How Big is the Sun?

In very rounded figures (so that the mathematically adept can easily calculate in their heads), the earth is about 100 million miles from the sun, and the moon is about one quarter of a million miles from the earth. The diameter of the moon is one quarter of the earth's diameter of 8000 miles. What is the diameter of the sun?

Answer:

800,000 miles.

Explanation: According to the information given, the diameter of the moon is 2000 miles. Also, according to the information given, the sun is 400 times as far from the earth as the moon. Since the apparent size of objects in line of sight is proportional to the distance (if you don't understand this statement, see the diagram below), then an object 400 times as far away from our eyes as a nearer object will be 400 times as large if the image appears the same size to our eyes. How do we know the relative size of the image of the moon versus the image of the sun to our eyes? That is easy if you have ever seen a solar eclipse (or a picture of one). By coincidence, the disc of the moon almost perfectly covers the disc of the sun, so that their images are the same size from our point of view. Therefore, the ratio of the diameters of the moon and sun are in a direct proportionality of 400 to 1, and 400 times 2000 equals 800,000.