Cosmos Notebook

Library · Experiment

Measure the Sun's diameter with a pinhole

Project a tiny image of the Sun through a pinhole and use similar triangles to work out how big our star is.

Astrophysics
Time
1 sunny hour
Cost
£0
Difficulty
1 of 3

Part of Measuring the Solar System (Measure the Sun)

Safety first. Never look at the Sun — not directly, not through the pinhole, not through binoculars, a telescope or a camera. In this experiment you stand with your back to the Sun and only look at the image on the card.

The question

The Sun is about 150 million km away. If I measure how big its image is through a pinhole, can I work out its real diameter?

Learn just enough first

  • Look up how a pinhole camera makes an image, and why it's upside down
  • Revise similar triangles

Kit

  • Two pieces of stiff white card, or a long cardboard box or poster tube (longer is better: 1–2 m)
  • Kitchen foil, tape and a pin
  • Ruler with millimetres, and a tape measure

My prediction

How many times wider than the Earth (12,700 km) do you think the Sun is?

Method

  1. Cut a small window in one card, tape foil over it and make one clean pinhole about 1 mm across.
  2. With your back to the Sun, hold the pinhole card so sunlight passes through it onto the second card (or the far end of the box). You'll see a small bright disc: that's the Sun.
  3. Move the cards apart until the disc is as large as you can get it while still sharp-edged — 1.5 to 2 m works well. Measure the distance \(L\) between pinhole and image.
  4. Measure the image's diameter \(d\) in millimetres. Measure across several directions and average.
  5. Repeat at two or three different distances.

Data

Distance \(L\) (mm)Image diameter \(d\) (mm)Ratio \(d / L\)

Result

The rays through the pinhole make two similar triangles — one from the Sun, one to your card — so

$$ \frac{D_\text{Sun}}{\text{distance to Sun}} = \frac{d}{L} \quad\Rightarrow\quad D_\text{Sun} = \frac{d}{L} \times 1.496 \times 10^{8}\ \text{km} $$

The accepted diameter is about 1.39 million km, so \(d/L\) should be close to 1/108. A 2 m distance gives an image about 18.6 mm across. The pinhole itself blurs the edge a little: subtracting the pinhole's width from \(d\) is a good correction.

Explain it to a friend

The Sun and its pinhole image make the same shape of triangle, just at different sizes. Knowing how far away the Sun is, the ratio of the image's size to its distance from the pinhole scales straight up to the size of the Sun — about 109 Earths across.

New questions

  • Why are the dappled patches of sunlight under a tree all round?
  • During a partial eclipse, what shape would the pinhole image be?