Determination of Diameter of Moon

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Let moon be the astronomical object of diameter D. Let E be the point on earth's surface. A telescope is focused on moon's surface and its image is observed as shown in figure   is measured. S is the distance between moon and the Earth's surface.

 The diameter AB of moon is considered as a circular arc of radius S.

Diameter of the moon can be found by knowing q and S.

This above formula holds good only if S is very large and D can be considered as a small arc of radius S.

Determination of distance of moon from earth (by parallax method)

Let the object O be viewed with our eyes which is at a distance of r, making an angle q between the two eyes as shown in the diagram.

The angle q, caused by the two lines drawn from the position of the two eyes to the object, is called angle of parallax.

If we can consider OA and OB as radius of a circle and the distance x (AB) as arc of the circle, then we have

.

By knowing the values of x and q, the distance of the object from the point of observation can be found out.

However, if we consider O, referred in the above diagram to be the moon or a nearby star, then the angle q is too small in the view of the large astronomical distance and the place of observation. Hence, in order to have a better and valid point of observation, two points on the surface of the Earth is taken as the basis for observation instead of the two eyes. In order to have simultaneous observation of the moon, we select a very distant star at O and measure the angle between O and the two points on the Earth, as shown in the diagram below

Thus, the distance of the moon or a distant star from the Earth can be found out.