S3.12.2 Chapter 2

How big and how far

How far apart are the planets? Could I make a model of them with a string?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A The planets are close together, like peas on a plate.
You picked A. Read on. At the end, the chapter comes back to your guess.
B The planets are far apart, but a model fits on a table.
You picked B. Read on. At the end, the chapter comes back to your guess.
C The planets are very far apart. A model needs a string as long as a playground.
You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Use a scale to turn real distances into model distances
Make a scale model of the planets along a long string

Space is far too big to draw as it is. So we make a model. A model is smaller than the real thing, but every part is in the right place.

To make a model, we choose a scale. A scale says how much real distance one piece of the model stands for.

Here is our scale. One metre of string stands for 100 million km. We write it as 1 m = 100 million km.

Draw it first

Put the planets on a string

1 Write the scale. 1 m of string stands for 100 million km. Put a stone for the Sun at one end.
2 Divide the real distance by 100. The Earth is 150 million km away, so 150 ÷ 100 = 1.5 m.
3 Do the same for every planet. Mark each one on the string.

The rule is short. The model distance is the real distance divided by the scale. Real distance ÷ scale = model distance.

The four rocky planets all fit on the first 2.5 m of string.

Now go out to Saturn, Uranus and Neptune. They are much farther out, so the string must be 50 m long. The scale and the rule stay the same.

Saturn, Uranus and Neptune on a string 50 m long. Jupiter would sit at 7.78 m, and the four rocky planets in the first 2.3 m.

See it three ways

As a picture

In words

Each row gives the real distance from the Sun and the model distance on the string. The metres are the million km divided by 100. Neptune goes 45 m out. Mercury goes 0.58 m, just over half a metre.

In symbols

Model distance = real distance ÷ 100. For Neptune: 4 500 ÷ 100 = 45 m.

Venus and Mars on the string. The next example finds the gap between them.

Worked example

On the model, 1 m stands for 100 million km. How far apart are Venus and Mars on the string?

Venus is about 108 million km from the Sun. Mars is about 228 million km.
Venus on the string: 108 ÷ 100 = 1.08 m.
Mars on the string: 228 ÷ 100 = 2.28 m.
Take away the smaller from the bigger: 2.28 − 1.08 = 1.2 m.

Answer: 1.2 m

Now think about the sizes of the planets. Use the same scale, 1 m = 100 million km. How wide are the Sun and the planets on the model?

The Sun would be a bead 1.4 cm wide. The Earth would be a speck of dust.

At this scale the Earth is only 0.13 mm wide. That is a speck you could hardly see. So a model of sizes and a model of distances need different scales. If you made the planets big enough to see, they would not fit on the string. If you used one scale for both, you could not see the planets.

Try it

Walk the solar system

You need: a long string or rope, or many strings tied together, 45 m long, a stick or a rope marked at 1 m, ten small stones, an open flat place, such as a playground or a field.

Be safe: Choose a flat place away from roads, holes and crowds. Do not leave string across a path where people walk.

Put a stone on the ground. It is the Sun.
Walk away from it, pulling the string tight. Measure each distance in the table with your 1 m stick.
Put a stone at 0.58 m for Mercury and 1.08 m for Venus. Put one at 1.5 m for Earth and 2.28 m for Mars. They are very close.
Walk on. Put stones at 7.78 m for Jupiter and 14.3 m for Saturn. Then 28.7 m for Uranus and 45 m for Neptune.
Stand at Neptune. Look back at the Sun stone. If 45 m is too long, use 1 m = 200 million km and halve every number.

What you will see: The four rocky planets bunch up near the Sun, in about 2 m of string. Then there is a long, long gap before Jupiter. Neptune stands 45 m from the Sun. Most of the solar system is empty space.

If you cannot try it, this is what happens.

A wrong idea many people have

A good model of the solar system shows the planets as big balls close together.

Why it feels right: Pictures in books squeeze everything onto one page, so the planets look like neighbours on a shelf.

The test that breaks it: Put the planets on the string. Mars is at 2.28 m and Jupiter is at 7.78 m. The gap is more than 5 m. At the same scale the Earth is a speck of dust.

What is true: The planets are tiny compared with the gaps between them. A picture in a book shows them big and close so you can see them. It is not to scale.

Key words

scale: how much real distance one piece of the model stands for.
model distance: the distance on the model, in metres.
real distance: the true distance in space, in million km.

Back to your guess

The answer is C: The planets are very far apart. A model needs a string as long as a playground.

The planets are very far apart. If 1 m of string stands for 100 million km, Neptune is 45 m from the Sun. That is a long walk.

Keep it

Copy this into your exercise book.

A scale says how much real distance a piece of the model stands for. Model distance = real distance ÷ scale. 1 m = 100 million km puts Neptune 45 m out.

Draw: A string with a Sun at 0, the Earth at 1.5 m and Neptune at 45 m. Write 1 m = 100 million km.