Unit 8: Understanding Big Numbers

Understanding large numbers is one of the most troubling deficits in the mind of the average adult. Science, not to mention economics, uses large numbers with great regularity, but almost no one in the public eye makes an effort to help the average citizen really understand what they mean.

The late astronomer Carl Sagan popularized the phrase “Billions and billions!” in his science series Cosmos in the 1980’s. Although Dr. Sagan said this with great excitement and a very melodious voice – he really failed to help us understand what the difference is between million, billion, and trillion. If our children are to understand science – and national finances! – we must help them gain a more fundamental understanding of large and small numbers.

Activity 21. Million, Billion, Trillion: Big Numbers and Money

If you teach in the K-8 classroom, you may know that most of your students will not become scientists. Why then is it important to understand big numbers? Although most of us are not professional scientists, very large numbers touch our daily lives in many ways – money is the most common.

imageWhen we listen to legislators discuss state or national budgets on the news, or when we see a local bond measure to allocate millions – even billions of dollars to a project like a bridge, highway, or a railroad line, most people don’t understand how much money we are talking about. Worse yet, they have no fundamental grasp of large numbers to help them understand the ideas being debated on their behalf.

This activity seeks to correct that deficit by giving students a physical model for the concepts of thousand, million, billion, and trillion – without too much tedious counting!

Academic Standards

Science and Engineering Practices

  • Asking questions and defining problems.
  • Developing and using models.
  • Using mathematics.
  • Obtain, evaluate, and communicate information.

Crosscutting Concepts

  • Scale, proportion, and quantity.

Next Generation Science Standards

  • Space systems (K-5, 6-8, 9-12).
  • Structure and function (K-5, 6-8, 9-12).

For the Educator

Facts you need to know

  1. We normally think of counting, multiplying in powers of 10 – One’s place, Ten’s place, Hundred’s place, etc.
  2. Large numbers: Thousand, Million, Billion, Trillion, are powers of 1000 – each one of these numbers is one thousand times larger than its predecessor.
  3. It is this change, from powers of 10 for everyday numbers to powers of 1000 for large numbers that confuses people.

Teaching and Pedagogy

Misconceptions about large numbers are some of the most persistent and troublesome bits of misinformation. Not just children, but a large fraction of adults in our society lack a good understanding of what large numbers are, how much larger a billion is than a million, and much more. Almost no one has a good visual concept of what a million of anything looks like. You can imagine a dozen doughnuts looks like and how large a box you need to put them in – but what does a million doughnuts look like?

When we reach the domain of millions, billions, trillions, and beyond, the names for our numbers now reflect powers of 1000. Psychologists and anthropologists tell us that humans have an ability to easily mentally conceptualize groups of up to five or so, and with a bit of practice (and the help of our fingers!) we can get pretty good at conceptualizing groups of ten. In this way, visualizing 100 as ten groups of ten is well within almost anyone’s grasp. In comparison to this, groups of 1000 are beyond anyone’s cognitive grasp. Yes, we handle numbers like these mathematically and numerically; but conceptually, we get lost pretty quickly.

Want proof? Try this mental experiment: Think of ten marbles. Got the picture mentally? Good! Now think of one thousand marbles. How big is it? How much does it weigh? How large a container will you need to hold them all? If you needed 1000 marbles and you saw a group of 750 marbles, could you tell by sight that you don’t have enough? I suppose if you had a job working with boxes of 1000 marbles all day long you might be able to tell, but generally, the answer to all these questions is cognitively beyond our grasp. As human beings, we just don’t mentally image or handle large numbers very well without a great deal of practice.

Computers add to the confusion for most students (and adults!) A computer with 200 megabytes of memory (200 million bytes) looks just like the model with 3 gigabytes of memory (3 billion bytes). A USB memory stick with 32 megabytes looks just like a USB stick with 32 gigabytes even though the capacity is one thousand time greater! Newspapers and broadcasters reading the news on television are no better; announcers will jump from one story about a fire causing three million dollars damage to a story about a two trillion dollar spending bill in Congress with no attempt to explain the difference between them. Activities like this one, and a through discussion of the ideas they contain, are essential for your students.

