Of all the heavenly bodies visible in the night from the Earth, the Moon is the most spectacular. It far outshines even the most brilliant planet, moves so quickly that you can see its motion against the stars, and provides a wealth of detail in the shadowy features of its disc. Yet its motion is the most difficult to predict and it is for that reason we have left it until last. It is of course in orbit about the Earth but the Sun and other members of the Solar System perturb that orbit to such an extent that many corrections are needed to calculate the Moon's position accurately.

In the next few sections we use a simple method to find the position of the Moon. The method takes account only of the principle perturbations to the orbit yet gives results which are accurate enough for most purposes. We also calculate the times of moonrise and moonset, the phases of the Moon, and the circumstances of both solar and lunar eclipses. The calculations are lengthy but the satisfaction you feel when you accurately predict, for example, the occurrence of a lunar eclipse, cannot be denied.

The Moon's orbit

To an Earth-bound observer, the Moon appears to be in orbit about the Earth, making one complete revolution with respect to the background of stars in 27.3217 days. This period is called the sidereal month. During this time the Earth moves on along its own orbit so that the Sun's position changes with respect to the stars.