Big Bang. Simon Singh

which is known as stellar parallax. You can see parallax in action at a local level by simply holding one finger in the air just a few centimetres in front of your face. Close your left eye and use your right eye to line your finger up with a nearby object, perhaps the edge of a window. Next, close your right eye and open your left one, and you will see that your finger has shifted to the right relative to the edge of the window. Switch between your eyes quickly and your finger will jump to and fro. So shifting your vantage point from one eye to the other, a distance of just a few centimetres, moves the apparent position of your finger relative to another object. This is illustrated in Figure 7(a).

      The distance from the Earth to the Sun is 150 million km, so if the Earth orbited the Sun then it would be 300 million km away from its original position after six months. The Greeks found it impossible to detect any shift in the positions of the stars relative to one another over the course of the year, despite the enormous shift in Earthly perspective that would happen if we orbited the Sun. Once more, the evidence seemed to point to the conclusion that the Earth did not move and was at the centre of the universe. Of course, the Earth does orbit the Sun, and stellar parallax does exist, but it was imperceptible to the Greeks because the stars are so very far away. You can see how distance reduces the parallax effect by repeating the winking experiment, this time fully extending your arm so that your finger is almost a metre away. Again, use your right eye to line up your finger with the edge of the window. This time, when you switch to your left eye the parallax shift should be much less significant than before because your finger is farther away, as illustrated in Figure 7(b). In summary, the Earth does move, but the parallax shift rapidly reduces with distance and the stars are very far away, so stellar parallax could not be detected with primitive equipment.

      Figure 7 Parallax is the apparent shift in the position of an object due to a change in an observer’s vantage point. Diagram (a) shows how a marker finger lines up with the left window edge when viewed with the right eye, but shifts when viewed with the other eye. Diagram (b) shows that the parallax shift caused by switching between eyes is significantly reduced if the marker finger is more distant. Because the Earth orbits the Sun, our vantage point changes, so if one star is used as a marker then it should shift relative to more distant stars over the course of a year. Diagram (c) shows how the marker star lines up with two different background stars depending on the position of the Earth. However, if diagram (c) were drawn to scale, then the stars would be over 1 km off the top of the page! Therefore the parallax shift would be minuscule and imperceptible to the ancient Greeks. The Greeks assumed that the stars were much closer, so to them a lack of parallax shift implied a static Earth.

      At the time, the evidence against Aristarchus’ Sun-centred model of the universe seemed overwhelming, so it is quite understandable why all his philosopher friends stayed loyal to the Earth-centred model. Their traditional model was perfectly sensible, rational and self-consistent. They were content with their vision of the universe and their place within it. However, there was one outstanding problem. Sure enough, the Sun, Moon and stars all seemed to march obediently around the Earth, but there were five heavenly bodies that dawdled across the heavens in a rather haphazard manner. Occasionally, some of them even dared to stop momentarily before temporarily reversing their motion in a volte-face known as retrograde motion. These wandering rebels were the five other known planets: Mercury, Venus, Mars, Jupiter and Saturn. Indeed, the word ‘planet’ derives from the Greek planetes, meaning ‘wanderer’. Similarly, the Babylonian word for planet was bibbu, literally ‘wild sheep’ — because the planets seemed to stray all over the place. And the ancient Egyptians called Mars sekded-ef em khetkhet, meaning ‘one who travels backwards’.

      From our modern Earth-orbits-Sun perspective, it is easy enough to understand the behaviour of these heavenly vagabonds. In reality, the planets orbit the Sun in a steady manner, but we view them from a moving platform, the Earth, which is why their motion appears to be irregular. In particular, the retrograde motions exhibited by Mars, Saturn and Jupiter are easy to explain. Figure 8(a) shows a stripped-down Solar System containing just the Sun, Earth and Mars. Earth orbits the Sun more quickly than Mars, and as we catch up to Mars and pass it, our line of sight to Mars shifts back and forth. However, from the old Earth-centred perspective, in which we sit at the centre of the universe and everything revolves around us, the orbit of Mars was a riddle. It appeared that Mars, as shown in Figure 8(b), looped the loop in a most peculiar manner as it orbited the Earth. Saturn and Jupiter displayed similar retrograde motions, which the Greeks also put down to looping orbits.

      These loopy planetary orbits were hugely problematic for the ancient Greeks, because all the orbits were supposed to be circular according to Plato and his pupil Aristotle. They declared that the circle, with its simplicity, beauty and lack of beginning or end, was the perfect shape, and since the heavens were the realm of perfection then celestial bodies had to travel in circles. Several astronomers and mathematicians looked into the problem and, over the course of several centuries, they developed a cunning solution — a way to describe looping planetary orbits in terms of combinations of circles, which was in keeping with Plato and Aristotle’s edict of circular perfection. The solution became associated with the name of one astronomer, Ptolemy, who lived in Alexandria in the second century AD.

      Figure 8 Planets such as Mars, Jupiter and Saturn exhibit so-called retrograde motion when viewed from Earth. Diagram (a) shows a stripped-down Solar System with just the Earth and Mars orbiting (anticlockwise) around the Sun. From position 1, we would see Mars move increasingly ahead of us, which continues as we observe Mars from position 2. But Mars pauses at position 3, and by position 4 is now moving to the right, and even further to the right when Earth arrives at position 5. There it pauses once more, before resuming its original direction of travel, as seen from positions 6 and 7. Of course, Mars is continually moving anticlockwise around the Sun, but it appears to us that Mars is zigzagging because of the relative motions of the Earth and Mars. Retrograde motion makes perfect sense in a Sun-centred model of the universe.

      Diagram (b) shows how believers in an Earth-centred model perceived the orbit of Mars. The zigzag of Mars was interpreted as an actual looping orbit. In other words, traditionalists believed that the static Earth sat at the centre of the universe, while Mars looped its way around the Earth.

      Ptolemy’s world-view started with the widely held assumption that the Earth is at the centre of the universe and stationary, otherwise ‘all the animals and all the separate weights would be left behind floating on the air’. Next, he explained the orbits of the Sun and Moon in terms of simple circles. Then, in order to explain retrograde motions, he developed a theory of circles within circles, as illustrated in Figure 9. To generate a path with periodic retrograde motion, such as the one followed by Mars, Ptolemy proposed starting with a single circle (known as the deferent), with a rod attached to the circle so that it pivoted. The planet then occupied a position at the end of this pivoted rod. If the main deferent circle remained fixed and the rod rotated around its pivot, then the planet would follow a circular path with a short radius (known as the epicycle), as shown in Figure 9(a). Alternatively, if the main deferent circle rotated and the rod remained fixed, then the planet would follow a circular path with a larger radius, as shown in Figure 9(b). However, if the rod rotated around its pivot and at the same time the pivot rotated with the main deferent circle, then the planet’s path would be a composite of its motion around the two circles, which mimics a retrograde loop, as shown in Figure 9(c).

      Although this description of circles and pivots conveys the central idea of Ptolemy’s model, it was actually far more complicated. To start with, Ptolemy thought of his model in three dimensions and constructed it from crystal spheres, but for simplicity we will continue to think in terms of two-dimensional circles. Also, in order to accurately explain the retrogrades of different planets, Ptolemy had to carefully tune the radius of the deferent and the radius of the epicycle for each planet, and select the speed at which each rotated. For even greater accuracy he introduced two other variable elements. The eccentric defined a point to the side of the Earth which acted as a slightly displaced