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Angles in the sky

Space and time · level 5, lesson 1 of 6

A question to start

Hold your little finger out at arm's length. Can it cover the full Moon?

The idea

Astronomers cannot measure the sky in metres, because they do not know how far away things are. So they measure angles.

  • A full circle round the sky is 360°. From the horizon to straight overhead is 90°.
  • Each degree splits into 60 arcminutes (60′).
  • Each arcminute splits into 60 arcseconds (60″). So \(1° = 3{,}600″\).

The Sun and the Moon both look about half a degree wide, about 31′. Planets look far smaller: Mars is never more than about 26″ across, so small that it looks like a dot without a telescope.

about 0.5°, or 31′angle drawn larger than it really is

Worked examples

1. Converting. The Moon is about 0.52° wide. \(0.52 \times 60 \approx 31\) arcminutes.

2. Mars at its biggest. 26″. \(26 \div 3{,}600 \approx 0.0072°\), about 70 times smaller than the Moon.

3. Your finger. A finger about 1.5 cm wide, held 60 cm from your eye, covers about \(57.3 \times \frac{1.5}{60} \approx 1.4°\). That is nearly three full Moons. (Where 57.3 comes from is in the next lesson.)

Try it

  1. How many arcseconds are in one degree?
  2. About how wide do the Sun and the Moon look?
  3. Convert 2° to arcminutes.
  4. Could your little finger at arm's length cover the full Moon?
Answers
  1. 3,600.
  2. About half a degree each.
  3. \(2 \times 60 = 120′\).
  4. Yes, easily: a finger covers more than 1°, and the Moon is only about 0.5°.

Common mistake

"The Moon looks as big as a plate." It covers only half a degree, less than your finger at arm's length. It just seems large near the horizon.

Where it leads