E. Earth and Space Science: Space Exploration · Space Exploration: The Sun, the Solar System and the UniverseMeasuring Space: Kilometres, AU and Light-Years
E2.5 A1.4About 70 minutes
Learning goals- I can write very large distances in scientific notation.
- I can choose an appropriate unit (km, AU or light-year) for a distance in space.
- I can convert between kilometres, astronomical units and light-years.
- I can explain why looking far into space means looking back in time.
- I can read and run a short program that calculates light travel times.
Words to know
scientific notation
A way to write very large or very small numbers as a number from 1 to less than 10 multiplied by a power of 10, such as 1.5 × 10⁸.
astronomical unit (AU)
The average distance between Earth and the Sun, about 1.5 × 10⁸ km (150 million km). Used for distances within the solar system.
light-year (ly)
The distance light travels in one year, about 9.46 × 10¹² km. Used for distances to stars and galaxies. It is a distance, not a time.
speed of light
About 300 000 km/s (3.0 × 10⁵ km/s) in space. Nothing travels faster.
parsec (pc)
A distance unit used by astronomers, about 3.26 light-years, based on the parallax method.
parallax
The apparent shift in position of a nearby object against a distant background when it is viewed from two different places.
Remember from Grade 6
In Grade 6 you learned that the Sun is about 150 million km away and met the light-year: the nearest star after the Sun is about 4.2 light-years away. In this lesson you will use these units like an astronomer: you will convert between them, write them in scientific notation, and choose the best unit for each job.
A measuring problem
Would you measure the length of your pencil in kilometres? Or the drive from Thunder Bay to Toronto in millimetres? Of course not. You choose a unit that fits the size of the thing. Space has the same problem, but much bigger: kilometres are far too small for most distances in space, so astronomers invented bigger units.
Scientific notation: taming huge numbers
The distance to the Sun is 150 000 000 km. Counting zeros is slow and easy to get wrong. In scientific notation we write it as
1.5 × 10⁸ km
- The first number (the coefficient) is at least 1 and less than 10.
- The exponent tells how many places the decimal point moved. Moving it 8 places left turns 150 000 000 into 1.5, so the exponent is 8.
To multiply, multiply the coefficients and add the exponents: (3 × 10⁵) × (2 × 10³) = 6 × 10⁸. To divide, divide the coefficients and subtract the exponents: (6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵.
Unit 1: the astronomical unit (AU), for the solar system
1 AU is the average distance from Earth to the Sun: about 1.5 × 10⁸ km.
AU is perfect inside the solar system: Mars is about 1.5 AU from the Sun, Jupiter about 5.2 AU, and Neptune about 30 AU. These numbers are easy to compare: Neptune is about 30 times farther from the Sun than Earth.
To convert: km = AU × (1.5 × 10⁸), and AU = km ÷ (1.5 × 10⁸).
Unit 2: the light-year (ly), for stars and galaxies
Light travels about 300 000 km every second (3.0 × 10⁵ km/s). A light-year is how far light travels in one year:
300 000 km/s × 31 557 600 s (one year) ≈ 9.46 × 10¹² km (about 9.5 trillion km).
A light-year is a distance, not a time! The name is confusing because it contains 'year'. Think of it like saying a town is '2 hours away': you are describing distance using travel time.
- Proxima Centauri, the nearest star after the Sun: about 4.24 ly.
- The centre of our Milky Way galaxy: about 26 000 ly.
- The Andromeda Galaxy: about 2.5 million ly.
Professional astronomers also use the parsec (1 pc ≈ 3.26 ly). It comes from the parallax method: as Earth moves around the Sun, nearby stars seem to shift slightly against faraway stars, and the size of the shift tells their distance.
Looking back in time
Because light takes time to travel, we always see objects as they were when the light left them.
- We see the Sun as it was about 8.3 minutes ago.
- We see Proxima Centauri as it was about 4 years ago.
- We see the Andromeda Galaxy as it was about 2.5 million years ago, long before any humans existed.