As adults, we are expected to work with computers which routinely use terms like mega (million), giga (billion), and terra (trillion). As voters, we are expected to select candidates for office by listening to their economic and taxation plans involving millions, billions, and yes, trillions of dollars. How can we prepare the children of today to do any of these things successfully if they do not have a fundamental understanding of these concepts? This activity will finally put the ideas of million, billion, and trillion on a solid physical, and visual, foundation.

Student Outcomes

What will the student discover?
  1. The fact that large numbers increase in powers of 1000 instead of the usual power of 10 makes them harder to visualize easily.
  2. Learning to visualize and comprehend the powers of 1000 in thousand, million, billion, trillion takes practice! We have to try imagining large numbers of various things to become familiar with these scales.
What will your students learn about science?
  1. These large numbers are of particular interest in astronomy, where distances and sizes vary so greatly. Our use of powers of 1000 makes it easier to discuss, and understand large sizes and distances.
  2. More advanced classes in science and mathematics (high school and college) use something called scientific notation to help handle these very large and very small numbers. Scientific notation is beyond the scope of this book, but these methods of writing and calculating with very large and small numbers helps us handle everything from the distance between stars to the tremendously small size of the atom.

Conducting the Activity

Materials

  1. A trillion dollars. No? Okay, how about a package of index cards or several manila file folders that we can cut up and color to represent money?
  2. A couple LEGO® figures or similar 2-inch toy action figure.
  3. Two, 3-foot square pieces of cardboard.
  4. Paints and markers (green, of course!), highlighters work well for this.
  5. Glue sticks and hot glue.

Building the Big Numbers Model

  1. Cut up index cards into ¼-inch wide strips. Cut each strip into ½-inch pieces. You are going to need a lot of these, so if each student does one card, you should have enough.
  2. Label five pieces with “$100” and glue them together so that they are fanned out like a hand of cards. When dry, color this stack over with green highlighter. Glue this fanned stack of cash into the hand of one of your small action figures to represent $10,000 – be sure to paint a smile on the little fellow’s face! Remind your students that it takes one hundred $100 bills to make $10,000 dollars.
  3. Now use glue sticks to glue stacks of these cut pieces of index card together – four pieces per stack. Once they are dry, label each stack “$10,000” in pen or black marker and color it over with green highlighter or pale green marker. Each stack now represents a pile of 100, one hundred dollar bills — $10,000 cash each!
  4. Make 100 of these piles. Yeah, each student in your class of 30 is going to have to produce 3-4 of these for you to have enough! Once you have one hundred of these piles – each representing $10,000 – then you have ‘printed’ one million dollars… and you now know how those folks at the U.S. Mint feel! Making money is a lot of work!
  5. Make a little cafeteria tray out of a piece of cardboard or plastic from a milk container. Glue this into the second action figure’s hands and stack the $1,000,000 dollars on it. You’ll have to stack neatly, it makes quite a tidy pile of cash, doesn’t it? This is a pretty good model for the physical size of one million dollars cash in $100 bills! (BIG smile, little guy!)

Exploring the Big Numbers Model

  1. Now it’s time to go big… it’s time to make a billion dollars! No, we aren’t going to need a lot more index cards, a single manila folder and some white glue and markers will do just fine.  One billion dollars is a stack of $100 bills that is one thousand times larger than our million dollar stack.  This is a neatly stacked cube of $100 bills that is eight feet long on each side.  Assuming your 2-inch tall action figure is 6-feet tall, let’s plan on a pile of play money that is a 2½-inch cube.  Take your manila folder and cut out 2.5 inch cube as shown in the diagram below, glue it together and decorate it.

