(10a) The Scale of the Solar System

  Remember how Hipparchus estimated the distance of the Moon? In a solar eclipse which was total in one location, at another location about 1000 kilometers away, only 80% of the Sun was covered. The body blocking the Sun--the Moon--was close enough that moving an observer by about 1000 kilometers shifted its apparent position in the sky by 1/5 the apparent size of the Sun, or about 0.1 degree.

  Tycho still accepted the erroneous estimate by Aristarchus of the Sun's distance, 20 times smaller than the actual one (see section about Aristarchus). Since the Sun's distance sets the scale of the entire solar system, Tycho believed Mars was close enough for its apparent position in the sky to be shifted measurably as the Earth's rotation carried an observer from one side of the globe to the other. Actually, the solar system is much bigger, and the shift was too small to be seen by Tycho's pre-telescope equipment. The story (which has additional twists) is told in "Tycho and the ton of gold" by Owen Gingerich in "Nature", vol 403, p. 251, 20 January 2000.

  If we know the proportions of all the orbits in the solar system, measuring just one actual distance in kilometers gives the scale of all orbits around the Sun. Kepler suggested measuring the distance to the planet Mercury when it passed in front of the Sun, but (as Halley noted) Venus is closer and offers a better choice. Now and then Venus passes in front of the Sun, and a telescope observing the Sun (by projecting its image, or using a dark filter) sees its dark disk on the bright solar background. By comparing where on the Sun's disk is the crossing seen from two far-apart points on Earth, and comparing the times Venus was observed crossing the edge of the Sun, one can calculate the distance to Venus and from it the scale of the solar system.

  Unfortunately, this never happened during Halley's lifetime. "Transits of Venus" occur in pairs, more than a century apart. One occured in 1639--too early. The next ones did not take place until 1761 and 1769, and astrtonomers were prepared for them. One of the goals of the famous expedition by Captain James Cook to the Pacific Ocean was to observe the transit from a point far from other observers.

  No transits of Venus occured in the 20th century, but the next one is due on June 8, 2004. Things being the way they are, you may very well have an opportunity to watch it over the world-wide web. To get ready, read the book June 8, 2004: Venus in Transit by Eli Ma'or, Princeton University Press, 2000, 186 pp., $22.95 (reviewed by Don Fernie in "Nature" vol 406, p. 562, 10 August 2000).

  Later astronomers realized that some asteroids passed quite close to Earth. Today we worry about any actually hitting us--but their discovery also made some astronomers happy. Because of their nearness, their distance could be measured much more accurately and it gave a much better estimate of the AU. Still later the giant radio telescope whose (fixed) dish is nestled in a valley near Arecibo, Puerto Rico, was used as a radar to bounce signals off the planet Venus, and timing their "echo" gave an even more accurate estimate of the AU. Today, of course, we also can use the orbital mechanics of space probes, tracked by radio as they pass near major planets.