The farther away we look, the further back in time we see. Astronomers use this to study what the universe was like long ago, as you will see in the lesson on the Big Bang.
Worked exampleExample 1: Converting AU to km
Saturn is about 9.5 AU from the Sun. Write this distance in kilometres in scientific notation.
- km = AU × (1.5 × 10⁸ km)
- = 9.5 × 1.5 × 10⁸
- = 14.25 × 10⁸ km
- Adjust so the coefficient is between 1 and 10: 14.25 × 10⁸ = 1.425 × 10⁹.
About 1.4 × 10⁹ km (1.4 billion km).
Worked exampleExample 2: How long does light take?
How long does sunlight take to reach Neptune, 4.5 × 10⁹ km from the Sun?
- time = distance ÷ speed
- = (4.5 × 10⁹ km) ÷ (3.0 × 10⁵ km/s)
- = 1.5 × 10⁴ s = 15 000 s
- Convert: 15 000 s ÷ 60 = 250 min; 250 min ÷ 60 ≈ 4.2 h.
About 15 000 seconds, or about 4.2 hours.
Worked exampleExample 3: Converting light-years to km
Sirius is about 8.6 light-years away. How far is that in kilometres?
- km = ly × (9.46 × 10¹² km)
- = 8.6 × 9.46 × 10¹²
- ≈ 81.4 × 10¹² = 8.14 × 10¹³ km
About 8.1 × 10¹³ km (81 trillion km).
Code it: light travel times (A1.4)
Computers are great at repeating the same calculation. This short Python program uses a dictionary to store distances, then a loop to calculate the light travel time for each one.
speed_of_light = 300000 # km per second
objects = {"Moon": 384400, "Sun": 149600000, "Neptune": 4500000000}
for name, distance in objects.items():
seconds = distance / speed_of_light
minutes = seconds / 60
print(name, round(seconds, 1), "s =", round(minutes, 1), "min")
# Output:
# Moon 1.3 s = 0.0 min
# Sun 498.7 s = 8.3 min
# Neptune 15000.0 s = 250.0 min
The program divides each distance (km) by the speed of light (km/s) to get seconds, then by 60 to get minutes. Try adding Mars or Jupiter to the dictionary.
Hands-on activityParallax with your thumb (and a home measuring challenge)
You need: your thumb, a wall with a picture or a window frame, a metre stick or measuring tape, a partner.
Part A: see parallax
- Hold your thumb up at arm's length in front of a picture on the far wall.
- Close your left eye, then open it and close your right eye. Switch back and forth. Your thumb seems to jump against the background.
- Now hold your thumb only halfway to your face and repeat. Does it jump more or less?
Part B: choose the unit
- List 6 distances: your thumb's width, the height of a door, the length of your home, the distance to your school, the distance to the Moon, and the distance to Proxima Centauri. For each, pick the best unit (mm, cm, m, km, AU or ly) and explain why.
What to look for: the closer thumb jumps more. Astronomers use the same idea: nearby stars shift more than distant stars as Earth moves around the Sun, and measuring the shift gives the distance. In Part B, sensible choices are mm or cm, m, m, km, km, and light-years; the Moon (about 384 400 km) is close enough that km still works well.
Just for funA light-year sounds like a measure of time, but it is a distance. So if someone says a test 'took light-years', they are technically saying it was very long, not very slow!
Your turn
1Write 384 400 km in scientific notation.
2Which unit would you use for the distance from the Sun to Jupiter? To the star Vega?
Jupiter: AU (about 5.2 AU). Vega: light-years (stars are far outside the solar system).
3Mars is 1.52 AU from the Sun. How far is that in km?
1.52 × 1.5 × 10⁸ = 2.28 × 10⁸ km (about 228 million km).
4Explain why a light-year is a unit of distance.
It is the distance light travels in one year, about 9.46 × 10¹² km. It measures how far, not how long.
5If a star is 50 light-years away, how old is the light you see from it tonight?
About 50 years old. It left the star 50 years ago.
6Calculate (4 × 10⁶) × (2 × 10³).