To give you some idea, our billion dollar pile contains ten million $100 bills.  This is like having a solid cube of dense wood 8-feet on a side – it would weigh ten tonnes (10,000 kg), and only the largest industrial forklifts could move it.

  1. Okay, big is a relative thing. What about one trillion dollars?  Well, let’s consider the standard school soccer field… yes, really.  If we took an American school soccer field of 100 yards x 60 yards, we get an area of 6,000 square yards.  On the other hand, if we have one thousand cubes of one billion dollars, that make 6,250 yards.  That means our stack of ten billion $100 bills would take up an entire soccer field, plus about 8 feet extra on either end to have room for the goals, and piled it eight feet deep in neatly stacked $100 bills… Yeah, a trillion dollars is a LOT of money.
  2. To keep in scale, we will need an area 10’4” x 4’2” and 2.5” tall. This may be a little much for your class to tackle, but if you want to build it in sections and put them next to each other – it makes a powerful display on the gymnasium floor… especially if you make little soccer goals and use a little gumball for a soccer ball and have several action figures running around on it!
  3. If modeling something this big is a little much, consider taking a 3-ft square of cardboard and measuring off and building a cube as shown below. Make it 30-inches long, 18-inches wide, and 1½-inches high.  At this scale, your figure is just about ¼-inch tall.  I’ve never seen an action figure or toy this small, I suppose you would just have to draw one on paper and glue it to your soccer field of money (don’t forget that big smile!)
  4. Oh, and if you want to model the national debt on the scale of our action figure? That’s a stack of billion dollar blocks, 10’4” long, 4’2” wide, and 4’ tall.  That’s Nineteen Trillion Dollars… and it’s collecting interest!
Discussion Questions
  1. You have won the lottery! They offer you your choice: One billion dollars today… or one million dollars a day for a year!  Which should you choose and why?
    • Answer: A billion is 1000x larger than a million. The year is only 365 days long – you would end up with only 1/3 of the money if you took the million a day!
  2. A new highway building project will cost 1.3 billion dollars. How much money does the .3 represent?
    • Answer: 300 million dollars!

Supplemental Materials

Going Deeper

Talking about money is fun, but students often don’t have a good grasp of money, especially when they are younger.  The million-billion-trillion problem can be fun in lots of ways, let’s make it about something most every student knows and loves – doughnuts.

You get 12 doughnuts in a 9x9x4 inch box.  Now ask your students to figure out the size and space for a larger amount of doughnuts.

  1. How many cubic inches in a doughnut box? (Length x width x height)

a. 324 in3

2. How many boxes to hold 1000 doughnuts? How many cubic inches is this?

a. 83.33 boxes, 27,000 in3 total

b. This is a 30-inch cube of doughnuts!

3. If a 30-inch cube holds 1000 doughnuts – how big will one million doughnuts be?

a. One million doughnuts is 1000 times bigger – our cube must be 10x bigger on each side: 300 inches or 25 feet wide, long, and tall!

b. This is three 25×25 foot classrooms with 8 ½ foot ceilings – completely full floor to ceiling with doughnuts!

4. How big are one billion doughnuts?

a. One thousand times bigger! Three thousand classrooms full of doughnuts!

5. How big are one trillion doughnuts?

a. One thousand times bigger! Three million classrooms full of doughnuts!

b. Three million classrooms with 25 students each would be 75 million students. This is about the number of students in the United States, Mexico, and Canada combined!

Being an Astronomer

What does million, billion, and trillion mean to an astronomer?  Let’s consider the size and scale of the solar system to get an idea.  One of the most important measurements that astronomers make is distance – how far away in space are planets, moons, and stars from one another?

One thousand kilometers.  This is a good scale to measure moons circling planets.  Few moons are larger than 1000 kilometers wide; most are between 100 and 1000 kilometers in diameter.  Our own Moon is about 3,500 kilometers wide and is one of the largest satellites in our solar system!

