The Story of Astronomy

by Peter Aughton

  In spite of his personal problems and his attachment to astrology, Kepler was an excellent mathematician and he was convinced that God had created the universe with a mathematical pattern. When Kepler came to study the planets he tried to fit regular plane polygons between their orbits. But despite his efforts he was unable to find any geometric pattern that fitted.

  Then, to his great delight, he found that when he modeled the problem in three dimensions instead of two, using the crystal spheres to carry the planets instead of plane circles, he could fit the five regular solids between the spheres. It seemed so perfect; the regular solids formed the framework that supported the spheres. The sphere was the perfect figure, but in terms of beauty and symmetry the regular solids ranked next. It seemed to explain why God had created the five regular solids and how they fitted into the universe. He published this finding with great enthusiasm in his Mysterium Cosmographicum of 1596.

  And then again it struck me, why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The Earth’s orbit is the measure of all things: circumscribe around it a dodecahedron, and the sphere containing this will be Mars; circumscribe around Mars a tetrahedron and the sphere containing this will be Jupiter; circumscribe around Jupiter a cube and the sphere containing this will be Saturn. Now inscribe within the Earth an icosahedron, and the sphere contained in it will be Venus; inscribe within Venus an octahedron, and the sphere contained in it will be Mercury. You now have the reason for the number of planets.

  A Meeting of the Minds

  Johannes Kepler first met Tycho Brahe early in the 17th century when Brahe was living in Prague. Brahe realized that Kepler had a good grasp of mathematics and would be the right person to help him complete and publish the Rudolphine Tables, named after his patron Rudolf II. On his deathbed Brahe pleaded with Kepler to finish his work on the planets and to publish his findings after his death. Kepler did his utmost to oblige. He worked very hard at studying the data, but try as he might he could not get the observations to fit the cycles and epicycles described by Ptolemy. The heretical work of Nicolaus Copernicus was of little help to him, for Copernicus had moved the Sun to the center of the universe and thereby he had simplified the calculations, but the system devised by Copernicus was no better than that devised by Ptolemy for predicting the future positions of the planets.

  In the year 1604 Kepler observed a new star in the sky. He was not the first person to observe it, however, that honor goes to a court official called Johann Brunowski, a keen amateur astronomer who told Kepler about the new star. At first Kepler did not believe the report, but when the clouds cleared from the Prague sky he could not miss it. It was October 17 and the star, in the constellation of Ophiuchus, was shining as brightly as the planet Jupiter. Kepler continued to observe the star—which became known, perhaps wrongly, as Kepler’s Star—for about two years, during which time it slowly faded away. Thus it was that both Brahe and Kepler had been fortunate enough to witness a supernova. It is a surprising coincidence that these two contemporaries should both find a new supernova in the sky, when we consider that it is such a rare event.

  Kepler was very moved by his astronomy and he left behind a record of his feelings:

  It is true that a divine voice, which enjoins humans to study astronomy, is expressed in the world itself, not in words or syllables, but in things themselves and in the conformity of the human intellect and senses with the sequence of celestial bodies and of their dispositions. Nevertheless, there is a kind of fate, by whose invisible agency various individuals are driven to take up various arts, which makes them certain that, just as they are part of the work of creation, they, likewise also partake to some extent in divine providence. When, in my early years, I was able to taste the sweetness of philosophy, I embraced the whole of it with an overwhelming desire, and with no special interest whatever in astronomy. I certainly had enough knowledge, and I had no difficulty understanding the geometrical and astronomical topics included in the normal curriculum, aided as I was by figures, numbers and proportions …

  Kepler’s Laws of Planetary Movement

  Kepler used Tycho Brahe’s observations when he constructed his famous laws of planetary movement. Kepler tried to fit the data for the planet Mars into an elliptical orbit instead of a circle. Eventually he found to his great joy that the data for an elliptical orbit fitted well, and it explained perfectly the errors of a few minutes of arc. The ellipse can be defined as a slanted section through a cone. Kepler knew much about the properties of the conic sections, for he had studied the work of the Greek mathematician Apollonius of Perga.

