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E2.5 · Use suitable units and scale to compare astronomical distances

Learn to use suitable units and scale to compare astronomical distances through clear examples and targeted practice.

Ontario Grade 9 Science

Earth and Space Science: Space Exploration

Ontario Grade 9 Science — study topic E2.5

A walk across a classroom can be measured in metres. A trip across a city might be measured in kilometres. In space, even kilometres can make a distance awkward to write and compare. The science question is: how can we choose units and a scale that make astronomical distances easier to understand? A unit is an agreed measure, such as a kilometre. A scale is a way to represent large distances using smaller, manageable numbers or lengths. The goal is not to make space fit on a page perfectly. It is to make comparisons clear and honest.

What you will learn

Choose a distance unit that suits the size of an astronomical distance.
Compare distances by using the same unit or by converting between units.
Read and create a simple scale model while recognizing its limits.

Start with the distance and its unit

A distance tells how far apart two places are. Before comparing distances, check what each number measures and which unit it uses. A distance from Earth to the Moon is not the same kind of comparison as a distance from the Sun to a planet. State the two places being compared.

A kilometre is useful for distances within the Solar System, but very large kilometre values can be difficult to read. Astronomers also use the astronomical unit, abbreviated AU, for distances within the Solar System. One AU is the average distance from Earth to the Sun, about 150 million kilometres. The AU gives a useful common unit for comparing a planet’s distance from the Sun with Earth’s.

For distances to stars, a light-year is often more suitable. A light-year is the distance light travels in one year. It is a unit of distance, not a unit of time. These units are not interchangeable by name: a value in kilometres must be converted before it can be directly compared with a value in AU or light-years.

1\ \mathrm{AU} \approx 150\,000\,000\ \mathrm{km}

Name the two places whose distance is being compared.
Check the unit before comparing the numbers.
AU is useful for Solar System distances; light-years are useful for distances to stars.

Use a shared unit to compare

A fair comparison uses the same unit for both distances. If the values already use the same unit, compare the numbers. If they use different units, convert one value first. Conversion means expressing the same distance in another unit; it does not change the distance.

For example, Earth is about 1 AU from the Sun, while Neptune is about 30 AU from the Sun. The distances share a reference point—the Sun—and a unit—AU. So Neptune’s distance from the Sun is about 30 times Earth’s distance from the Sun. This comparison is much easier to read than writing both distances as enormous numbers of kilometres.

Be careful with the reference point. “Moon to Earth” and “Earth to Sun” are both distances, but their starting and ending places differ. They can still be compared as lengths if they use a common unit, but a model should label each distance so readers do not mistake what is being measured.

distance in AU = distance in km \div 150 000 000

A direct numerical comparison requires a shared unit.
Keep the reference points clear, especially in diagrams.
A larger number in the same unit means a greater distance.

Represent large distances with a scale

A scale model shrinks or enlarges distances by the same chosen amount. For a diagram, a scale might say that 1 cm represents 1 AU. A planet 5 AU from the Sun would then be placed 5 cm from the Sun in that model. The model preserves the relative distances it represents, as long as the same scale is used throughout.

A scale can also be a number line or a table rather than a drawing. A table is often clearer when the distances are extremely different. For instance, putting the Moon and a star on the same page at one exact scale may make the Moon’s position too close to the reference point to see. A separate close-up or a table can help, but it must be labelled as a different view or scale.

Every model has limits. A small diagram cannot show every object at its true size and distance. A scale diagram may leave out objects, show planets as dots, or use a different scale for a close-up. These choices help explain distances, but they are not observations of the objects’ actual apparent sizes.

1\ \mathrm{cm} \text{ represents } 1\ \mathrm{AU}

Use one stated scale consistently within each model.
Label the reference point, distances, and units.
Say when a view is simplified or uses a different scale.

Evidence, models, and careful claims

Astronomical distance values come from scientific observations and measurements. In this lesson, the rounded values are standard approximate astronomy values, included for practice. They are not new measurements made by a class. Rounding makes comparisons easier, but it means the numbers are not exact.

A scale diagram is a model: a simplified representation used to show a feature, such as relative distance. It is not the same as the evidence used to determine a distance. A model can help answer “Which is farther?” or “How much farther?” while leaving out details that are not needed for that question.

When presenting a comparison, include the unit and identify the reference points. Avoid claiming that a diagram is perfectly to scale if it is not. These habits make a comparison easier for another person to check.

Rounded published values are suitable for practice, but they are approximate.
A model helps show a comparison; it is not the original evidence.
Clear labels and honest limits make a distance model more useful.

Picking a distance unit

Distance being considered	Useful unit	Why it helps
Across a town or region	Kilometres	A manageable everyday distance unit
Between the Sun and Solar System objects	Astronomical units (AU)	Avoids very large kilometre values
To stars	Light-years	Keeps immense distances easier to compare

Worked example

Compare two Solar System distances

Earth is about 1 AU from the Sun. Neptune is about 30 AU from the Sun. Compare their distances from the Sun using a suitable unit.

