Estimating the Moon Size

We first assume that the moon has been painted the correct size.  As the distance from the moon to the earth is almost constant, the angle subtended by the diameter of the moon is a constant 0.5.  This forms the entire basis of our arguments.   

Next, we select an object in the painting that we can estimate the size of in real life.  We then compare it to the diameter of the painted moon.  Let the diameter of the moon in the painting be D.  If the width or height of the object in the painting is nD, the angle subtended by it is n(0.5). 

Fig. 49 Angle subtended by an object relative to the moon.

We next make a judicious guess of nD in real life.  This value of nD, along with the value of n(0.5), will give us the distance from the painter to the object ( X1 or X2 ). 

Fig. 50 Calculating the distance between the painter and the object.

If the angle n(0.5) is small, tan[n(0.5)] sin[n(0.5)].  It follows that X1 X2.  Hence, either X1 or X2 will give a reasonable approximation of the distance between the painter and the object. 

If the distance from the painter to the object turns out to be ridiculously large, we can immediately suspect that the painter has represented the moon the wrong size.