Wonders of the Universe

THE SEARCH FOR A COSMIC CLOCK

In the early seventeenth century, King Philip III of Spain offered a prize to anyone who could devise a method for precisely calculating longitude when out of sight of land. The technological challenge of building sufficiently accurate clocks was too great, so scientists began to look for high-precision natural clocks, and it seemed sensible to look to the heavens. Galileo, having discovered the moons of Jupiter, was convinced he could use the orbits of these moons as a clock, as they regularly passed in and out of the shadow of the giant planet. The principle is beautifully simple; Jupiter has four bright moons that can be seen relatively easily from Earth, and the innermost moon, Io, goes around the planet every 1.769 days, precisely. One might say that Io’s orbit is as regular as clockwork, therefore by watching for its daily disappearance and re-emergence from behind Jupiter’s disc you have a very accurate and unchanging natural clock. Thus by using the Jovian system as a cosmic clock, Galileo devised an accurate system for keeping time. Observing the eclipses of these tiny pinpoints of light around three-quarters of a billion kilometres (half a billion miles) from Earth from a rolling ship was impractical, however, so although the logic was sound, Galileo failed to win the King’s prize. Despite this, it was clear this technique could be used to measure longitude accurately on land, where stable conditions and high-quality telescopes were available. Thus observing and cataloguing the eclipses of Jupiter’s moons, particularly Io, became a valuable astronomical endeavour.

By the mid-seventeenth century, Giovanni Cassini was leading the study of Jupiter’s moons. He pioneered the use of Io’s eclipses for the measurement of longitude and published tables detailing on what dates the eclipses should be visible from many locations on Earth, together with high-precision predictions of the times. In the process of further refining his longitude tables, he sent one of his astronomers, Jean Picard, to the Uraniborg Observatory near Copenhagen, where Picard employed the help of a young Danish astronomer, Ole Romer. Over some months in 1671, Romer and Picard observed over one hundred of Io’s eclipses, noting the times and intervals between each. He was quickly invited to work as Cassini’s assistant at the Royal Observatory, where Romer made a crucial discovery. Combining the data from Uraniborg with Cassini’s Paris observations, Romer noticed that the celestial precision of the Jovian clock wasn’t as accurate as everyone had thought. Over the course of several months, the prediction for when Io would emerge from behind Jupiter drifted. At some times of the year there was a significant discrepancy of over twenty-two minutes between the predicted and the actual observed timings of the eclipses. This appeared to ruin the use of Io as a clock and end the idea of using it to calculate longitude. However, Romer came up with an ingenious and correct explanation of what was happening.

These sketches (published in Istoria e Dimonstrazione in 1613) show the changing position of the moons of Jupiter over 12 days. Jupiter is represented by the large circle, with the four moons as dots on either side.

Ole Romer’s recorded observations show his detailed research into the movement of Io.

Jupiter appears spotty in this false-colour picture from the Hubble Space Telescope’s near-infrared camera. The three black spots are the shadows of the moons Ganymede (top left), Io (left) and Callisto. The white spot above centre is Io, while the blue spot (upper right) is Ganymede. Callisto is out of the image to the right.

NASA

Romer noticed that the observed time of the eclipses drifted later relative to the predicted time as the distance between Jupiter and Earth increased as the planets orbited the Sun, then drifted back again when the distance between Jupiter and Earth began to decrease. Romer’s genius was to realise that this pattern implied there was nothing wrong with the clockwork of Jupiter and Io, because the error depended on the distance between Earth and Jupiter and had nothing to do with Io itself. His explanation, which is correct, was simple. Imagine that light takes time to travel from Jupiter to Earth; as the distance between the two planets increases, so the light from Jupiter will take longer to travel between them. This means that Io will emerge from Jupiter’s shadow later than predicted, simply because it takes longer for the light to reach you. Conversely, as the distance between Jupiter and Earth decreases, it takes the light less time to reach you and so you see Io emerge sooner than predicted. Factor in the time it takes light to travel between Jupiter and Earth and the theory works. Romer did this by trial and error, and was able to correctly account for the shifting times of the observed eclipses. The number that Romer actually calculated was the light travel time across the diameter of Earth’s orbit around the Sun, which he found to be approximately twenty minutes. For some reason, perhaps because he felt the diameter of Earth’s orbit was not known with sufficient precision, he never turned this number into the speed of light in any Earth-based units of measurement. He simply stated that it takes light twenty-two minutes to cross the diameter of Earth’s orbit. The first published number for the speed of light was that obtained by the Dutch astronomer Christiaan Huygens, who had corresponded with Romer. In his ‘Treatise sur la lumière’ (1678), Huygens quotes a speed in strange units as 110 million toises per second. Since a toise is two metres (seven feet), this gives a speed of 220,000,000 metres per second, which is not far off the modern value of 299,792,458 metres (983,571,503 feet) per second. The error was primarily in the determination of the diameter of Earth’s orbit around the Sun.

ROMER’S THEORY: predicting the emergence of io from behind jupiter, as seen from earth, is affected by the varying distance between earth and jupiter.

No consensus about the speed of light was reached until after Romer’s death in 1710, but his correct interpretation of the wobbles in the Jovian clock still stands as a seminal achievement in the history of science. His measurement of the speed of light was the first determination of the value of what scientists call a constant of nature. These numbers, such as Newton’s gravitational constant and Planck’s constant, have remained fixed since the Big Bang, and are central to the properties of our universe. They are crucial in physics, and we would live (or not live, because we wouldn’t exist) in a universe that was unrecognisable if their values were altered by even a tiny amount