Tag Archives: Mathematics

Walking to Pluto: Step 3

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Step 3: Making the Journey

If you skipped Part 1, then you need to know know that in this activity, you will build a scale model of the Solar System as far as Pluto. You will use familiar objects and easy, approximate measurements—mostly simply pacing off distances. This is not a project about being extremely precise; the goal is to develop a strong perception of just how big the solar system is and how small the planets are within that system.

For preparation, you need only to assemble the collection of properly-sized objects listed in the requirements table (See Step 2) and print out the “cheat sheet” you’ll carry on the Walk. A glance at a map of your local area will help you decide which way to take your expedition and to identify some landmarks to stand in for more-distant things like the far edge of the Oort Cloud.  To build your own interest and enjoy some discoveries of your own, check out some of the links I’ll include in the references section (Step 4).

You can feel free to substitute alternate model planets, using the scaled sizes as a guide; however, most of the items called for can be found in an average family home, borrowed from classroom parents, or purchased at a very modest outlay. While modern kids may not find the contents of kitchen spice jars terribly fascinating, using an allspice or peppercorn seed as your “Earth” model will give them a lifelong reference point–they’ll be smelling pumpkin pie or watching a chef grind pepper and that spark of memory will remind them of this project.

Because the scaled planets range from the size of a pin point to the size of a jacks ball, it also makes sense to attach each object to something larger, such as an inverted cup or a 4 by 6 index card. If you have access to sports equipment, the bright-colored cones often used for laying out a temporary playing field are helpful. You can position the planet-holder and also tape a “Please Leave Our Experiment Here” sign to the top of the cone. And the bright colors and signs help the explorers to look back and spot the distant planets. Again, be creative! There is no need to run out and buy sports equipment—any handy rock or a brick will do to keep your objects and notes in place.

Here's my Walk kit, ready to go.

Here’s my Walk kit, ready to go.

When reviewing the Cheat Sheet, you’ll see that this model describes our solar system as far as the outer edge of the Oort Cloud. However, to go all the way to the Oort Cloud in this model is a journey of 75 miles (100 km), so don’t expect to travel that far. Instead, as part of your preparation, identify a few local landmarks 1 or 2 miles from your start point and also pick some regional and further-off destinations to match the scaled distances for such key locales as the Oort Cloud, the heliopause, the estimated positions of the Pioneer and Voyager spacecraft, the far edge of the Kuiper belt, and our further neighbors in the Universe. If you’re too short on time, the Cheat Sheet includes some general destinations, but your own localized ones will be much more meaningful to the group. If your group won’t have time to walk all the way to Pluto, find out where Pluto would be in that locale and point ahead to that location before you do turn back.

Once in the classroom, before launching your exploratory mission, start with a quick review of the concept of scale. Regardless of your target age group, toys which are also scale models of cars or airplanes or trains are helpful examples. Quickly walk through a sample of numerical proportions to give a sense of how it goes when you are creating your own scale model: for instance, sketch on the board or a sheet of poster paper a rough scale drawing of the classroom room at 1 inch per foot (5 cm per m). Rather than slowing down the project with extra work, prepare for this session by making your own rough measurements of the classroom dimensions in advance—simply pace off the length and width and note any additional features to the room. Remember, the idea is to illustrate your point, not to create an architectural drawing.

Moving on to the Solar System, start with the Sun…an 8-inch-diameter playground ball or an ordinary soccer ball fits our scale. Ask if anyone can guess what size the Earth should be to go with this “Sun”. The guesses are very likely to be way off, because most “models” used in classrooms and the pictures in the textbooks are not at all to scale. In those, Earth is shown as a recognizable ball appearing as much as a tenth the size of the Sun.

