Science Puzzle
Solar Eclipse Geometry
During a total solar eclipse, the Moon covers the Sun almost perfectly. The Sun is about 1.4 million kilometres wide. The Moon is only 3,474 kilometres wide, about 400 times smaller.
How can the tiny Moon cover the enormous Sun so exactly?
The Answer
Because the Sun is also about 400 times further away. The Moon is 384,000 km from Earth; the Sun is 150 million km away, almost exactly 400 times the distance.
Angular size depends on both the real size and the distance. An object twice as far appears half the size. If one object is 400 times larger but also 400 times further away, both objects subtend the same angle at the observer's eye and appear the same size in the sky.
This is an extraordinary coincidence. No other planet in the solar system has a moon that produces such precise total eclipses. Astronomers note that this has given us useful opportunities to study the Sun's corona, and philosophers note that it is one of the more striking accidents in our corner of the universe.
The principle: Angular diameter. The apparent size of an object depends on its actual size divided by its distance. Two objects subtend the same angle if their size-to-distance ratios are equal, regardless of their true sizes.