  There is some irony in the fact that Ptolemy would accept nothing but the perfect circle to describe the motions in the heavens, when all the time he had the work of Apollonius available to him. To the uninitiated, Kepler’s ellipses seem just as ridiculous as his idea of the five regular polyhedrons. Why should the planets, in their orbits around the Sun, be forever following a path represented by the section through a cone? What had slanted sections of cones to do with the system of the world? But as Kepler developed his theory he discovered that this really was the case. He was absolutely right and he had made a major step forward. He formulated his three laws of planetary motion as follows:

  Law 1. The orbits of the planets are ellipses with the Sun at one focus. The focus is not at the center of the ellipse. The ellipse has two symmetrically placed foci on its longer axis. The circle is a special case of the ellipse where both the foci coincide with the center. The foci are so called because if a ray of light from one focus is reflected by the surface of the ellipse, then whatever its direction it will always be reflected through the second focus.

  Law 2. The radius vector sweeps out equal areas in equal times. As the planet moves around the Sun, the line joining Sun and planet sweeps out equal areas in equal time intervals. Once the constants of the orbit are known this law can be used to predict the position of the planet at any time in the future. It is a special case of the law of conservation of angular momentum.

  Law 3. The cubes of the planets’ mean distances from the Sun are proportional to the squares of their periods. There is some uncertainty about what is meant by the “mean distance” from the Sun, but it can be taken as the geometric mean of the maximum and minimum distances. Using this law, if we know the period of a planet (time to orbit the Sun) then we can calculate its mean distance from the Sun, and vice versa.

  Laws 1 and 2 enable the position of any planet to be predicted once the orbital plane—in other words, the period and the position of the perihelion—are known. Kepler was particularly pleased with his third law for he liked discovering numerical relationships. Kepler did not produce a popular scientific work like that of Copernicus before him or Galileo after him. Instead he edited and published the Rudolphine Tables. The Holy Roman Emperor Rudolf II was, like Kepler himself, more interested in casting horoscopes than in astronomy. The tables brought together the most accurate set of astronomical observations ever made (those of Tycho Brahe) and the most perfect theory for the motions of the planets (the elliptical theory of Johannes Kepler).

  The tables first became available to the world at large in 1628, but scientific knowledge traveled only very slowly in the early 17th century. The first people in England to make use of the Rudolphine Tables were the young astronomer Jeremiah Horrocks and his friend William Crabtree, in 1639, after they had spent two years trying to make sense of earlier tables.

  7

  GALILEO

  The Great Telescope Maker

  This famous Italian astronomer believed in Copernicus’ view of a heliocentric universe. Galileo’s own observations of the stars and planets convinced him of it even more. But at the time such views were heretical and contrary to the account given in the Bible, and they brought Galileo into sharp conflict with the church, forcin
g him to recant his theory even though it was correct.

  The Italian philosopher and cosmologist Giordano Bruno (1548–1600) was a follower of Copernicus. He deduced from Copernicus that the other planets in the solar system, like the Earth, were all worlds in their own right. He believed that if they orbited the Sun and were much the same size as the Earth, then it was a logical deduction that they were also inhabited. He also suggested that the stars were so far away they could, in fact, be distant suns. The Copernican system showed that our world was not unique in the universe. Bruno was not strictly a scientist nor an astronomer; he was simply someone who had reached the conclusion that the Earth may not be the only inhabited world as created by God. The Catholic Church had no doubt that Bruno was wrong in his assumption that other worlds could exist. In 1600 Giordano Bruno became a martyr to science when he was burned at the stake for refusing to renounce his opinions.