Once you have a few guesses on record, share the key data. Write on the board or a flip chart as you go, to keep the presentation lively. (Nothing kills attention like a PowerPoint!) The Sun’s diameter is about 800,000 miles (1400 thousand km), and we’re using an 8-inch (18 cm) ball, so each inch stands for 100,000 miles (or, a cm stands for 75,000 km). The Earth’s diameter is only 8,000 miles (12,700 km). So how big will the model Earth be? It turns out we need something less than 1/10th of an inch across, only 0.08 inches (0.17 cm). So now you can pass around your “Earth”…a peppercorn will work, so will an allspice seed. (And, yes, you can get away with crumbling up a bit of paper and claiming it’s a spitwad you found.) If you have a spice-jar worth of seeds, everyone can have their own Earth to keep. Let the students take a moment to actually compare the sizes of Earth and Sun. It’s a dramatic difference, nothing like what their textbooks show.

Now it’s time to figure out where the Earth and Sun should be to fit in with this scale. Start by inviting students to guess…they will likely assume you can fit the Earth-Sun model easily inside the room. So now, add the distance data they need and we can “step” through the necessary calculation:

  • The Earth is roughly 93 million miles (150 million km) from the sun.
  • In our scale model, that’s 930 inches (2000 cm)
  • or 78 feet (20 m),
  • or 39 steps of about 2 feet (40 steps of 0.5 m)

Notes:

  • In our model we’re using a pace distance reasonably close to the average woman’s step length and not too far off the step length of a child who is supposed to be walking but can’t resist running. If your group is adult men or tall women, you can use the worksheet to adjust the number of steps accordingly.
  • Our scale in SI (Système international, or metric) is slightly different than in English units, so that those using the SI version can also use simple round figures.

At this point, try to keep a straight face while pretending to start building the model inside the classroom. Dramatically place the “Sun” at one end of the room and try to pace off 39 or 40 steps. Unless you’re doing this activity in a large lecture hall or a cafeteria, you will quickly run out of space (pun intended). By now, it should be clear to the students that this is to be an outdoor activity.

If the group is not too insanely anxious to get outdoors, you can take one more minute to assemble a part of the model which will fit in the room—the Earth-Moon system. Our Moon is nearly ¼ the diameter of Earth, so it’s actually an important body in its own right. And it’s close by. In our scale model, the Moon—which can be represented by a single nonpareil or cake “décor” candy—is 2 3/8” or 5 cm from Earth—so Earth & Moon can be stuck to a card or piece of paper. Keep in mind that if your group is too anxious to get outside, you can choose to save this step for your arrival at the Earth’s position in the model outside.

Earth and Moon are stuck together

Earth and Moon are stuck together

Set the very few ground rules for the mission plan. The model is built by counting steps—the students will be the ones to do the counting and you (the project leader) will expect them to try hard and in return will not be too fussy about precision or how the measurement accuracy may be affected when leadership shifts from short to tall students.   The group will remain cohesive, so no-one misses out on any important discoveries—and no one will charge ahead lest they get “lost in space”. And everyone should understand the time constraints.

When the group is large, I’ve had success assigning small subgroups to accompany one adult leader as the “vanguard” to each planet, leaving the rest behind until they have “landed,” then allowing the followers to run full-speed to catch up. If you do this, it’s important to ensure everyone has a turn to be in the vanguard at least once. If the students have been studying the planets, the vanguard students can also be asked to provide just a few key bits of information to the other explorers as features they have “discovered” about the planet they just reached. However, resist the urge to turn each stop into a seminar—the goal is to travel as far as possible across the system quickly enough to return before class time ends.

Remind the group that it’s a long walk across the solar system and then get started for real. Carry your Sun to a central location outside. If you can park Sol near a tall landmark (such as a flagpole), you’ll find it easier to point back to the “center of the Solar System” as you move further away. Take your Cheat Sheet in hand (the page from the resource kit listing your step-off distances) and read out the number of steps from the sun to Mercury. Send the Mercury explorer team ahead to place Mercury in its position, and quickly join them with the rest of the group. If the vanguard has some cool facts to share about Mercury, give them time to speak. And move on to Venus and the rest of the inner planets.

The asteroid belt portion is the first region containing many objects. If you pause at Ceres, the biggest dwarf planet in the inner Solar System, it helps reduce the stigma of Pluto being “only” a dwarf planet. The fun part in these “belt” regions is to pretend to dodge the small asteroids or other objects—while you may mention that there really isn’t any significant risk of running into an asteroid, that is no reason to turn down the chance to pretend you’re in a crowded mess of obstacles just like in the movies. Even Neil deGrasse Tyson, in his reboot of Cosmos, includes a sequence in which his Ship of the Imagination zigs and zags through, first, a crowded Asteroid Belt and later a densely-packed Oort Cloud.

