Human Universe. Andrew Cohen

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СКАЧАТЬ ourselves to be in motion and the Sun, Moon, planets and stars appear to sweep across the sky around us. However, a little careful observation reveals that the situation is in fact more complicated than this. In particular, the planets perform little loops in the sky at certain times of year, reversing their track across the background stars before continuing along their paths through the constellations of the zodiac. This observational fact, which is known as retrograde motion, occurs because we are viewing the planets from a moving vantage point – the Earth – in orbit around the Sun.

      This is by far the simplest explanation for the evidence, although it is possible to construct a system capable of predicting the position of the planets months or years ahead and maintain Earth’s unique stationary position at the centre of all things. Such an Earth-centred model was developed by Ptolemy in the second century and published in his most famous work, Almagest. The details are extremely complicated, and aren’t worth describing in detail here because the central idea is totally wrong and we won’t learn anything. The sheer contrived complexity of an Earth-centred description of planetary motions can be seen in Ptolemy’s Model, which shows the apparent motions of the planets against the stars as viewed from Earth. This tangled Ptolemaic system of Earth-centred circular motions, replete with the arcane terminology of epicycles, deferents and equant, was used successfully by astrologers for thousands of years to predict where the planets would be against the constellations of the zodiac – presumably allowing them to write their horoscopes and mislead the gullible citizens of the ancient world. And if all you care about are the predictions themselves, and your philosophical prejudice and common-sense feeling of stillness require the Earth to be at the centre, then everything is fine. And so it remained until Copernicus became sufficiently offended by the sheer ugliness of the Ptolemaic model to do something about it.

      Copernicus’s precise objections to Ptolemy are not known, but sometime around 1510 he wrote an unpublished manuscript called the Commentariolus in which he expressed his dissatisfaction with the model. ‘I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion.’

      The Commentariolus contained a list of radical and mostly correct assertions. Copernicus wrote that the Moon revolves around the Earth, the planets rotate around the Sun, and the distance from the Earth to the Sun is an insignificant fraction of the distance to the stars. He was the first to suggest that the Earth rotates on its axis, and that this rotation is responsible for the daily motion of the Sun and stars across the sky. He also understood that the retrograde motion of the planets is due to the motion of the Earth and not the planets themselves. Copernicus always intended Commentariolus to be the introduction to a much larger work, and included little if any detail about how he had come upon such a radical departure from classical ideas. The full justification for and description of his new cosmology took him a further 20 years, but by 1539 he had finished most of his six-volume De revolutionibus, although the completed books were not published until 1543. They contained the mathematical elaborations of his heliocentric model, an analysis of the precession of the equinoxes, the orbit of the Moon, and a catalogue of the stars, and are rightly regarded as foundational works in the development of modern science. They were widely read in universities across Europe and admired for the accuracy of the astronomical predictions contained within. It is interesting to note, however, that the intellectual turmoil caused by our relegation from the centre of all things still coloured the view of many of the great scientific names of the age. Tycho Brahe, the greatest astronomical observer before the invention of the telescope, referred to Copernicus as a second Ptolemy (which was meant as a compliment), but didn’t accept the Sun-centred solar system model in its entirety, partly because he perceived it to be in contradiction with the Bible, but partly because it does seem obvious that the Earth is at rest. This is not a trivial objection to a Copernican solar system, and a truly modern understanding of precisely what ‘at rest’ and ‘moving’ mean requires Einstein’s theories of relativity – which we will get to later! Even Copernicus himself was clear that the Sun still rested at the centre of the universe. But as the seventeenth century wore on, precision observations greatly improved due to the invention of the telescope and an increasingly mature application of mathematics to describe the data, and led a host of astronomers and mathematicians – including Johannes Kepler, Galileo and ultimately Isaac Newton – towards an understanding of the workings of the solar system. This theory is good enough even today to send space probes to the outer planets with absolute precision.

      At first sight it is difficult to understand why Ptolemy’s contrived mess lasted so long, but there is a modern bias to this statement that is revealing. Today, a scientifically literate person assumes that there is a real, predictable universe beyond Earth that operates according to laws of nature – the same laws that objects obey here on Earth. This idea, which is correct, only emerged fully formed with the work of Isaac Newton in the 1680s, over a century after Copernicus. Ancient astronomers were interested primarily in predictions, and although the nature of physical reality was debated, the central scientific idea of universal laws of physics had simply not been discovered. Ptolemy created a model that makes predictions that agree with observation to a reasonable level of accuracy, and that was good enough for most people. There had been notable dissenting voices, of course – the history of ideas is never linear. Epicurus, writing around 300 BCE, proposed an eternal cosmos populated by an infinity of worlds, and around the same time Aristarchus proposed a Sun-centred universe about which the Earth and planets orbit. There was also a strong tradition of classic orthodoxy in the Islamic world in the tenth and eleventh centuries. The astronomer and mathematician Ibn al-Haytham pointed out that, whilst Ptolemy’s model had predictive power, the motions of the planets as shown in the figure here represent ‘an arrangement that is impossible to exist’.

      The end of the revolution started by Copernicus around 1510, and the beginning of modern mathematical physics, can be dated to 5 July 1687, when Isaac Newton published the Principia. He demonstrated that the Earth-centred Ptolemaic jumble can be replaced by a Sun-centred solar system and a law of universal gravitation, which applies to all objects in the universe and can be expressed in a single mathematical equation:

      The equation says that the gravitational force between two objects – a planet and a star, say – of masses m₁ and m₂ can be calculated by multiplying the masses together, dividing by the square of the distance r between them, and multiplying by G, which encodes the strength of the gravitational force itself. G, which is known as Newton’s Constant, is, as far as we know, a fundamental property of our universe – it is a single number which is the same everywhere and has remained so for all time. Henry Cavendish first measured G in a famous experiment in 1798, in which he managed (indirectly) to measure the gravitational force between lead balls of known mass using a torsion balance. This is yet another example of the central idea of modern physics – lead balls obey the same laws of nature as stars and planets. For the record, the current best measurement of G = 6.67 × 10^-11 N m²/kg², which tells you that the gravitational force between two balls of mass 1kg each, 1 metre apart, is just less than ten thousand millionths of a Newton. Gravity is a very weak force indeed, and this is why its strength was not measured until 71 years after Newton’s death.

       NEWTON’S LAW OF GRAVITY

       F

      Force between the masses

       G

      Gravitational constant

       m₁

      First mass

       m₂ СКАЧАТЬ