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How big Mars looks

Space and time · level 5, lesson 6 of 6

A question to start

Some months Mars is one of the brightest things in the night sky. Other months it is easy to miss. Why?

The idea

Mars and Earth both go round the Sun, so the gap between them keeps changing: from about 54.6 million km at closest to about 401 million km at farthest. That is more than 7 times as far.

How big Mars looks changes by the same factor:

  • At closest, Mars is about 25.6″ across.
  • At farthest, it is only about 3.5″.

It is brightest near opposition, when Earth passes between Mars and the Sun. Then Mars is opposite the Sun in our sky: it rises at sunset and is up all night. This happens about every 26 months.

Even at its biggest, Mars is about 70 times narrower than the Moon looks. A telescope magnifying 75 times makes it look about as wide as the Moon does to the eye.

closest: 25.6″farthest: 3.5″

Worked examples

1. At closest. \(57.3 \times \frac{6{,}792}{54{,}600{,}000} \approx 0.0071°\). Times 3,600: about 25.6″.

2. At farthest. \(57.3 \times \frac{6{,}792}{401{,}000{,}000} \approx 0.00097°\), about 3.5″.

3. The telescope. The Moon is about 1,870″ wide. \(1{,}870 \div 25.6 \approx 73\). A telescope magnifying 73 to 75 times makes Mars look Moon-sized.

Try it

  1. Why does Mars look bigger some months than others?
  2. What is opposition?
  3. How many times bigger does Mars look at closest than at farthest?
  4. Mars is 100 million km away. About how many arcseconds wide does it look?
Answers
  1. Its distance from Earth changes a lot as the two planets go round the Sun.
  2. When Earth is between Mars and the Sun, so Mars is opposite the Sun in our sky.
  3. \(25.6 \div 3.5 \approx 7\) times.
  4. \(57.3 \times \frac{6{,}792}{100{,}000{,}000} \times 3{,}600 \approx 14″\).

Common mistake

"Mars is brightest when it is high in the sky." Its brightness depends mostly on its distance from Earth, so it is brightest near opposition, wherever it is in the sky.

Where it leads