Cosmic Dawn
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Kepler’s work marked a turning point in the history of astronomy. To measure the orbits of the planets as Kepler did is a stunning achievement. Let us remind ourselves that the data he had at hand were accurate planetary positions in the sky. It took quite some ingenuity to calculate the exact shapes of planetary orbits using these data. Using a circular-orbit model for Mars, Kepler predicted that Mars should be off by one quarter of a moon diameter from Tycho’s measured position. Kepler noticed that the difference between the predicted position for the planet and the observed position was larger than the errors Tycho quoted for the observed position. He trusted Tycho’s error estimates and thus decided that the orbit could not be a circle. In science we always associate error estimates with measurements. I could quote my height as 180 ± 0. 5 cm, for example. If a theory predicts my height to be exactly 184 cm, it’s not a bad effort, but we can be sure the theory is wrong. The minutiae of error analysis and measurement make possible the quantitative comparison of theory and observation.
Kepler was fascinated by numbers. He thought that the spacings of five solids inscribed within one another could explain the spacings of the planets. Examples of such solids are the cube and the pyramid. The idea was to inscribe an orbit within such a solid so that it just touched the faces. We believe this is a mere coincidence today. Kepler is often described as being something of a mystic, but I find some astonishingly modern ideas in his writing. Speculating about his laws of planetary motion, Kepler thought that the increase in speed of a planet as it gets closer to the Sun might be due to a property of the Sun. He was looking for causal effects. There was something about the Sun that caused a planet to speed up as it approached the Sun. The Sun was somehow acting at a distance and producing an effect on the planets. Kepler thought this force might be magnetic, since a magnet could perceptibly influence the motion of pieces of iron placed at a distance from it. In other words, the Newtonian concepts of force and action at a distance are already present in Kepler’s writing.
Kepler argued against Bruno’s viewpoint that the universe was infinite. Kepler stated that if the universe was infinite and filled with stars like the Sun the night sky would be much brighter than it actually is. We shall return to this subject later in this chapter.
The Telescope and the Starry Messenger
While Kepler was developing these ideas, laying the foundations for a new cosmology, Galileo (1564–1642) was making surprising discoveries using a new device called a telescope to study the heavens. He saw spots on the Sun, and valleys and mountains on the Moon. These observations were in conflict with the Greek view of the cosmos, which maintained that the heavens were perfect. Galileo also noted that Venus went through a complete set of phases, thereby proving that Venus orbits the Sun and not the Earth. In the Ptolemaic system, Venus is always almost in front of the Sun, so that its maximum phase would be a crescent. Galileo also discovered four moons orbiting Jupiter. This latter discovery clearly showed that moons could orbit a planet while that planet orbits the Sun, thereby removing one chief objection to the motion of the Earth and its moon around the Sun. Galileo also showed that the Milky Way is composed of individual stars. And, in an example of the uneasy marriage between science, technology and society, Galileo showed that the telescope could serve as an early warning system. It could be used to give the inhabitants of a port advance warning of attacking ships, much as another scientific advance, radar, would do in World War II.
Galileo strongly advocated the Sun-centered system and ended up antagonizing the Catholic Church. He wrote a book entitled Dialogue Concerning the Two Chief World Systems published in 1632. This book was calculated to make fools of the establishment. The prevailing view of an earth-centered universe was put in the mouth of a naive character called Simplicio. To make matters worse, a third, supposedly unbiased character, continuously sided against Simplicio in the discussions depicted in the book. Galileo probably could have gotten away with much of what he wanted to say if he had done it in a less provocative and polemical manner. Direct provocation of the powers that be is not always a good strategy. Of course, scientifically, Galileo was perfectly correct.
The question still remained as to why the planets obey Kepler’s laws. Kepler and, in particular Galileo had developed the beginning of a science of dynamics, but it was Isaac Newton (1642–1727) who would develop a complete theory of motion and gravitation.
Who were the contemporaries of these men of science? Luther, Magellan, Michelangelo, and Leonardo da Vinci were among Copernicus’s contemporaries. Galileo, Tycho, and Kepler numbered Shakespeare and Milton as contemporaries while Newton’s life overlapped with that of Rembrandt, Voltaire, and J. S. Bach. It is interesting that word of Newton’s achievements reached the continent through Voltaire, a French novelist, philosopher and playwright. It is perhaps as if, in more recent times, T. S. Eliot had come back to the United States bringing news of the structure of the atom.
Newton is an intimidating figure in the history of science. Through his mathematical creations, deep physical insights, and inventions he dominated many fields. His theories of motion and gravity broke down the barrier between the heavens and earth once and for all. The same laws that govern the motion of objects on the Earth’s surface govern planetary motion. The force that pulls my keys to the ground when I drop them also keeps the Moon in its orbit.
