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How big is Mars?

Measurement · level 4, lesson 7 of 7

A question to start

Mars is about half as wide as Earth. So you might guess it is about half as big. But "big" can mean three different things: how wide, how much surface, how much space inside.

  • Across the middle, Mars is about half as wide as Earth.
  • All the land on Mars put together is about as big as all the dry land on Earth, even though Earth's land is only a small part of Earth's surface.
  • It would take between six and seven Mars-sized balls (melted down and poured in) to fill the space inside Earth.

Half, about equal, and a seventh: three true answers to "how big?". This lesson uses everything from this level, lengths, areas and volumes, to see how they can all be true at once.

The idea

The measurements

Spacecraft have measured Mars very carefully. Here are the diameters (the distance straight across, through the middle) of three worlds. Mars and Earth are both a little squashed, slightly wider at the equator than from pole to pole, so these are averages.

World Diameter (about)
Earth 12 742 km
Mars 6 779 km
the Moon 3 475 km

Compare them by dividing. \(6779 \div 12\,742 \approx 0.53\), so Mars is about 0.53 times as wide as Earth: a little more than half. Two Marses side by side would be \(2 \times 6779 = 13\,558\) km wide, just a bit wider than Earth.

Earth: 12 742 kmMars: 6 779 kmMars: 6 779 km 13 558 km

The Moon is about \(3475 \div 6779 \approx 0.51\) times as wide as Mars, about half again.

Drawing them to scale with a ruler

A scale drawing shrinks every length by the same amount, so the drawing keeps the right shape and the right comparisons. Choose a scale where 1 cm on the page stands for 1000 km. Then:

  • Earth's circle has a diameter of \(12\,742 \div 1000 \approx 12.7\) cm;
  • Mars's circle has a diameter of \(6779 \div 1000 \approx 6.8\) cm;
  • the Moon's circle has a diameter of \(3475 \div 1000 \approx 3.5\) cm.

With a ruler and a pair of compasses (or round things to trace) you can draw all three on one sheet. Here they are, smaller, but still to the same scale as each other:

EarthMarsMoon 2000 km

A ball model

You can build the same comparison in three dimensions with balls. Let a basketball, about 24 cm across, be Earth. Every real length is then shrunk by the same factor, so each model size is the real size × (24 cm ÷ 12 742 km).

  • Mars: \(24 \times 6779 \div 12\,742 \approx 12.8\) cm: about the size of a large grapefruit.
  • The Moon: \(24 \times 3475 \div 12\,742 \approx 6.5\) cm: about the size of a tennis ball.

Now place them. The Moon is about 384 400 km from Earth. In the model that is \(384\,400 \times 24 \div 12\,742 \approx 724\) cm, about 7 metres: across a classroom. When Mars is at its very closest to Earth, it is still about 55 million km away. In the model that is about 1 km, a long walk down the road, for a grapefruit. And the Sun would be a ball about 26 metres across. Space is mostly empty.

Around the middle

The distance around a circle is a bit more than 3 times its diameter. The exact number, about 3.14, is called \(\pi\) ("pi"); you will meet it properly in Geometry. So:

  • around Earth's middle: about \(3.14 \times 12\,742 \approx 40\,000\) km;
  • around Mars's middle: about \(3.14 \times 6779 \approx 21\,300\) km.

Notice that the distance around is also about 0.53 times as long for Mars. Every length on Mars, compared with the matching length on Earth, is multiplied by the same 0.53.

Surface: square the comparison

In level 3 you found that making every length 2 times as long makes an area \(2 \times 2 = 4\) times as big. The same rule works for any number, including 0.53. Mars's surface is about

\[0.53 \times 0.53 \approx 0.28\]

times Earth's surface: a bit more than a quarter. Now the surprise from the start. On Earth, oceans cover most of the surface; dry land is only about 29 out of every 100 parts, about 0.29. So the whole surface of Mars (0.28 of Earth's surface) is about the same as all of Earth's dry land (0.29 of Earth's surface). Mars has no oceans, so all of it is land. In numbers, Mars's surface is about 144 million km², and Earth's land about 149 million km².

Volume: cube the comparison

In lesson 5, making every edge 2 times as long made the volume \(2 \times 2 \times 2 = 8\) times as big. For Mars, every length is 0.53 times Earth's, so its volume is about

\[0.53 \times 0.53 \times 0.53 \approx 0.15\]

times Earth's volume: about 15 parts in 100. And \(1 \div 0.15 \approx 6.6\), so it would take between six and seven Marses to fill Earth. Halving the width cuts the volume to an eighth; Mars is a bit more than half as wide, so it has a bit more than an eighth of the volume.

So all three answers in the opening question come from one number, 0.53, used once for length, twice for area and three times for volume.

