What it shows
An object’s apparent size depends on its distance. A coin held at arm’s length that just covers the Moon gives the Moon’s angular size, about half a degree, and then its real diameter can be estimated.
The science
Angular size is the angle the object takes up in your view. For small angles it is the width divided by the distance, in radians. If the coin just covers the Moon at a distance d from your eye, the Moon’s angle equals coin width divided by d, and the Moon’s diameter equals that angle multiplied by the Moon’s distance.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A one-rupee coin of known width, 2.5 cm
- A metre ruler or a long stick
- A friend to measure
- A notebook and calculator
- A reference for the Moon’s distance, about 384,000 km
Safety
For this project: Observe from a safe place at night with an adult, and do not walk backwards while looking up.
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 rulesStep 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.
Tape the coin to the end of the ruler or stick so it is standing upright.
Hold the other end of the ruler against your cheek so the coin is a distance from your eye you can measure.
Look at the full Moon and move the coin until it just covers it, as seen with one eye.
Measure the distance from the coin to your eye with a tape.
Divide the coin diameter by this distance to find the angle in radians.
Change radians to degrees by multiplying by 57.3.
Multiply the angle in radians by 384,000 km to estimate the Moon’s diameter.
Compare with the true value of about 3,474 km and write the percentage error.
What you should see
An angle near 0.5 degrees and a Moon diameter of roughly 3,000 to 4,000 km, showing that a household coin can be used for astronomy.
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 angular size?
The angle an object covers in the view of the observer.
2Why does the Moon look the same size as the Sun?
The Sun is about 400 times wider but also 400 times farther.
3Why use one eye?
Two eyes give two slightly different views and spoil the match.
4What are the main errors?
Judging when the coin just covers the Moon, and the distance measurement.
Take it further
Measure the Moon near the horizon and high in the sky to test the Moon illusion.
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
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