# THE THOUSAND-YARD MODEL,or The Earth as a Peppercorn

## Can you picture the dimensions of the solar system?

### Probably not, for they are of an order so amazing that it is difficult either to realize or to show them.

You may have seen a diagram of the Sun and planets, in a book. Or you may have seen a revolving model of the kind called an orrery (because the first was built for an Earl of Orrery in 1715). But even the largest of such models--such as those that cover the ceilings of the Hayden Planetarium in New York and the Morehead Planetarium at Chapel Hill-are far too small. They omit the three outermost planets, yet still cannot show the remaining ones far enough apart.

The fact is that the planets are mighty small and the distances between them are almost ridiculously large. To make any representation whose scale is true for the planets sizes and distances, we must go outdoors.

The following exercise could be called a Model, a Walk or a Happening. Since it is simple, it may seem suitable for children only. It can, indeed, be done with children down to the age of seven. Yet it can also be done with a class consisting of professors of astronomy. It will not waste their time. They will discover that what they thought they knew, they now apprehend. To take another extreme, the most uncontrollable high-school students or the most blase college students unfailingly switch on their full attention after the first few paces of the excursion.

There is one other party that may profitably take the planet-walk, and that is yourself, alone. Reading the following description is no substitute: you must go out and take the steps and look at the distances, if the awe is to set in.

## First, collect the objects you need. They are:

### Sun-any ball, diameter 8.00 inches Mercury-a pinhead, diameter 0.03 inch Venus-a peppercorn, diameter 0.08 inch Earth-a second peppercorn Mars-a second pinhead Jupiter-a chestnut or a pecan, diameter 0.90 inch Saturn-a hazelnut or an acorn, diameter 0.70 inch Uranus-a peanut or coffeebean, diameter 0.30 inch Neptune-a second peanut or coffeebean Pluto- a third pinhead (or smaller, since Pluto is the smallest planet)

You may suspect it is easier to search out pebbles of the right sizes. But the advantage of distinct objects such as peanuts is that their rough sizes are remembered along with them. It does not matter if the peanut is not exactly .3 inch long; nor that it is not spherical.

A standard bowling ball happens to be just 8 inches wide, and makes a nice massive Sun, so I couldn't resist putting it in the picture. But it may not be easy to find and certainly isn't easy to carry around. There are plenty of inflatable balls which are near enough in size.

The three pins must be stuck through pieces of card, otherwise their heads will be virtually invisible. If you like, you can fasten the other planets onto labeled cards too.

Begin by spilling the objects out on a table and setting them in a row. Here is the moment to remind everyone of the number of planets -9- and their order--MVEMJSUNP. (This mvemonic could be made slightly more pronounceable by inserting the asteroids in their place between Mars and Jupiter: MVEMAJSUNP.)

The first astonishment is the contrast between the great round looming Sun and the tiny planets. (And note a proof of the difference between reading and seeing: if it were not for the picture, the figures such as "8 inches" and ".08 inch" would create little impression.) Look at the second peppercorn--our "huge" Earth--up beside the truly huge curve of the Sun.

## Establishing a Distance Scale

### Having set out the objects with which the model is to be made, the next thing is to ask: "How much space do we need to make it?" Children may think that the table-top will suffice, or a fraction of it, or merely moving the objects apart a little. Adults think in terms of the room or a fraction of the room, or perhaps the corridor outside. To arrive at the answer, we have to introduce scale.

This peppercorn is the Earth we live on.

The Earth is eight thousand miles wide! The peppercorn is eight hundredths of an inch wide. What about the Sun? It is eight hundred thousand miles wide. The ball representing it is eight inches wide. So, one inch in the model represents a hundred thousand miles in reality.

This means that one yard (36 inches) represents 3,600,000 miles. Take a pace: this distance across the floor is an enormous space-journey called "three million six hundred thousand miles."

Now, what is the distance between the Earth and the Sun? It is 93 million miles. In the model, this will be 26 yards.

This still may not mean much till you get one of the class to start at the side of the room and take 26 paces. He comes up against the opposite wall at about 15!

## Clearly, it will be necessary to go outside.

Hand the Sun and the planets to members of the class, making sure that each knows the name of the object he or she is carrying, so as to be able to produce it when called upon.

You will have found in advance a spot from which you can walk a thousand yards in something like a straight line. This may not be easy. Straightness of the course is not essential; nor do you have to be able to see one end of it from the other. You may have to "fold" it back on itself. It should be a unit that will make a good story afterwards like "All the way from the flagpole to the Japanese garden!"

## Take a Hike!

Put the Sun ball down, and march away as follows. (After the first few planets, you will want to appoint someone else to do the actual pacing-call this person the "Spacecraft" or "Pacecraft"-so that you are free to talk.)

10 paces. Call out "Mercury, where are you?" and have the Mercury-bearer put down his card and pinhead, weighting them with a pebble if necessary.

Another 9 paces. Venus puts down her peppercorn.
Another 7 paces. Earth

Already the thing seems beyond belief. Mercury is supposed to be so close to the Sun that it is merely a scorched rock, and we never see it except in the Sun's glare at dawn or dusk-yet here it is, utterly lost in space! As for the Earth, who can believe that the Sun could warm us if we are that far from it?

The correctness of the scale can be proved to skeptics (of a certain maturity) on the spot. The apparent size of the Sun ball, 26 paces away, is now the same as that of the real Sun-half a degree or arc, or half the width of your little finger held at arm's length. (If both the size of an object and its distance have been scaled down by the same factor, then the angle it subtends must remain the same.)

Another 14 paces. Mars

### Now come the gasps, at the first substantially larger leap:

Another 95 paces to Jupiter
Here is the "giant planet"-but it is a chestnut, more than a city block from its nearest neighbor in space!

### From now on, amazement itself cannot keep pace, as the intervals grow extravagantly:

Another 112 paces. Saturn
Another 249 paces. Uranus
Another 281 paces. Neptune
Another 242 paces. Pluto

## You have marched more than half a mile!

(The distance in the model adds up to 1,019 paces. A mile is 1,760 yards.)

To do this, to look back toward the Sun ball, which is no longer visible even with binoculars, and to look down at the pinhead Pluto, is to feel the terrifying wonder of space.

That is the outline of the Thousand-Yard Model. But be warned that if you do it once you may be asked to do it again. Children are fascinated by it enough to recount it to other children; they write "stories" which get printed in the school paper; teachers from other schools call you up and ask you to demonstrate it.

So the outline can bear variation and elaboration. There are different things you can remark on during the pacings from one planet to the next, and there are extra pieces of information that can easily be grafted on. These lead forward, in fact, to the wider reaches of the universe, and make the planet walk a convenient introduction to a course in astronomy. But omit them if you are dealing with children young enough to be confused, or if you yourself would prefer to avoid mental vertigo.

## Establishing the scale

While you are talking and introducing the idea of the model, it may be helpful (depending on the age of the audience) to build up on a blackboard something like this:

```				real			in model
Earth's width			8,000 miles		8/100 inch
Sun's width			800,000 miles		8 inches
therefore scale is		100,000 miles		1 inch
therefore			3,600,000 miles		36 inches or 1 yard
and Sun-Earth distance		93,000,000 miles	26 yards
```

## Back to the Top

The "Thousand-Yard Model or, The Earth as a Peppercorn" is copyrighted 1989 by Guy Ottewell of the Astronomical Workshop. Click for a look at some other books he's written.

### Where are the planets now?

WWW by Daniel A. Washburn
for NOAO Educational Outreach