Chapter 3: The Copernican Revolution

Eratosthenes' measurement of the Earth's circumference. Syene (S) is located on the Tropic of Cancer, so that at summer solstice the Sun appears at the zenith, directly overhead. In Alexandria (A) the Sun is φ south of the zenith at the same time. So the circumference of Earth can be calculated being 360°/φ  times the distance δ between A and S. Erastothenes measured the angle φ to be 1/50 of a circle. His knowledge of the size of Egypt gave a north/south distance δ between Alexandria and Syene of 5000 stadia. His circumference of the Earth was therefore 250,000 stadia. Certain accepted values of the length of the stadia in use at the time give an error of less than 6% for the true value for the polar circumference.

The first real progress came in accurately measuring the size of the planet we live on. Eratosthenes did this with a dramatic application of geometric reasoning around 200 B.C. He was a researcher and librarian at the great library in Alexandria, Egypt, where books containing much of the knowledge of the ancient world were stored. He completed a catalog of the 675 brightest stars, but his most famous achievement was measuring the size of planet Earth. Told that the Sun at summer solstice shone straight down a well to the south, near Aswan, he noted that on the same date in Alexandria, the Sun's direction was off vertical by about 6°, or 1/50 of a circle. Eratosthenes realized that this difference was due to the curvature of the Earth and that the north-south distance from Alexandria to Aswan must be 1/50 of the circumference of the Earth. Measuring the distance in an ancient unit called stadia and multiplying by 50, he got an estimate of the Earth's size that was within (depending on the definition of stadia) 1-20% of the correct answer. At a time when few people traveled more than 50 miles in their lives, and when the first circumnavigation of the Earth was still more than 1000 years away, most educated Greeks knew the size of the planet they lived on! (And knew the Earth was round.)

The inner solar system.

At the same time that Galileo was working on rearranging the solar system, Kepler was working to define the mathematics behind the planets' motions. Using Kepler's laws, astronomers can give the relative distances of all the planets from the Sun, based strictly on observing how long it takes to complete a single orbit. This doesn't give the absolute distances in units like kilometers, however. The best we could do, with the distance between the Earth and the Sun as a constant, was express the rest of the distances using the Earth-Sun distance.

Photograph of John Harrison's H1 clock. 

There are two complications in using the parallax method to measure the distance to Venus. First, the Earth is spinning. The observations have to be made at exactly the same time, and an error in time measurement on a spinning planet leads to an error in distance, and thus an error in the measurement of parallax. Timekeeping is also important in navigation. The angle of stars can be used for navigation in latitude (for example, the use of Polaris). But accurate timekeeping is required for navigation in longitude. The Earth spins at 15° per hour, so a clock that is off by only half an hour after a long sea voyage would give a navigational error of 7.5° / 360° times the circumference of the Earth, or 1000 kilometers! Poor clocks were the reason for most shipwrecks and for the famously poor navigation of Christopher Columbus. This problem was solved in the middle of the 18th century when the British government realized that an accurate clock was the key to mastery of the seas. In response to a competition for a prize of £20,000, John Harrison produced a clock accurate to 5 seconds over 80 days, which is an outstanding timekeeping device in any era.

Jeremah Horrock's observation of Venus transit across the Sun in 1639. From his work Venus in sole visa, printed 1662

Another problem with observing a transit of Venus was that you had to be lucky since pairs of Venus transits only occur twice every 110 years. Before Johannes Kepler died in 1630, he predicted that a transit of Venus would occur in 1631 — but unfortunately, no one observed it because it happened during the night for European observers. A young astronomer and clergyman named Jeremiah Horrocks was able to predict and observe the next transit in 1639. He recorded a portion of the event until sunset obscured the remainder. Using the relative sizes of the disk of Venus and the disk of the Sun, he calculated the Earth-Sun distance to be 14,700 Earth radii (98 million kilometers), which was much better, and much larger, than any previous measurement.

Sketches of the 1769 Venus Transit, by Captain James Cook and Charles Green.

Knowing that a set of good observations of a Venus transit would fix the scale of the solar system, astronomers had to wait more than hundred years until the next pair of transits in 1761 and 1769. Edmond Halley predicted these transits in 1716. Aware that he would not live to see them, he urged future astronomers to make careful observations. His exhortations succeeded, and many scientific expeditions set out around the globe to get the necessary observations at well-separated latitudes. Even then, adventurers endured arduous sea voyages, only to be thwarted by pirates, typhoons, or clouds. Captain James Cook made a famous trip to observe the 1769 Venus transit in Tahiti. His observations, combined with those of other astronomers from around the world, established the distance from the Earth to the Sun to within 10% of its modern value of 150 million kilometers.