Head office, Rana Pratap Bagh, Delhi011 2721 1512+91 97116 99511

Science project idea

Parallax: measuring distance to a tree with a thumb and your eyes

A nearby object appears to shift against a far background when you view it from two places. Measuring the shift and the baseline gives its distance, the same method astronomers use for nearby stars.

Make it yourself8 numbered steps, the materials and the science, all free.Go to the stepsGet a ready-made kitReady-made models, kits and spare parts in the store under Science.Browse ScienceAsk on WhatsAppAsk the head office whether a model or kit for this idea is available.Send a message

What it shows

A nearby object appears to shift against a far background when you view it from two places. Measuring the shift and the baseline gives its distance, the same method astronomers use for nearby stars.

The science

When you see a nearby object from two points separated by a baseline b, it appears at two different angles against the distant background. If the angular shift is p, the distance d to the object is about b divided by tan p, or b / p when p is in radians and small. Your own eyes are about 6.5 cm apart, so a thumb at arm’s length 65 cm away shifts by about 6 degrees. For stars the baseline is the Earth’s orbit, with a width of 300 million km, and the shifts are less than one arc second even for the nearest star.

Materials

Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.

  • A measuring tape of 5 m or more
  • A long straight ruler or a marked stick
  • A nearby object such as a tree, pole or post on open ground
  • A distant background such as a building or hill
  • Two flags or pencils for baseline ends
  • A phone camera on a tripod or steady surface
  • A calculator with tan inverse

Safety

For this project: Do the work in a safe open space away from traffic and ask an adult to supervise. Do not look at the Sun.

Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.

All the safety rules

Step by step

8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.

  1. Measure the distance between your eyes with a ruler, about 6 to 7 cm, and the length of your arm.

  2. Hold your thumb up at arm’s length and look at a distant object with one eye shut and then the other. Notice the thumb jumps sideways against the background.

  3. Calibrate: the thumb is a known distance away, so the shift in terms of the background object’s width gives your eyes’ angle. Measure the shift as a fraction of a known width on the far building.

  4. To measure the tree, face it and pick a distant object that lies behind it. Mark the baseline of 3 m along the ground, at right angles to the line to the tree.

  5. From each end of the baseline take a photo of the tree with the same zoom and note the angle the tree appears to move against the background, using the phone’s horizontal field of view or a protractor on a sighting board.

  6. Calculate the distance using distance = baseline / tan(angle).

  7. Measure the distance directly with the tape or by pacing and compare the two values.

  8. Repeat with a baseline of 1 m and with 6 m and see which gives the more reliable result.

What you should see

A distance to the tree that agrees with the tape within about 10 to 15 per cent, and a clear sense that a longer baseline gives a larger shift that is easier to measure.

Viva questions

A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.

1What is parallax?

The apparent shift of a nearby object against a far background when the observer moves.

2Why does a longer baseline work better?

It makes a bigger angle, which is easier to measure accurately.

3What baseline do astronomers use for stars?

The diameter of the Earth’s orbit around the Sun, by looking six months apart.

4Why can parallax not measure the distance to very faraway stars?

The shift becomes too tiny to measure.

Free ebook: Viva Questions for Science Projects

Take it further

Estimate the distance to a hill or a building at least 500 m away using a baseline of 20 m and compare with a map.

Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.

Free ebooks for this project

WhatsApp us