If time is short or you are working with younger children, it is reasonable to make it to Jupiter (don’t forget to dodge the asteroids on the way out) point out roughly where the outer planets, Pluto, and the further objects would be found and then head back to Earth.

In any case, carry some ordinary first-aid supplies and be sure to have extra adults on hand to slow down those who want to jump to lightspeed. Don’t worry if you don’t have a straight route to use…twisting and turning your way around the streets of a neighborhood is equally impressive. If time will permit, participants can bring lunches and picnic in the Kuiper Belt before returning. And remember, as you return to collect the planet models, it is just as fun to rediscover the distances on the way back.

 

 

 

Walking to Pluto: Step 2

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Step 2: The List of Requirements:

Don’t worry.  This is one of the least expensive major science projects you’ll put together.

You’ll need:

Note that

I found a sunny yellow ball for my Sun.

1) Any ball roughly 8” (19mm) in diameter—a basic playground ball is likely to work, as will a standard soccer ball. FIFA size 5 works for the English-units model; the SI model is slightly smaller, so a youth-sized FIFA size 4 is appropriate—but don’t get bogged down in the details. Visually, when compared with the planet models, all of these ball sizes look the same.  It’s most likely that you already own or can borrow a ball for this project; if you simply must buy a ball, you should be able to find one for under $10.

 

 

2)  A set of eleven objects to represent each of the eight planets, our Moon, and two of the dwarf planets:

Mars or Venus

Mars or Venus

Pluto or Ceres

Pluto or Ceres

a)  four pins (two pin heads represent Mars and Venus, two pin points represent Ceres and Pluto),

The Moon Is Made Of Green Candy

The Moon Is Made Of Green Candy

b) one tiny candy nonpareil (cake décor or “sprinkle”) for the Moon

Earth Gets Spicy

Earth Gets Spicy

c) two peppercorns or allspice seeds for Earth and Venus

 

Having a Ball with Jupiter

Having a Ball with Jupiter

d) one jacks-size ball (Jupiter)

This jellybean could be Uranus or Neptune

This jellybean could be Uranus or Neptune

e) two jelly beans (or coffee beans) for Neptune and Uranus

 

Saturn represented by a large swirly peppermint

Saturn represented by a large swirly peppermint

f) and a ¾” (19mm) “shooter” marble or a big round piece of candy (also 3/4″ or 19mm) for Saturn.  (It’s just so nice to have something extra-cool and colorful for our most spectacular planet.)

 

 

Total cost: less than a dollar US; ideally, rummaging about an average home or allowing participants to bring contributions should turn up most of these objects for free. To splurge, pick up a whole jar of fresh peppercorns for around $5 and share them out among the students.

2) Eleven inexpensive holders for your objects, with the object names written on them. Empty clear yogurt containers or plastic drink cups work very well (see photos), as the pins can be pushed through the cups and others attached with glue to the cup bottoms…such that the cups then serve as mini-pedestals for the model objects. However, don’t feel bound by guidelines here—a set of index cards will do the job if that’s what you have handy. It does help to secure each object to its support. However, be sure that students can see the actual object clearly so that everyone has a feel for the scale. Cost: as much as 10 cents

3) A few signs printed on regular-sized paper to leave with objects that will be waiting for your return, such as:  “Please Leave This Experiment Undisturbed — (Teacher’s Name).”   Cost: 10 cents

4) Weights to keep each sign from blowing away in a breeze—anything from a handy rock to a water bottle to an actual sports-field marker from your supply closet.   Cost: negligible

5) Your basic first-aid kit and/or other equipment required by local protocols for a field trip.

6) Water as needed (Up to $10 if you need to buy each student some bottled water; negligible if students can bring refillable water bottles.) You may choose to make the walk as short as a half-mile (kilometer) or as long as twice that. For a short walk, you should only need modest supplies; for a long walk, snacks and water will be welcome.

