Wonders of the Universe. Andrew Cohen

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

SPEED LIMITS

      Everything in our universe has a speed limit, and for much of the twentieth century humans seemed obsessed with breaking one of them. In the 1940s and 1950s the sound barrier took on an almost mythical status as engineers worldwide tried to build aircraft that could exceed the 1236 kilometres per hour (768 miles per hour) at which sound travels in air at twenty degrees Celsius. But what is the meaning of this speed limit? What is the underlying physics, and how does it affect our engineering attempts to break it?

      Sound in a gas such as air is a moving disturbance of the air molecules. Imagine dropping a saucepan lid onto the floor. As it lands, it rapidly compresses the air beneath it, pushing the molecules closer together. This increases the density of the air beneath the lid, which corresponds to an increase in air pressure. In a gas, molecules will fly around to try to equalise the pressure, which is why winds develop between high and low pressure areas in our atmosphere. With a falling lid, some of the molecules in the high-pressure area beneath it will rush out to the surrounding lower-pressure areas; these increase in pressure, causing molecules to rush into the neighbouring areas, and so on. So the disturbance in the air caused by the falling lid moves outwards as a wave of pressure. The air itself doesn’t flow away from the lid (this would leave an area of lower pressure around it that would have to be equalised), it is only the pulse of pressure that moves through the air.

      Once we reached 12,800 metres, the pilot put the Hawker Hunter into the roll and we dived down through the clouds, upside down. Almost immediately, we broke through the sound barrier.

      The speed of this pressure wave is set by the properties of the air. The speed of sound in air depends on the air’s temperature, which is a measure of how fast the molecules in the air are moving on average, the mass of the air molecules (air is primarily a mixture of nitrogen and oxygen) and the details of how the air responds when it is compressed (known as the ‘adiabatic index’). To a reasonable approximation, the speed of the sound wave depends mainly on the average speed of the air molecules at a particular temperature.

      The speed of sound is therefore not a speed limit at all; it is simply the speed at which a wave of pressure moves through the air, and there is no reason why an object shouldn’t exceed this. This was known long before aircraft were invented, but it did not satisfy those who wanted to propel a human faster than sound. Many attempts were made during World War II to produce a supersonic aircraft, but the sound barrier was not breached until 14 October 1947, when Chuck Yeager became the first human to pilot a supersonic flight. Flying in the Bell–XS1, Yeager was dropped out of the bomb bay of a modified B29 bomber, through the sound barrier and into the history books.

      The speed of sound is not a speed limit at all; it is simply the speed at which a wave of pressure moves through the air, and there is no reason why an object shouldn’t exceed this.

      Today, aircraft routinely break the sound barrier, but the routine element hides the fascinating aerodynamic and engineering challenges that had to be overcome so that humans could travel faster than sound. Test pilot Dave Southwood demonstrated these to me in the making of the programme in a beautiful aircraft that was not designed to break the sound barrier in level flight – the Hawker Hunter.

      Designed in the 1950s, the Hawker Hunter is a legendary British jet fighter of the post-war era. Designed to fly at Mach 0.94, this aircraft cannot fly supersonic in level flight, but in the right hands it can exceed the 1,200 kilometres (745 miles) per hour to take me through the sound barrier. We climbed to 12,800 metres (42,000 feet), flipped the Hunter into an inverted dive, then plunged full-throttle towards the Bristol Channel. In just seconds the jet smashed through the sound barrier and the air flow surrounding the jet changed, which is heard on the ground as an explosion, or a sonic boom.

      Once we reached 12,800 metres, the pilot put the Hawker Hunter into the roll and we dived down through the clouds, upside down. Almost immediately, we broke through the sound barrier.

      So the sound barrier is not a barrier at all; it is a speed limit only for sound itself, determined by the physics of the movement of air molecules. Is the light barrier the same? It would seem from our description of light as an electromagnetic wave that is so. Why shouldn’t a sufficiently powerful aircraft or spacecraft be able to fly faster than a wave in electric and magnetic fields? The answer is that the ‘light barrier’ is of a totally different character and cannot be smashed through, even in principle. The reason for this is that light speed plays a much deeper role in the Universe than just being the speed at which light travels. A true understanding of the role of this speed, 299,792,458 metres (983,571,503 feet) per second, was achieved in 1905 by Albert Einstein in his special theory of relativity. Einstein, inspired by Maxwell’s work, wrote down a theory in which space and time are merged into a single entity known as ‘spacetime’. Einstein suggested we should not see our world as having only three directions