There exists a folk tale that the size of the Moon is larger when it is near the horizon than when it is high in the sky. To prove this fact or refute it, it is necessary to do an experiment and measure the size of the Moon in both positions. More than that, it is very important to estimate the real size of the Moon in the end of this experiment.
For measurement of the apparent size of the Moon, the method with the ruler is chosen. It seems to be the easiest and most available for everybody way of estimating the Moon size.
The measurement of the Moon width with the help of the ruler has shown the following results. The width of the Moon in its widest part to the nearest 0,1° is 0, 7 cm, the distance from the eye to the ruler is 65 cm.
According to these figures, the angular diameter has been estimated with the help of the equation ??″ =206265, where D is the distance between fingers, and d is the distance from the eye to the ruler. The estimated angular diameter is about 2221″. The same actions have been done to measure the size of the Moon when it is higher in the sky. This time the figures are as follows: D=0,5 cm, d=65 cm. Accordingly, the angular diameter of the Moon is about 1587″.
Unfortunately, it cannot be regarded as absolutely accurate result. According to this method the angular diameter of the Moon changes when it changes position. It is also very important to mention that the moon is viewed differently in different parts of the world. Moreover, people see the Moon from different distances. The distance From the Moon to the viewer also changes its size.
As for the possible errors during the measurement, there can be a lot of them. Slightest change in both distance to the ruler or distance between the fingers changes the outcome. For example, if we change the distance to the ruler from 65 cm to 62 cm the angular diameter of the Moon changes from 2221″ to 2329″. This fact shows the imperfection of this method. Errors can also be made because of the imprecise measurement instrumentation. In this case, it is impossible to measure accurately the width of the Moon.
It is also true that the Moon seems to be bigger near the horizon than it is high in the sky. Nevertheless, there exists a common mistake that the atmosphere of the Earth influences the size of the Moon. Though, it is not so. It is the so-called "moon illusion" (Simanek, 2010). This type of the illusion can exist with other objects at long distances, for example, mountains, clouds or the Sun. According to the theory of apparent size, the visual size of an object depends on the size of other objects surrounding it. Near the horizon the Moon is in the surrounding of such objects as mountains, fields, trees against the background of which it seems to be bigger. In such position the Moon is thought to be closer to the viewer. It is just an optic illusion.
Finally, to identify the actual diameter of the Moon the figures of the experiment and the distance from the centre of the Earth to the centre of the Moon are necessary. The actual diameter of the Moon is calculated with the help of the equation where x is the actual diameter of the Moon which is about 4092 km. This calculation shows inaccurate results, as according to the sources, the factual diameter of the Moon is 3474,8 km.
Having performed these experiments and identified the actual size of the Moon, the conclusion about imperfect nature the ruler method of the angular diameter of the Moon measuring. Any error made during the experiment influences the outcome and does not allow estimating the actual size of the Moon.
Simanek, Donald E. (June 2010). The Moon illusion, an unsolved mystery.