Library · Experiment
Measure distance by parallax
Start with your thumb jumping as you blink, then measure the distance to a faraway landmark — the same idea astronomers use for the nearest stars.
- Time
- 1 afternoon
- Cost
- £0
- Difficulty
- 2 of 3
Part of Measuring the Solar System (Find your way around)
The question
Astronomers measure the distance to nearby stars by how much they shift against the background as the Earth goes round the Sun. Can I measure the distance to something across a field the same way, without walking to it?
Learn just enough first
- Hold your thumb up at arm's length and blink one eye, then the other. Watch it jump against the background — that jump is parallax
- Look up the small-angle rule: an angle in radians ≈ size ÷ distance
- Read how the parsec is defined from parallax
Kit
- A long tape measure (20 m or more) or a measured stride
- A protractor taped to a board, with a drinking straw pinned at its centre as a sight (or a phone compass app)
- An open space with a landmark 50–150 m away — a tree or post — and something much further behind it (a distant hill or building)
My prediction
Guess the distance to your landmark before measuring. Then check it later on an online map's "measure distance" tool.
Method
- The thumb version: measure the distance between your pupils (about 6 cm) and how far your thumb is from your eyes. Estimate the jump angle, then flip it round: from the angle and your eye spacing, work out your arm's length.
- The real measurement: mark point A. Sight along the straw to the landmark and note the angle between it and the far-off background object.
- Walk sideways — at right angles to the landmark — a measured baseline \(B\) of 20–30 m to point B. Take the same reading.
- The difference between the two angles is the parallax angle \(p\). Take each reading three times. Keep clear of roads while you do this.
Data
| Point | Angle to landmark from background object (°) |
|---|---|
| A | |
| B |
Baseline \(B\) = __ m. Parallax \(p\) = __ °.
Result
Convert \(p\) to radians (multiply degrees by \(\pi/180\)). For small angles,
For stars, the baseline is the Earth's orbit. A star whose parallax is 1 arcsecond (1/3600 of a degree), measured from a baseline of 1 astronomical unit, is by definition 1 parsec away — about 3.26 light years. The nearest star, Proxima Centauri, has a parallax of only about 0.77 arcseconds.
Explain it to a friend
Things that are closer seem to shift more when you move. Measure how far you moved and how much something shifted, and you can work out how far away it is. Astronomers do exactly this with the Earth's orbit as the baseline — it's how we know the distances to nearby stars.
New questions
- How much does a 1° error in my angles change the answer? Would a longer baseline help?
- Why can't we measure the distance to faraway galaxies this way?