
appropriately shaped from each other, on their index card with both appropriately labeled.
The distances that the objects will be from the Sun in the model are:
Mercury
97 cm (about 1 M)
Venus
1.8 m
Earth
2.5 m
Mars
3.8 m
Jupiter
13 m
Saturn
23.8 m
Uranus
47.8 m
Neptune
75 m
Pluto
98.5 m
Once all the groups have (1) determined the diameter of their planet and its
distance from the Sun, (2) selected something to represent their planet, (3) taped it to
their index cards, and (4) written the required information on the card, (it is a good idea
the check their work to make sure they have the correct distances), take the class outside
and begin arranging the model. Start by placing the “Sun” on the ground. Tell the
students that as you move out from the Sun you want them to keep track of the distance
and let you know when to stop so they can mark the position of their planets. Begin
measuring the distance as you move outward. At 97 cm have someone from the Mercury
group lay down the Mercury card at the correct spot. At 1.8 m have the Venus card
placed on the ground, and continue on outward in a similar fashion. When Earth is placed
in position have someone from the group point out how close the Moon is to Earth at this
scale. Point out that the Moon is the only extraterrestrial object that a human has ever
landed on. As you continue out from Earth, remind the students that NASA has recently
been charged by the president to develop plans for sending a human to Mars. Ask them to
keep the distance from Earth to the Moon in mind as you mark off the distance to Mars.
This will help them gain an appreciation for how challenging a manned mission to Mars
would be. After you have placed Mars in position, remind the class that Mercury, Venus,
Earth and Mars are often referred to as the inner planets. Have them keep that in mind as
you mark off the five outer planets. You may also want to remind them that the asteroid
belt lies between the orbits of Mars and Jupiter. If you are using a tape measure that is
less than 100 meters long you can have a student mark the position of the end of the tape
measure as you shift it outward.
If the weather is windy you may need to have one member from each group stand
on a corner of their card to keep it from blowing away. If this is the case, you should have
another member from their group replace them at this time so that they can walk around
and see the positions of the other planets. Once all the planets have been marked off and
all the students have had an opportunity to walk around and see them, you can bring the
class back inside or, in the students and the weather are both cooperating, have a
discussion outside. A good way to start off is to ask the students what they noticed about
the arrangement of the planets after constructing the model. Hopefully they noticed how
far apart the outer planets are compared to the inner planets and how far apart the inner
planets are compared to the distance between the Earth and the Moon. You should point
out that right now all the planets are at their closest position to each other. Most of the
time they are at different positions in their orbits around the Sun and therefore much
farther away from each other, even though their distance from the Sun is about the same.
You might also point out that Pluto has the most eccentric orbit of the 9 planets. As it is
currently represented in the model it is at its average position. Sometimes its orbit takes it
even farther away than it is depicted, and sometimes it is closer, occasionally even
crossing over the orbit of Neptune so that Pluto briefly becomes the 8th planet out from
the Sun and Neptune the 9th.
If time permits, you can let the students see how large the Sun appears on different
planets. Start by having them stand near Earth and hold up the object representing the
Sun. At that distance it should look similar in size to the Sun in the sky. As they move in
closer it will look larger, but what is even more dramatic is to have them move out to see
how small it looks on the different outer planets.
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
Planets change their positions against the background of stars.
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.
6.3.2 - Observe and describe that planets change their position relative to the background of
stars.
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.
The Universe
8.3.1 – Explain that large numbers of chunks of rock orbit the sun and some of this rock interacts
with Earth.
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