There is something mystical about action at a distance. We say that the force of gravity keeps the Moon in its orbit but no mechanism is specified. Between the Earth and moon lies nothing but empty space, yet the Moon behaves as if a giant string were attached to it, pulling it to the center of the Earth. Described with words, the concept of gravity is not very useful. I might as well tell you that plixes keep the Moon in its orbit. Plixes are, of course, little orange creatures whose job it is to keep the planets in their orbit. The power of Newton’s theory lies in the fact that it enables one to calculate the orbits of the planets with very high precision. Newton’s theory can be used to plot the trajectories of man made objects in space. Newton’s laws also explain the phenomenon of tides. In 1669 Newton was named Lucasian Professor of Mathematics at Trinity College Cambridge, where he remained for many years. Newton published his results in July 1687 in a book entitled Mathematical Principles of Natural Philosophy. I was present at the inaugural lecture that Stephen Hawking gave in 1981 when he was elected to that same position. The feeling of a continuous tradition extending hundreds of years is a conspicuous feature of the older European universities.
Newton was undoubtedly a man of genius. Despite his achievements, he does not emerge as a very admirable personality. Maybe this is the price one pays for having the strength of character to do something really outstanding.
Descartes expressed the idea of an evolving unbounded universe. Newton showed that we can discover the fundamental physical laws of matter within the universe. Combine these two ideas and you have the basis of modern cosmology.
The period we are describing was one of world exploration. European nations were sending out ships to look for new lands and riches. These ships had considerable trouble keeping track of their position at sea. North-south position did not present trouble, but east-west position, or longitude, was another story. In 1714 the British government offered a large reward for the solution of this problem. It boiled down to finding a reliable way of telling the time. This could be done mechanically using a clock or using the celestial clockwork. To illustrate this idea, let us imagine that a friend called you up (at midday, while you are having lunch) on his cell phone and said, “I am at sea but I have no idea where I am.” You could have a clue as to his location by asking him what time it is. If he says, “Right now, its about the middle of the night,” you know that he is on the other side of the Earth from you. He could avoid calling you by having a clock set to your local time. By comparing his local time with yours he would know how far away from you he is. In the absence of cell phones and other modern gadgets, the only way to do t
his was to find an accurate method of keeping time at sea.
William Hamilton attacked the problem by building increasingly accurate clocks. The astronomers, of course, favored using the relative position of the Sun and the Moon to tell the time. A forerunner of today’s global positioning system was proposed: ships anchored at sea would fire cannons at specified times. It is good to be ahead of your time but not too far ahead. The longitude problem led to the creation of the Royal Greenwich Observatory in 1676. It was a rare occasion when astronomy could serve society directly. Realizing in the 1990s that the longitude problem had been solved for quite a while, the British government shutdown the Royal Greenwich Observatory.
Why Is the Sky Dark at Night? Meditations on an Infinite Universe
As early as 1576, Thomas Digges had suggested that the outer sphere in the Copernican model be done away with, that the universe was in fact infinite (Fig. 1.3). This was a natural continuation of the Copernican revolution. Copernicus had removed the Earth from the center of the universe. If the Sun is but one of many stars scattered through space, it is plausible that the Sun is not at the center of the universe. Giordano Bruno (1548–1600) even suggested that there are planetary systems surrounding other stars. Almost 400 years later, Michel Mayor and Didier Queloz detected a planet orbiting a star other than our Sun. Currently almost 1,000 planets outside our solar system are known to exist. Bruno also suggested the existence of a universe, without a center, which agrees with our modern ideas of cosmology. Descartes (1596–1650) in his book Principia philosophiae proposed the idea that the universe was without center and without limits. He also believed the Sun to be a star like many other stars. He came up with the idea that the universe was not empty but structured with vortices that guide the planets in their orbits. He countered the idea that the universe was created in one moment with the modern idea that the universe evolves with time. This is a key concept of the Big Bang theory. The question of whether space is full or empty has a long history in cosmology. Newton dismissed Descartes’ vortices, but the idea that space was not empty resurfaced with the attempt to understand electric and magnetic fields and the propagation of light through space. This idea was dismissed by experiments and by Einstein in his special theory of relativity. The discovery of dark energy has revived the idea that space is not empty.
Fig. 1.3This image first published by Camille Flammarion could be seen as showing man’s attempt to look beyond the universe of spheres into the workings of an infinite universe
When Newton envisioned an infinite universe that was populated by stars scattered randomly in space, he realized that there was a potential problem. If we think of concentric shells surrounding the solar system, we might expect the stars in the more distant shells to exert less pull on the Earth. Gravity is an inverse square law, meaning that the gravitational force between two objects decreases as the square of distance between them. Note, however, that the volume of a shell of finite thickness increases as the square of its radius. In other words, the pull of a star in a shell that is twice as distant as a nearby shell is four times weaker, but the distant shell contains four times more stars. If the universe were slightly more dense in one direction than another, the gravitational forces would be enormous. Newton realized that an infinite universe would have to have a uniform density or the Earth would be subjected to enormous gravitational forces.