7) A printout of your “Cheat Sheet” for either the English-units or SI-units version of the project Walk to Pluto, Miles or Walk to Pluto, km   (Just click to download the desired document) Whichever measurement system you’re using, it’s just one sheet, front & back, and includes short comments you can make as you take your trek. Cost: 15 cents, if your printer ink is expensive, because it does have colors.

Total cost of essential supplies: normally about a dollar, assuming most items can be gathered at home or borrowed.   For bottled water, if needed, budget an additional 50 cents per student

If you purchase all new supplies, you could spend as much as $40 for a brand-new soccer ball, a jar of nonpareils, a jar of peppercorns, a packet of pins, a jacks game, a bag of marbles with a shooter, and a package of jellybeans.

Interested in more details about the project calculations?  Here are copies of the complete worksheets:  Walk to Pluto Databank, miles and Walk to Pluto Databank, km

(For workbook copies in Excel format, ready for editing, I can send you a copy via Facebook messaging.  Just connect to one of my pages, Pixel Gravity or Cometary Tales.  Say, while you’re there, “like” the page.  Either way, you’ll receive the file in a return message.  The beauty of this approach is that you don’t even need a copy of Excel to use the workbook—Facebook will prompt you to choose whether to open it in Office Online or to download it.  The alternative is to email me via cometary@cometarytales.com.)

 

 

 

 

Walking to Pluto: Step 1

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Compare the sizes of Earth and Pluto & Charon Image Credit: NASA

Compare the sizes of Earth and Pluto & Charon (Pluto’s shadow isn’t that big on Earth!) Image Credit: NASA

It’s been a super-fantastic #PlutoFlyby day (see the video for a Pixel Gravity simulation of New Horizons’ close approach path on 7/15/2015), and I can’t resist going to one of my favorite astronomy projects:  building a scale model of the Solar System that takes you out of the house, out of the classroom, and under the sky.  (Where maybe Pluto’s shadow, cast by a distant star, will pass over you.)

As a reminder, you can look for the following in any Messy Monday project:

  1. A set of notes for project leaders, sketching the key elements of the project and the science topic it is meant to address
  2. A detailed supply list, structured to make it simple to purchase supplies for either a one-shot demonstration or for a classroom-sized group activity.
  3. A set of instructions for working through the project with students, including commentary to help cope with common classroom-management issues, questions that are likely to arise, and issues to keep in mind from safety to fairness.
  4. A rough estimate of the cost to run the project.

 

As before, I’ll break down the presentation into four postings, to spare readers trying to scroll through a 5000-word document, but I’ll post them quickly, so you can jump ahead if you are raring to go or want to access the reference materials first.  In other projects, we built our own comets. In this project, we travel out into the solar system, hoping to reach the source of that comet.

 

Step 1: Space is Big

It’s a long way to Pluto. But as far as the Universe is concerned, Pluto’s in our condo’s tiny back yard. What would it be like, though, to take a hike to Pluto? Like the New Horizons Spacecraft spacecraft buzzing past Pluto and its cluster of moons, but, well, maybe taking a bit less time about it. Nine years (the explorer was launched in early 2006) is longer than even the above-average student’s attention span. What if we could shrink the Solar System down to a reasonable size for nice walking field trip?

Paths of the nine planetary objects orbiting the Sun for many years.

Paths of the nine planetary objects orbiting the Sun for many years (A Pixel Gravity simulation result.)

No surprise here: it’s been done. Six ways to Sunday, in fact. While no one person claims to own the idea of building a scale model of the solar system, my favorite advocate of such models is Guy Ottewell, who likes a scaling factor that makes the model a reasonable size for the average person to walk. You can buy his book on the subject (now with cartons!) at the books page on his website. As a bonus, you’ll also find the most current editions of all of his other books on astronomy and much more.   (He self-effacingly describes his annual Astronomical Calendar as “widely used”; a more-accurate description would be “fanatically used by serious amateur astronomers”.)  No disclaimer necessary;  we’re not friends, I’m just one of his (many) Twitter followers.