One million kilometers.  This is a good scale to measure the orbits of moons circling around planets.  If you look at all the moons in our solar system (there are hundreds of them!), almost all are within 1,000,000 km of the planet they orbit.  Our own Moon circles the Earth at an average distance of about 385,000 km – about one third of a million kilometers away!

One billion kilometers.  This is a good scale to measure the distance from a star out to its planets.  Our own solar system’s outermost major planets are about three billion kilometers from the Sun.  The Sun’s influence extends only about 20 billion kilometers – farther away than this, the Sun’s gravity and magnetic field have no influence at all.  Astronomers call this interstellar space.

Only the two Voyager spacecraft have made it this far away from Earth.  They were launched 40 years ago in 1977, both probes are now about 20 billion km from Earth and moving away from us at about 60,000 kph.  At this rate, they will reach the one trillion kilometer mark in their journey in about two thousand years!

One trillion kilometers.  This is a good scale to measure the distances between stars.  It takes a beam of light one year to travel six trillion kilometers – this is called a light year.  The nearest star to us is just over four light years away, or about 25 trillion kilometers away!

 Following Up

Look for examples in the news that use the terms million, billion, or trillion.  It will help if you look for examples that talk about money such as national or state budgets.  Science websites that have space news like www.space.com have many stories that deal with large numbers.

Activity 22: The Thousand-Meter Solar System

My first exposure to models of the solar system was a poster in my third grade classroom which showed a portion of the Sun, and then artistic representations of all the planets. Mercury, Venus, Earth and Mars were all the same size, while Jupiter and Saturn were almost twice as large as the Earth, Uranus and Neptune were a bit smaller than Saturn. All the planets out to Pluto were shown in a neat line with a little paragraph beneath each one telling us something about it. You may remember something similar from your school days; you may even have such a poster in your room now!

Imagine my shock when I learned that almost everything this poster had shown me was wrong! Some of the material was just inaccurate out of ignorance, other things were so badly off that it would be charitable to classify them as anything other than outright lies! We learned in our last activity that big numbers can be a bit deceptive, but if I tell you that Earth is 100 million miles from the Sun, Saturn is a billion miles away, and Pluto is four billion miles out, after doing Activity #21, you probably have a better idea of what that means.

Academic Standards

Science and Engineering Practices

  • Developing and using models.
  • Analyzing and interpreting data.
  • Using mathematics.
  • Obtain, evaluate, and communicate information.

Crosscutting Concepts

  • Scale, proportion, and quantity.
  • Systems and system models.

Next Generation Science Standards

  • Space systems (K-5, 6-8, 9-12).
  • Gravitation and orbits (6-8, 9-12).

For the Educator

Facts you need to know

Because of the problem with big numbers (see Activity #21) virtually all models and posters of the solar system you can find for your classroom are deceptive, even blatantly false.

We can make an accurate model, but it takes outdoor space and effort! With the Sun the size of a basketball, our solar system is 2 kilometers wide (almost a mile and a half!)

We will save space by lining up all of the planets in a row (this happens only once every few centuries.) We will also not try to show the planets’ circular orbits – just their distances from the Sun.

Teaching and Pedagogy

Size and scale are solid bits of scientific data, and our children deserve to know – and understand – the truth about these ideas. We will make a real scale-model of the solar system you can use in your classroom… well, on the streets around your school, anyway! Our model will do the things that poster failed to do – it will show the various planets and Sun in their respective sizes in scale to one another, and it will place the planets at the correct distances away from the Sun on the same scale as the size of the planets.

For instance, the Sun is about 100 times wider than the Earth is. The Earth is 100 times farther away than the Sun is wide. Our model will remain true to both of these facts. One scale mile on our model is always the same whether we are measuring the size of a planet, or its distance from the Sun. You and your students will quickly realize that the solar system is a very big place, and even the largest planets are relatively tiny specks lost in the vast darkness of deep space! So get your walking shoes on and let’s get started!

