# Diameter of the Moon

##### Class Practical

An estimate of the diameter of the Moon using a photograph of a lunar eclipse.

#### Apparatus and materials

Photograph of a partial eclipse of the Moon, as below.

#### Health & Safety

Image courtesy of FreeDigitalPhotos.net.

#### Procedure

1 Enlarge a photograph of a partial eclipse of the Moon. Preferably get students to take this photograph themselves, firmly securing the camera during the exposure to avoid camera shake.

2 On the photograph, estimate the radius of the shadow-bite on the Moon and the radius of the moon itself. The diameter of the moon can be calculated if the diameter of the Earth is known (as from the experiment The Moon’s distance from Earth).

#### Teaching notes

1 The Greek method of estimating the distance of the Moon is to know the Moon’s diameter and then calculate that it is 110 Moon diameters away. See the experiment The Moon’s distance from Earth.

An early Greek method was to measure the time that the Moon spends in a total eclipse and work out from that the size of the Earth’s shadow in Moon diameters.

Diagrams to illustrate eclipses are often drawn with incorrect proportions as in figure 1 which shows an eclipse of the sun and in figure 2 which shows an eclipse of the Moon. However that figure does show how the Moon’s shadow just tapers to a point by the time it reaches the Earth. We know that must be so because the Sun and Moon look the same size. Also, in an eclipse of the Sun, the Moon just manages to blot the Sun out.

The true proportions are shown in figure 3. There you can imagine that you see the moon’s shadow tapering to nothing at the Earth and the Earth’s shadow also growing smaller with the same angle of taper.

By watching a total eclipse of the Moon, the Greeks found that the Earth’s shadow is 2.5 Moon diameters wide out at the Moon (found by rough timing methods). The shadow has had the whole radius of the Moon’s orbit in which to taper. Knowing that such tapering makes a shadow lose one Moon diameter in that distance, you expect the Earth’s shadow to be 3.5 Moon diameters just behind the Earth. Therefore the Earth’s diameter is 3.5 Moon diameters.

The Greeks already knew the diameter of the Earth, about 13,000 km and so they could then calculate the Moon’s diameter (3700 km). As the Moon is 110 Moon diameters away then the Moon’s distance from Earth is more than 400 000 km away.

When an eclipse happens today then the length of time for an eclipse is given and could be used in the measurements. (For the purist, these times are arrived at by using information which we are trying to calculate.)

This diagram illustrates why the true radius of the Earth is one moon diameter larger than its shadow of the Moon.

2 From the value obtained from the Moon’s diameter from this experiment and knowing that the Moon is 110 Moon diameters away from the Earth then the distance of the Moon can be calculated.

This experiment was safety-checked in July 2007