Distances from the Sun

Approximate practice values in AU. This schematic compares distance only; the spacing and planet sizes are not a complete, to-scale picture of the Solar System.

Check the comparison
Both distances start at the Sun and are given in AU, so their values can be compared directly.
Compare the values
Divide Neptune’s distance by Earth’s distance. The result says how many Earth–Sun distances fit into the Sun–Neptune distance.
$30 \div 1 = 30$

Answer: Neptune is about 30 times as far from the Sun as Earth is.

Check: The comparison uses the same reference point and unit, so the ratio is meaningful.

Worked example

Compare Moon–Earth and Earth–Sun distances

The average Earth–Moon distance is about 384,400 km. The average Earth–Sun distance is about 150,000,000 km. About how many Earth–Moon distances fit into the Earth–Sun distance?

Two average distances in kilometres

Approximate distances for comparison. Each value describes a different pair of places; this schematic is not a to-scale spatial layout.

Use one unit
Both distances are already in kilometres. The question asks how many shorter distances fit into the longer one, so divide the Earth–Sun distance by the Earth–Moon distance.
$150\,000\,000 \div 384\,400 \approx 390$
Interpret the rounded result
The result is approximate because the distance values are rounded and the Moon’s distance from Earth changes. The division compares lengths; it does not mean the two distances have the same reference points.

Answer: About 390 Earth–Moon distances fit into the average Earth–Sun distance.

Check: The larger distance divided by the smaller distance gives a number greater than 1, as expected.

Worked example

Choose a useful unit for stars

Two stars are about 4.2 light-years and 8.6 light-years from the Sun. Which is farther, and by about how much?

Approximate distances to two stars

Hypothetical practice values, both measured from the Sun. The schematic compares distances only; it does not show actual star sizes or positions in the sky.

Keep the suitable unit
Both distances are to stars and are already given in light-years. This unit keeps the values manageable, so no conversion to kilometres is needed.
Find the difference
Subtract the smaller distance from the larger distance to find how much farther the second star is from the Sun.
$8.6 - 4.2 = 4.4\ \text{light-years}$

Answer: The star at 8.6 light-years is farther. It is about 4.4 light-years farther from the Sun.

Check: Both values use the same unit and reference point, so subtraction compares the stated distances.

Common mistakes and how to avoid them

Comparing 5 km directly with 2 AU as if the numbers use the same unit.

Correction: Convert one distance so both use the same unit, or use another suitable shared unit.

Calling a light-year a measure of time because it contains the word “year.”

Correction: A light-year is a distance: how far light travels in one year.

Treating a simplified scale diagram as an exact picture of space.

Correction: Check its labels and caption. A diagram may show distance but not true object sizes or every object’s position.

Leaving out the places named by a distance.

Correction: State the reference points, such as Earth to Moon or Sun to Neptune.

Lesson summary

Name the places whose distance is being compared.
Choose a unit suited to the size of the distance.
Use the same unit before comparing values.
A scale represents distances in a consistent, smaller form; label its limits.
A light-year measures distance, while an AU is based on the average Earth–Sun distance.

Check your understanding

Question 1

Earth is about 1 AU from the Sun and Saturn is about 9.5 AU from the Sun. About how many times farther from the Sun is Saturn than Earth?

About 9.5 times
About 8.5 times
About 0.1 times
About 10,000 times

Show answer and explanation

About 9.5 times

The values share the Sun as their reference point and use AU. Dividing 9.5 by 1 gives about 9.5.

Question 2

Which statement about a light-year is correct?

It is a distance that light travels in one year.
It is the time light takes to reach the Moon.
It is the average distance from Earth to the Sun.
It is a unit used only for distances within a classroom.

Show answer and explanation

It is a distance that light travels in one year.

A light-year is a distance unit. An AU, not a light-year, is based on the average Earth–Sun distance.

Question 3

A diagram uses the scale 1 cm for 2 AU. How far from the Sun should a planet at 6 AU be placed on the diagram?

3 cm
4 cm
6 cm
12 cm

Show answer and explanation

3 cm

At 2 AU per centimetre, 6 AU takes 3 cm on the diagram. The same scale is used throughout.

Key terms

Astronomical unit (AU): A distance unit equal to about the average distance from Earth to the Sun.
Distance: How far apart two places or objects are.
Light-year: The distance light travels in one year; it is a unit of distance.
Scale: A stated relationship between distances in a model and the distances they represent.
Scale model: A simplified representation that uses a consistent scale to show selected features.
Unit: An agreed measure used to describe a quantity, such as a kilometre.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 9 Science (SNC1W), expectation E2.5. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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