How far away is the Sun?

How far away is the Sun?

This was an even more difficult question the Greek astronomers asked themselves, and they didn't do so well. They did come up with a very ingenious method to measure the sun's distance, but it proved too demanding in that they could not measure the important angle accurately enough. Still, they did learn from this approach that the sun was much further away than the moon, and consequently, since it has the same apparent size, it must be much bigger than either the moon or the earth.

Their idea for measuring the sun's distance was very simple in principle. They knew, of course, that the moon shone by reflecting the sun's light. Therefore, they reasoned, when the moon appears to be exactly half full, the line from the moon to the sun must be exactly perpendicular to the line from the moon to the observer (see the figure to convince yourself of this). So, if an observer on earth, on observing a half moon in daylight, measures carefully the angle between the direction of the moon and the direction of the sun, the angle a in the figure, he should be able to construct a long thin triangle, with its baseline the earth-moon line, having an angle of 90 degrees at one end and a at the other, and so find the ratio of the sun's distance to the moon's distance.

The problem with this approach is that the angle a turns out to differ from 90 degrees by about a sixth of a degree, too small to measure accurately. The first attempt was by Aristarchus, who estimated the angle to be 3 degrees. This would put the sun only five million miles away. However, it would already suggest the sun to be much larger than the earth. It was probably this realization that led Aristarchus to suggest that the sun, rather than the earth, was at the center of the universe. The best later Greek attempts found the sun's distance to be about half the correct value (92 million miles).