Constructing a model of the solar system



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) = 70 cm (diameter of the exercise ball)

? km 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 = Diameter of object, in cm

20,000 km 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 Size of Model |Possible Object of Approximate 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 |Bead or large ball bearing |

| | | |Bead or large ball bearing (should be slightly larger |

|Earth |12,756 km |6.5 mm |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 |Tennis ball |

| | | |Large marble “shooter” or super ball |

|Uranus |51,118 km |2.6 cm | |

| | | |Same as Uranus, but should not be larger |

|Neptune |49, 532 km |2.5 cm | |

| | | | |

|Pluto |2,274 km |1 mm |Poppy seed or small grain of sand |

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 |Diameter |Distance from Sun |

| | | |

|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 |

| |Diameter |Distance from Earth |

|Earth’s Moon |3,475 km |384,400 |

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