# How big is the Moon?

## How do you measure the size of the Moon using triangles?

### You will need:

- A ruler or measuring tape
- A 5 cent coin
- BluTac
- Scissors
- You must be able to see the Moon, a Full Moon near the horizon is preferable but you can do it during the day if it is visible.

### What to do:

- This activity is best done when the Moon is close to a Full Moon. Sydney Observatory has a Moon Phase Calendar that will help you find a suitable date:
- Attach the 5 cent coin to an object such as the top of a fence or small pole with the BluTac.
- Stand with the coin between you and the Moon as shown by the diagram.
- Move forward or backward until the Moon appears to be the same size as the disc in front of it.
- Measure the distance from the disc to your eyes in metres. You may need to do this measurement a number of times and calculate the average.
- Use the mathematical formula below to calculate the diameter of the Moon. It uses the concept of ratios.

### What is happening?

Mathematics has always been important to astronomers. It has helped them to calculate distances and events in astronomy such as eclipses, rising times of planets and tides. In ancient Greek times, the mathematician Erastosthenes was able to calculate the diameter of the Earth by measuring the angle of shadows in two different places at the same time of the year.

Astronomers were able to calculate the distance to the Moon by observing its position in the sky from two different locations on the Earth, similar to Erastosthenes’ experiment. Using a mathematical form of measurement known as parallax, they could calculate the distance. Once this measurement was accurately known, astronomers used the mathematical technique of similar triangles to calculate the diameter of the Moon.

Today telescopes equipped with lasers are aimed at the Moon’s surface to calculate its distance to an accuracy of 30cm. Australia currently has two of these Satellite Laser Ranging Facilities, one on Mount Stromlo near Canberra and one at Yarragadee, south east of Geraldton in Western Australia. You can find out more here.