One last thing, none of this “Pluto isn’t a real planet” stuff in your classroom please! When we say things like: “Pluto isn’t a planet, it’s a dwarf planet!” this is grammatically akin to saying things like “Short people aren’t people,” or “Billy isn’t a real child, he’s a naughty child!” The farther we take this the sillier (and more offensive!) it becomes! Truth is, we classify planets many ways; by size, by composition, by the kind of atmosphere they have, or what their surfaces are made of. We even classify planets by where they are located, in our solar system, orbiting around other stars, or even drifting through space with no star to orbit at all!

As long as a body is large enough that its own gravity has pulled it into a spherical shape (and it’s not a star!), it is a planet. If it is shaped like a potato, it’s an asteroid. While it is true that we haven’t seen some of our minor planets up close enough yet to tell if they are actually spherical or not, we’re going to give them the benefit of the doubt here. It is also true that while we may demote some of these to asteroid status someday, we will undoubtedly discover more planetary bodies in our solar system in the future.

Pluto was discovered in 1930 by my late friend Clyde Tombaugh, a great American scientist and astronomer. In 1978, James Christy discovered Pluto’s companion Charon, and in 2005, scientists using the Hubble Space Telescope discovered that Pluto-Charon is actually a double planet – a binary world where two planets of almost equal size are locked face-to-face in an orbit 15 times closer together than the Earth and Moon. The New Horizons spacecraft from NASA confirmed Pluto-Charon’s status as a binary planet with 5 little moons in orbit around it. Pluto-Charon was the first dwarf planet discovered in our solar system – we now know of many more, and our solar system model has room for them all!

Student Outcomes

What will the student discover?
  1. The solar system is very vast. As large as planets are, they are tiny specks compared to the great distances between the worlds.
  2. Earth is not a very large world. More than a million Earths would fit inside the Sun, even Jupiter is hundreds of times more massive than our planet and more than ten times the size of our world.
  3. There is a great difference between the compact inner solar system (Mercury, Venus, Earth, and Mars) compared to the widely spaced outer solar system (Jupiter, Saturn, Uranus, and Neptune, plus almost a dozen known dwarf planets.)
What will your students learn about science?
  1. Making accurate scientific models take time and effort. All too often our desire to make things easily or simple to understand requires too many compromises and results in an inaccurate model.
  2. Accurate models of things that are very large or small requires a knowledge and understanding of how very big (and very small!) numbers work. Without a solid grasp of big numbers, it is impossible to comprehend a model of a solar system.

Materials

1. A package of 25 golf tees

2. A package of craft beads from very small (2mm) to medium size (5mm)

3. A package of glass marbles (mix of large and small)

4. One standard (40mm) ping-pong ball

5. One tube of silicone glue

Note: Silicone glue cures slowly – give it a full 24 hours to dry before you or your students do anything with the models!

6. An emery board or small piece of fine sand paper (See activity #16)

7. One basketball, volleyball, or dodge ball (Any 12-inch ball will do. Larger is better, but exact size and color isn’t crucial here as long as it is 10-14 inches in size.)

8. White glue, construction paper, markers

9. Some modeling clay or salt dough to use as stands for a few of our models

10. Pedometer (many free smartphone apps work well)

11. Binoculars or small telescope (optional)

12. Parent volunteer helpers (the more the merrier!)

Building the Solar System Model

  1. Let’s begin by making a construction paper sign for each of our planets. Once you create the sign, your class can look up some things about the planet and write them on the sign, too. You will need signs for all of these 18 of these listed below! (Yes, Virginia; our solar system has 18 planets… and counting!) Let’s include a sign for the Sun as well, just to be complete. Make sure you have signs for all of these:

Sun, Mercury, Venus, Earth, Mars, Vesta, Ceres, Jupiter, Saturn, Chiron, Pholus, Uranus, Neptune, Pluto-Charon, Quaoar, Haumea, Make-make, Eris, Sedna, and Planet X.