8 × 10⁹ (multiply 4 × 2 = 8, add exponents 6 + 3 = 9).
7In the Python program, what would it print for Mars at 225 000 000 km?
225 000 000 ÷ 300 000 = 750 s; 750 ÷ 60 = 12.5 min. It prints Mars 750.0 s = 12.5 min.
More practice: warm-up
1About how far is 1 AU in km?
About 1.5 × 10⁸ km (150 million km).
2What is the speed of light, approximately?
About 300 000 km/s (3.0 × 10⁵ km/s).
3Write 9 460 000 000 000 in scientific notation.
4How long does sunlight take to reach Earth?
About 8.3 minutes (8 min 20 s).
5Write 2.5 × 10⁶ in standard form.
More practice: on your own
1Uranus is about 19.2 AU from the Sun. How long does sunlight take to reach it? (Hint: light takes 8.3 min to travel 1 AU.)
19.2 × 8.3 min ≈ 159 min, or about 2.7 hours.
2Proxima Centauri is 4.24 ly away. Express this in km.
4.24 × 9.46 × 10¹² ≈ 4.01 × 10¹³ km (about 40 trillion km).
3Convert 7.5 × 10⁸ km to AU.
7.5 × 10⁸ ÷ 1.5 × 10⁸ = 5 AU (about Jupiter's distance).
4Why do astronomers not use AU for distances to other galaxies?
The numbers would be enormous and hard to compare (the Andromeda Galaxy is about 1.6 × 10¹¹ AU away). Light-years (or parsecs) give smaller, easier numbers.
5Mission control sends a command to a rover on Mars when Mars is 3.0 × 10⁸ km from Earth. How long until the rover receives it, and why does this matter?
(3.0 × 10⁸) ÷ (3.0 × 10⁵) = 1.0 × 10³ s = 1000 s ≈ 16.7 min. The delay means the rover cannot be driven in real time; it must follow pre-planned commands and use some self-driving software.
Challenge
1At Voyager 1's speed of about 17 km/s, roughly how long would it take to travel 4.0 × 10¹³ km (the distance to Proxima Centauri)? Give your answer in years (1 year ≈ 3.16 × 10⁷ s).
time = 4.0 × 10¹³ ÷ 17 ≈ 2.35 × 10¹² s. In years: 2.35 × 10¹² ÷ 3.16 × 10⁷ ≈ 7.4 × 10⁴ years, about 75 000 years.
2A galaxy is 10 million light-years away. A student says, 'We are seeing that galaxy exactly as it is today.' Correct the student.
The light left the galaxy 10 million years ago, so we see it as it was then. It may have changed since, but we cannot know yet.
3Modify the Python program so it prints travel times in hours instead of minutes. What would it print for Neptune?
Change minutes = seconds / 60 to hours = seconds / 3600 and print round(hours, 1), "h". For Neptune: 15000 ÷ 3600 ≈ 4.17, so it prints Neptune 15000.0 s = 4.2 h.
Quiz
1. Which unit is best for the distance between the Sun and Saturn?
3. What is (3.0 × 10⁸) ÷ (1.5 × 10³)?
4. If a star is 100 light-years away, the light we see from it left the star:
5. About how long does light take to travel from the Sun to Earth?
6. Which is 1.5 × 10⁸ in standard form?
Big idea: SNC1W expectation E2.5 asks students to quantify distances in the solar system and the universe, using relative distances and sizes and appropriate units. The ministry notes the link to mathematics: this lesson uses scientific notation and unit conversions. The Python program supports A1.4 (coding to model scientific relationships).
Common difficulties:
- Thinking a light-year is a time. Keep repeating: 'distance light travels in a year'.
- Scientific notation errors: coefficients that are not between 1 and 10 (like 14.25 × 10⁸), and adding exponents when dividing.
- Unit conversions: encourage your teen to write the units at every step.
How to help: pick a distance from the news (for example, a spacecraft's distance) and ask your teen to convert it to AU or to light travel time. If you have a computer, try running the Python code at a free online Python site.