Let AB represent a fixed star, and CD the moon.
AB, though much the larger body, will appear no bigger than EF; whereas the moon (CD) will appear as big as the line CD to the spectator G.
The moon is 240,000 miles from the earth, not quite a quarter of a million of miles. The nearest fixed stars are 20,000,000,000,000. (i. e.. 20 billions.)
If a ball went 500 miles an hour, it would reach the moon in twenty days: but it would not reach the nearest fixed star in 4,500,000 years. Had it begun, therefore, when Adam was created, it would be no further on its journey than a coach (which has to go from the bottom of Cornwall to the top of Scotland) after it has past about three-quarters of a mile.
Q. Why does the moon (which is a sphere) appear to be a flat surface?
A. It is so far off, that we cannot distinguish any difference between the length of the rays which issue from the edge, and those which issue from the centre.
The rays AD and CD appear to be no longer than the ray BD; but if all the rays seem of the same length, the part B will not seem to be nearer to us than A and C, and therefore ABC will look like a flat or straight line.
The rays AD and CD are 240,000 miles long.
The ray BD is 238,910 miles long.
Q. Why do the sun and stars (which are spheres) appear to be flat surfaces?
A. Because they are such an immense way off, that we can discern no difference of length between the rays which issue from the edge, and those which issue from the centre of these bodies.
The rays AD and CD appear no longer than BD; and as B appears to be no nearer than A or C, therefore ABC must all seem equally distant; and ABC will seem a flat or straight line. (See last figure.)
Q. Why does distance make an object invisible?
A. Because the angle (made by the perpendicular height of the distant object with our eye) is so very acute, that one line of the angle merges in the other.