2. Now it’s time to make our planets. For the largest planet, Jupiter, we will use a ping-pong ball. Take a look at some photos of Jupiter with its colorful cloud bands and beautiful red spot. Use markers or paints to decorate your ping-pong ball to look like Jupiter. Once you’ve decorated it, use some silicone glue to attach the ping-pong ball to a golf tee, then stick the tee in a 1-inch ball of clay that you have flattened a bit to make a good stand. Allow the Jupiter model to dry overnight.

Note: White glue and super glue do not work well on ping-pong balls. From many experiments, I have found that silicone glue works best!

image3. Saturn, Uranus, and Neptune are made from marbles, and placed on golf-tee stands exactly the same way as we did in the last step. Uranus should be a green marble, Neptune is blue, and use a larger ‘shooter’ marble for Saturn (A yellow marble is best if you have one!) Use your emery board to roughen the surface of the marble before you glue it to the golf tee with silicone glue and stand it in its ball of clay to dry.

4. For Saturn, you also need rings! I made mine out of an index card, using a compass to draw a first circle the same size as the marble, and a second circle three times as wide (it will look a bit like a target!) Cut the rings out with scissors and decorate them if you wish. Use a toothpick to put a ring of silicone glue around your marble, then slip the rings on and let them dry. In real life, the rings of Saturn are tipped a bit, so you can glue them at a jaunty angle if you like!

5. Now it is time to make our larger terrestrial planets, Earth and Venus. Use a 5mm bead for these – blue for the Earth and yellow for Venus. I simply turn the golf tee upside down and glue the beads to the pointy tip. If you put a blob of silicone glue on an index card, then dip the tip of the golf tee in the glue, the beads will stick perfectly.

6. For all the smaller planets, we will use the tiny, 2mm beads. These are actually just about right for Mars and Mercury, but quite a bit too big for the dwarf planets like Pluto-Charon, Ceres, and the rest. The correct size for these planets in our model would be a single grain of salt – but this is far too small to work with and cannot be seen easily! Use a red bead for Mars and dark blue or grey beads for everything else.