Kepler examined the idea of an infinite universe and raised an important objection that was to be argued about for hundreds of years. In 1610 Kepler wrote a short book in which he presented his argument. If the universe is infinite we would expect to see more and more stars as we stare into space in such a way that the night sky should be as bright as the surface of the Sun. It is the same argument as Newton’s argument for a homogeneous universe. Both gravity and light flux fall off as inverse-square laws. Although more distant stars are fainter, there are more of them to cover a distant patch of sky. These two effects cancel one another in such a way that we keep adding more and more light until the night sky is as bright as the disk of the Sun. The British astronomer Edmund Halley suggested that the light from distant stars was too faint to have any effect, but this is a mathematically incorrect argument.
The problem of the dark night sky is known as Olbers’ paradox. A Swiss astronomer, Jean-Philippe Loys de Cheseaux (1718–1751), suggested in 1744 that some medium lying between the stars was absorbing the starlight. A distinguished German astronomer, Heinrich Olbers (1758–1840), put forth the same hypothesis in 1823. John Herschel (1792–1871), an English astronomer argued that this proposed solution was incorrect because the light from the stars would heat up the intervening medium, which, in turn, would start glowing.
The correct answer to the paradox lies in the finite age of the universe. Light has a finite travel speed, therefore we cannot see the whole universe today but only those regions close enough for light to have reached us since the beginning of the Big Bang. The universe has been around a long time, 15 billion years or so. This is not long enough for the accumulated light from stars to create a very bright sky background. It is interesting that when we take very faint images with large optical telescopes, about a third of the sky is covered with galaxies.
As well as thinking of the universe as a whole, people were turning their thoughts to the structure of the universe. Thomas Wright (1711–1786) published his ideas in a book entitled An Original Theory of the Universe. The idea he propounded is that the stars are distributed in a spherical shell around the center of the universe. If we were located somewhere in a sufficiently large shell the stars close to us would appear as if they were distributed in a plane in which we are embedded. This would explain the appearance of the Milky Way in the night sky. Remember that Galileo had shown, using his telescope, that the Milky Way could be resolved into tens of thousands of stars.
Immanuel Kant (1724–1804) suggested in 1755 that the Milky Way is a flattened disk that rotates about its center. This, as we shall see, is our modern view of our galaxy. Kant also believed in the existence of other galaxies–an idea that came to be known as the island universe hypothesis. It is surprising to what extent Kant’s cosmological speculations were correct, given the complete lack of supporting evidence at the time.
Pierre Simon Laplace (1749–1827) made a big impact on the public with his book Exposition du système du monde. He suggested that the solar system originated from a large flattened slowly rotating cloud of gas and also stated that many other stars may well have their own planetary systems. Laplace also formulated our modern idea of a galaxy containing billions of stars. We then have a universe in which stars are not randomly distributed in space but located inside galaxies. As if this was not enough Laplace came up with the first clear description of what we mean by a black hole, namely an object from which even light cannot escape.
Late Night Thoughts on the Structure of Our Galaxy
William Herschel (1738–1822) took an observational approach to these questions. As well as studying our galaxy, he discovered the planet Uranus and demonstrated that the orbits of double star systems obeyed Kepler’s laws. Herschel assumed that stars were uniformly distributed in space. From this it follows that if more stars are counted in a given direction than another it is because the galaxy extends further in space in that direction. Accordingly he set out to map the shape of our galaxy by counting stars in 683 regions of the sky. Using this method of star gauges, Herschel mapped out a shape of our galaxy. Unfortunately, this method is flawed because starlight can be absorbed and scattered by intervening matter, which biases the number counts of stars. One must take into account observational biases in order to draw reliable conclusions from survey data.
Like Galileo, Herschel earned a pension from the government by pleasing the king with one of his discoveries. Herschel had earned his living as a musician before turning to astronomy. He was able to turn full-time to astronomy, thanks to a pension awarded him by King George III. Herschel discovered many nebulae, cloudy patches
of light whose origin was uncertain. He managed to resolve some of these into clusters of stars and believed that all nebulae were actually star clusters. In 1790, Herschel discovered a planetary nebula, an object consisting of a cloud of gas surrounding an evolved star. This confused the issue for Herschel, since the nebula itself clearly could not consist of stars. One hundred years after his observation the first photographs of planetary nebulae were taken. Roughly 100 years after that, the first photographs of planetary nebulae were taken with the Hubble Space Telescope. The improvement in observing techniques is really impressive, as the contrast between photographs taken 100 years apart can testify.
With the work of Herschel we see for the first time statistical methods in action and also the planning and execution of a major survey. This approach has proven to be the most fruitful one in modern cosmology. It is not very glamorous, because it is laborious and repetitive work that can take several years, but, in the long run, surveys yield the most information. Herschel made a catalog of 2,500 nebulae, which included the famous list of 103 objects compiled by the French astronomer Charles Messier (1730–1817). He found that 29 of the Messier nebulae were in fact collections of stars. Messier’s catalog had originally been compiled to help comet hunters to distinguish the fuzzy nebulae from comets–that is, to separate objects at the time considered boring from objects of genuine interest. Many of the “boring” objects in Messier’s catalog are currently the subject of very detailed studies at all wavelengths.