Subtending an Angle

It is a well-known fact that the moon occupies only a tiny portion of the hemispherical vault of the heavens.  Yet there are many artists who exaggerate the size of the moon on purely aesthetic grounds.  There is a simple mechanism by which we can check if a painting has its moon painted the correct size.

Prior to a discussion of the approximation method, it is imperative to understand what is meant by “subtending an angle”.  Consider an observer shown in Fig. 48.  The object under scrutiny is in the observer’s pyramid or cone of vision.  The angle subtended by the object is then defined as the angle q between the two limiting rays to the eye. 

Fig. 48 – Angle subtended by an object.

It follows that as the distance L between the observer and the object decreases, the angle subtended by the object increases.  Hence, q is inversely proportional to L.