Exploring the Solar System Model

  1. The pieces of our model are complete, but the model hasn’t yet been assembled properly! To do this, we will need to go outside – and we will need some room to walk! Parent volunteers are also essential at this point in the exercise.
  2. If you want to show the inner solar system – out as far as Jupiter, you can do that on an athletic field, a soccer or football field works well. Begin with the Sun in one corner of the soccer field, then activate the pedometer app on your smart phone and begin walking diagonally across the field. This model is calibrated in meters, but if your app will show yards, that works just as well for our purposes. Don’t have a pedometer? Make big steps and just count them off!
  3. Mercury is placed 10 m (or 10 large steps!) away from the Sun. Once you get this far, have one student stand at this point and hold the model up, while another student holds the sign that names and tells about planet Mercury.
  4. We’re going to keep walking to get to the positions of the other planets. We placed Mercury 10 meters (or steps) away from the Sun – now keep walking and counting your steps! Venus is 19 m away – about twice as far from the Sun as Mercury. Have two more students stand here with the model and its sign.
  5. Earth is 26 m out from the Sun.
  6. Keep walking! Mars is 39 m from the Sun. If you are walking diagonally across a football or soccer field, you should now be about 1/3 of the way across. These four inner planets are referred to as the inner solar system.
  7. Vesta, our first dwarf planet, is 65 m from the Sun.
  8. Ceres, another dwarf, lies 72 m from the Sun.
  9. Jupiter is 134 m away in our model. If you are on a football field, you are now all the way across the field diagonally from where you started! From here, you can see the entire inner solar system tucked in close to our Sun. The signs will help you tell the planets apart – but you are probably too far to read them!
  10. If you want to use your telescope or binocular, this is the good place to do this. Place your telescope near the Earth and look at your model of Jupiter through the glass – how much detail can you see? Try looking at the minor planets Ceres and Vesta, can you even see them? Certainly there is no detail to be seen! Ask your students to imagine if they were looking at a salt grain at that distance! This is why astronomers use enormous telescopes – to see tiny and faint objects far out in the vastness of space.
  11. If you wish to make a more complete model of the solar system than this, you will probably need to walk down a local street. Start as you did before, but this time, place a parent volunteer with each pair of students as they hold up the planet and its sign. Alternatively, you can ask parents to hold the planet models and signs and have all the children walk with you. Having all the students walk with you is the better option if you can do it, because it gives every student a feeling for the real distances in our model – and they get some good exercise, too! Let’s pick up where we left off…
  12. The next planet is Saturn, this goes 247 meters away from your Sun, almost three football fields away.
  13. Chiron is 465 meters out, and dwarfed by the next major planet, Uranus, at 497 m. Uranus is half a kilometer away from our model Sun, about a third of a mile out.
  14. Keep walking! Pholus is 774 meters out and great Neptune is 777 meters away. You have now walked half a mile from your Sun model. By this point, your students should have a very solid grasp of the immense size of the solar system compared to the relatively tiny planets that orbit the Sun.
  15. The next four planets are out beyond the 1-km mark: Pluto-Charon at 1014 m, Quaoar at 1109 m, Haumea at 1114 meters, and Make-make at 1182 meters. Look how far away and tiny the Sun looks from out here! Pluto-Charon and the others are sometimes called Kuiper Belt Objects after Dutch-American astronomer Gerard Kuiper who predicted their existence half a century before most of these outer bodies were ever seen.
  16. If you are willing to make the effort, Eris is out at 1756 meters, and tiny Sedna is at 2220 meters, more than a mile and a half away from our Sun. If you walked this far with students, it probably took you 45 minutes or more to get here!
  17. The new ‘Planet X’ some scientists are talking about has been detected, but little is known about it. Scientists think that it is about the size of Uranus (10x more massive than Earth and about 4x as wide.) Even so, on our model, this outer giant would be 12,600 meters away from our Sun model – that’s almost 8 miles away! Only dedicated Scouts and hikers would want to make this journey!
Discussion Questions
  1. Why do we need a telescope to study planets if they are in our own solar system?
    • Answer: The planets are tiny compared to the distances that separate them. Without a telescope to magnify the images, planets appear as bright stars, not disks like our Moon.
  2. What things are not included in our solar system model?
    • Answer: Like all scientific models, we’ve left out lots of things!

i. The Asteroid Belt (and all the asteroids!)

ii. The comets

iii. The moons around the planets (Jupiter & Saturn have over 60 each!)

iv. Planetary surface features!

v. Dozens of spacecraft!

vi. All the undiscovered stuff! (We should never be so arrogant as to think we’ve found everything!)

Supplemental Materials

Going Deeper

Like so many good science activities, this one is about discovery! If you tackle this activity with the help of some parents, you are sure to see some smiles on parent’s faces when you hear: “Are we there yet?” The scope of the solar system is truly vast. We are taught to think of planets as enormous objects, but we rarely teach children about the tremendous empty spaces between them. Models, diagrams, posters, illustrations in books, even video clips from reputable television programs distort the vastness of space rather terribly.

Once you get all the planets in place, it is very worthwhile to have a telescope and a pair of binoculars with you. Set up where the Earth is and ask children to look at the planets with binoculars. How many can they see? (Probably out to Saturn, maybe Neptune, but certainly no further.) Try again with the telescope, can they see any surface features on the planets or the rings of Saturn? This is quite challenging! Ask the students how large a telescope they think they would need to see the surface of Mars, of Jupiter, or of Pluto!

Being an Astronomer

If you have a telescope, or you can make it to a meeting of a local astronomy club, try your hand at observing some of the planets. Jupiter and Saturn make delightful targets – you can see colored cloud bands, a number of moons, and the rings of Saturn will amaze you! Think about how far away these planets are! Jupiter is half a billion miles away and Saturn is over a billion miles out – its ring system is about the same size and the orbit of our Moon!