The goal of this project is for everyone involved to obtain a personal sense of the feature of Outer Space that is hardest to conceptualize by reading books and trolling the internet: Space is BIG. (Yes, you may pause to reread the opening to The Hitchhiker’s Guide to the Galaxy, by Douglas Adams.)  Indeed. Really Really Big.

Our neighbor galaxy, Andromeda (Image Credit:  ESA/Hubble)

Our neighbor galaxy, Andromeda (Image Credit: ESA/Hubble)

On top of that, the places you can stop—the non-empty bits—are few and very tiny compared with the distances between them.  And it takes a long time to get from one stop to another.

So, when assembling materials and presenting this project, keep these two key goals in mind. It’s not important whether you model Earth as a peppercorn (Ottewell’s model) or an allspice seed (easier to find in my own kitchen) or a spitwad from the ceiling that happens to be about a tenth of an inch across.   What’s important is that the Earth is not only extremely teensy compared to the Sun, but you can’t even fit the Sun and Earth into an ordinary classroom. And you have to hike at least a half a mile (a kilometer) if you want to make it to Pluto. With any luck, you can make practical use of the excess energy in a classroom-full of kids and also amaze them. If you’re doing this as a classroom helper and the teacher is used to taking advantage of the time to catch up on infinite paperwork, this is a time to persuade that teacher to shove the paperwork aside and join the expedition. There will be no regrets!

The objects used to represent planets and other bodies should be chosen for familiarity, because you want the participants to absorb the scale comparisons effortlessly. “Everyone knows” how big a jellybean is, a pin is familiar—both the pushing end and the painful poking end—a soccer ball is a known object, and so on. It doesn’t matter if the object you use is not exactly the design diameter—and no one is going to care that jellybeans or coffee beans are bumpy ovoids, not spheres. The next time you’re eating a jellybean (or slurping a Starbucks), at the back of your mind will be “I had to hike a half-mile just to get to this little Neptune here”.   Plus, “Yum, astronomy is delicious.”

If you’re interested in the underlying concepts, I encourage you to stop by the National Optical Astronomy Observatory’s website and read Guy Ottewell’s original 1989 description of his Thousand Yard Model; however, if you consider yourself a mathphobe, don’t let the arithmetical computations worry you. I’ve made you an Excel worksheet to do that task. Running a mind-expanding science project should help relieve that condition, not make it worse.

If you have visited a museum’s scale model, read Ottewell’s book, or done a similar project in the past, there are a few differences you may encounter in this project. In particular, I suggest you avoid having planets represented by peanuts. Including nuts in school projects, can be problematical if any student (or parent helper) with nut hyper-allergy could possibly be affected. (I have relatives with this allergy, and there is nothing quite like coping with anaphylactic shock to ruin a day’s outing.)

Dwarf Planet Ceres Image Credit:  NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

Dwarf Planet Ceres Image Credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

I’ve included a few more “destinations”—such as the ever-popular asteroid “belt” and my personal favorite of Pluto’s fellow dwarf planets. The number of steps taken between planets (and other destinations) is greater, because kids take shorter steps than grown-ups. (Also, other models I’ve seen assume a stride length more typical of men—and the majority of teachers and parent volunteers are still women, with shorter strides than men.) And I’ve included the current (for now, at least) locations for a few more distant “destinations” that we can look out towards from our turnaround point at Pluto.

The tables I’ve provided are in both English and SI units. The scales are slightly different between the two, in order to yield intuitively-scaled results in either set of units. And I’ve provided a “cheat sheet” of the key data for a teacher or other presenter to carry as a reference source on the walk. If anyone would like to get completely precise and build their own model matching their pace length exactly, or adjusting to a different scale, you can request a copy of my Excel workbook for this project to create your individualized pace-off. Or if you know a Senior Girl Scout or Boy Scout in need of a Gold Star or Eagle project, a community solar system model would be a very cool service project. (C’mon, Scouts, do you really want to build another park bench?)

Speaking of space, and coolness, and peanuts, and bigness, by the time your group finishes this project—everyone who participates should wholeheartedly agree:  Space is Big

A Sign From NASA

A Sign From NASA

 

 

 

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