Big things on a smaller planet

Mars is smaller than Earth, but some of its features are enormous.

  • Olympus Mons, a volcano, rises about 22 km above the land around it, compared with under 9 km for Mount Everest above sea level. It is about two and a half Everests tall.
  • Valles Marineris, a huge system of canyons, is about 4000 km long, longer than the straight-line distance from Toronto to Vancouver (about 3400 km).

Mars also pulls less strongly. Its mass is only about a tenth of Earth's, and a person standing on Mars would weigh a bit less than two fifths of what they weigh on Earth (their mass would not change; see Mass and capacity).

Worked examples

1. A scale drawing. At 1 cm for 500 km, how wide is Mars's circle?

\(6779 \div 500 \approx 13.6\) cm. (Earth's would be \(12\,742 \div 500 \approx 25.5\) cm, too wide for a page held upright.)

2. A smaller ball model. If Earth is a ball 30 cm across, how big is Mars?

Mars is about 0.53 times as wide: \(30 \times 0.53 \approx 16\) cm. (More exactly, \(30 \times 6779 \div 12\,742 \approx 16.0\) cm.)

3. Driving round Mars. A car drives around Mars's middle at 100 km per hour, without stopping. How long?

\(21\,300 \div 100 = 213\) hours. A day is 24 hours, and \(213 \div 24 \approx 8.9\), so about 9 days non-stop.

4. Comparing areas with squares. The Moon is about 0.51 times as wide as Mars. About what part of Mars's surface is the Moon's surface?

\(0.51 \times 0.51 \approx 0.26\): about a quarter.

5. Comparing volumes. How many Moons would fill Mars (melted down)?

Volume compared: \(0.51 \times 0.51 \times 0.51 \approx 0.13\). Then \(1 \div 0.13 \approx 7.5\): about 7 or 8 Moons.

6. Olympus Mons on the model. On the basketball model (Earth 24 cm), how tall would Olympus Mons be?

Shrink 22 km the same way: \(24 \times 22 \div 12\,742 \approx 0.04\) cm, which is 0.4 mm: thinner than a sheet of card. Even the biggest volcano in the solar system is a tiny bump on its planet.

Try it

  1. Write the three diameters (Earth, Mars, Moon) rounded to the nearest thousand kilometres. Which is about half of which?
  2. At a scale of 1 cm for 2000 km, how wide would you draw Earth, Mars and the Moon?
  3. In a model where Earth is a ball 10 cm across, about how wide is Mars? The Moon?
  4. Every length on a model car is \(\tfrac{1}{10}\) of the real car. What part of the real car's paint area does the model's paint cover? What part of the volume?
  5. About how far is it around Mars's middle, to the nearest thousand kilometres? If you walked 30 km every day, how many days would it take?
  6. Mars's surface is about 0.28 of Earth's surface. Earth's surface is about 510 million km². About how big is Mars's surface?
  7. Mars is about 0.53 times as wide as Earth. A friend says "so Mars has 0.53 of Earth's volume". What would you tell them?
Answers
  1. Earth about 13 000 km, Mars about 7000 km, Moon about 3000 km. Mars is about half of Earth, and the Moon is about half of Mars.
  2. Earth \(12\,742 \div 2000 \approx 6.4\) cm; Mars \(6779 \div 2000 \approx 3.4\) cm; Moon \(3475 \div 2000 \approx 1.7\) cm.
  3. Mars about \(10 \times 0.53 \approx 5.3\) cm. The Moon about \(10 \times 3475 \div 12\,742 \approx 2.7\) cm.
  4. Area: \(\tfrac{1}{10} \times \tfrac{1}{10} = \tfrac{1}{100}\) of the paint. Volume: \(\tfrac{1}{10} \times \tfrac{1}{10} \times \tfrac{1}{10} = \tfrac{1}{1000}\).
  5. About 21 000 km. At 30 km a day, \(21\,000 \div 30 = 700\) days: nearly two years (and there are no oceans to stop you).
  6. \(0.28 \times 510 \approx 143\) million km², close to the 144 million km² found more exactly.
  7. Volume grows with all three directions, so multiply three times: \(0.53 \times 0.53 \times 0.53 \approx 0.15\). Mars has only about 0.15 of Earth's volume, not 0.53.

Common mistake

Using the length comparison for area or volume. "Half as wide, so half as big" is only true for lengths. For areas, multiply the comparison by itself (twice in all); for volumes, three times. Half as wide means a quarter of the surface and an eighth of the volume.

Mixing scales in one model. If the Earth ball is to one scale and the distance to the Moon to another, the model tells you nothing about the real distance. Use one scale factor for every length in a model.

Where it leads