Don’t have a telescope? Check on Google or your local yellow pages for local astronomy clubs. Every club member I’ve ever met has been thrilled to offer interested people a chance to look through the eyepiece. Many clubs have outreach programs and would be willing to have their members bring their equipment to your school some night and provide a star party for your students, parents, and faculty. I’ve hosted many similar events myself and often had hundreds of excited children and parents show up for a few hours of star gazing out on the athletic field behind the local school.

Encourage your students to make a drawing of what they see in the telescope – you will be amazed at what your young astronomers can do!

Being a Scientist

Choose a planet that is your favorite and imagine what it would be like to play your favorite sport there! You cannot choose Jupiter, Saturn, Uranus, or Neptune – these are gas giants and have no solid surface you can land and walk around on! The giant moons of these planets are small worlds of their very own, you can choose one of them if you like!

What is your favorite planet like? Is it colder or hotter than Earth? Is there an atmosphere there? Would you need a space suit, or perhaps just an oxygen mask!? Differences in temperature, gravity, and atmosphere change everything. If the gravity is lower than Earth, you will be able to jump and throw much farther than you can on Earth. In the thin atmosphere of Mars, throwing a curve ball would be essentially impossible, but the wind would never blow a home run ball back into the park either!

If you can kick a soccer ball farther, would you need a larger field? More players? If you can jump three times higher on Mars, would you have to change Martian basketball hoops and make them higher? Think how much air, gravity, and temperature affect the games you play, then write a story or draw a picture showing how your favorite game would be different if it was played on another planet!

You might not think of this imaginative exercise as ‘real science’, but in fact it is! Science has a powerful imagination component; we rarely stumble on an important discovery by chance. Instead, many scientist imagine how the Universe might work and build creative models to show their ideas to others. Careful experiments show which models are valid, and which must be discarded.

Following Up

One of the best things about this activity is the wonder that it generates in the students who participate in it. Although everyone is impressed by the size of the solar system and the relative insignificance of the planets that orbit in the vast deep of space, take a minute to remind your students that each of these planets circles the Sun at these distances. This would be a great place to take out your Earth-Moon model, stretch it out in the playground, and then have someone chalk in the circle of the Moon’s orbit again. If you go out to the orbit of Sedna (2220 meters out in our model), you would need a square field 2.5 miles on a side (that’s 4000 acres!) just to chalk out the circle of Sedna’s orbit.

Like the Million, Billion, Trillion activity, this solar system model is all about beginning to appreciate the real scale of large numbers. Remind everyone that this model is true to scale – the planets and Sun are modeled on the same scale as the size of the orbits. Although the planets are very large compared to a human being or a small spacecraft, one can easily see that navigating a spacecraft across such vast distances and trying to arrive at such small targets is very difficult. In fact, the reason that we haven’t stopped at any planet farther out than Saturn is that by the time we get a space vehicle going fast enough to get to these distant places in any reasonable amount of time, it is difficult to slow down enough to enter safely into orbit.

Space craft travelling to Mars, Jupiter, or Saturn often fly through the planet’s atmosphere like a meteor or shooting star and allow the air friction slow them down. The trip to Mars takes about six months, flying to Jupiter takes at least a year. NASA went ‘economy class to Saturn – it took about 7 years for the Cassini space probe to get there. But the real long-distance champ is New Horizons, which was launched in 2005, and arrived at Pluto-Charon in 2015 – a ten year trip!

New Horizons is the fastest spacecraft ever built, flying at over 85,000 mph, far too fast to stop at essentially airless Pluto-Charon! This spacecraft performed a flyby, whizzing through the Pluto-Charon system in just a few days, taking as many photos and measurements as it could while the spacecraft went zooming past the tiny binary planet and its moons. We will still be getting new photos and data from New Horizons for at least another year, and the data sent back will fascinate scientists for many decades to come.

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Astronomy for Educators by Daniel E. Barth, PhD is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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