  Galileo’s Early Years

  Galileo Galilei (1564–1642) was also a follower of Copernicus. Although he was not burned at the stake like Giordano Bruno, his beliefs brought him into conflict with the pope. Because of this he, too, will be remembered as someone who was persecuted for their scientific beliefs. Vincenzo Galilei, Galileo’s father, was a musician who moved from Florence to Pisa in about 1563, just before Galileo was born. When Galileo was about ten his family moved back to Florence. At the age of 17 we find Galileo back again in Pisa studying medicine at the university. Galileo therefore knew both Florence and Pisa very well. His interests did not lie in medicine, however; he was much more interested in mathematics and its application to physical science. The anecdotal story of Galileo watching the pendulum swing of the chandelier in the cathedral of Pisa is well known—he recognized that the period of the swing was constant and did not vary with the amplitude (the distance from one extremity of an oscillation to the middle point), and he deduced that the pendulum could therefore be used to regulate a clock.

  In 1585 Galileo’s father experienced financial difficulties and as a result he could no longer support his eldest son at university. Galileo returned again from Pisa to Florence to help with the ailing family business, and he took work as a private tutor to add a little to the family finances. At this time he made a device called a hydrostatic balance, which could be used for measuring the specific gravity of bodies. It was based on the principle of Archimedes, the Greek philosopher from the third century BC and a man whom Galileo ranked far above Aristotle as a scientist. In 1589 Galileo returned again to Pisa; this time he came as professor of mathematics at the university. Although he had no formal qualifications for the job he was by this time well known, and he had frequently demonstrated his mathematical skills. He enjoyed his new profession and quickly immersed himself in the life of the university. As well as mathematics he taught astronomy, including the works of Ptolemy, and at the same time he was able to develop his interests in mechanics.

  Rolling Balls and Falling Bodies

  One of Galileo’s experiments involved rolling balls down inclined planes and then measuring the balls’ speeds as they passed various markers set up along the planes. The measurement of time was no easy matter; in the 16th century primitive watches existed, but there was no such thing as a stopwatch. In his youth, when timing the chandelier in the cathedral at Pisa, Galileo had used his own pulse to measure the time intervals. As a young man he measured small time intervals using a simple pendulum of his own—a simple device based on his observations of the one at Pisa. He was able to formulate the concepts of velocity and acceleration and to show that the speed of his rolling balls increased uniformly as they rolled down the inclined plane.

  Galileo turned his thoughts to bodies in free fall. He reasoned that all bodies accelerated as they fell to Earth, but that they all fell at exactly the same rate. If, for example, a large object and a smaller, lighter object were dropped together from the same height, they would both strike the ground at much the same time. How could Galileo resist using the Leaning Tower of Pisa for his experiments? What better place could he have for testing his theories about falling bodies? He dropped a cannon ball and a musket ball from the same height from the highest level of the tower. We now know that the effects of air resistance would cause the heavier ball to reach the ground before the lighter one. So the question facing us is: did Galileo ever perform the experiment or is the story apocryphal? Viviani, Galileo’s first biographer, states that he repeated the experiment many times, and this seems in keeping with the truth, for it was his nature to experiment using different masses and other refinements.

  Bringing the Heavens into Focus

  Galileo never married, but he had two daughters and a son by a woman called Marina Gamba. His father died in 1591, and in that year he moved from Pisa to Padua university and soon afterward he moved from Padua to Venice.

  It was during his time at Padua and Venice, in the first decade of the new century, that Galileo heard about a wonderful new instrument fashioned by a spectacle maker called Hans Lippershey (1570–1619), who had a practice at Middelburg in Holland. By peering through a tube containing lenses this instrument somehow made distant objects appear to be nearer and larger. This amazing device was the telescope. Soon Galileo had discovered how the telescope was constructed and was making his own version of the instrument, which he sold to merchants and others.

  Galileo was pleased with his commercial success, but then went on to develop his instrument even further and to use it to examine the skies. He was not the first astronomer to use the telescope for this purpose, but he had a great flair for the instrument. He made his astronomical telescopes with two convex lenses. This required a longer tube but gave better results, even though the convex lenses produced an inverted image. He was soon making new discoveries.

  Galileo turned his telescope toward the Moon, marveling at how close the telescope seemed to bring it. He saw craters and mountains and what he thought were seas. All these had been seen before but never with such brightness and detail. He looked at the planets, and on nearly every one of them he saw something new. By looking in the direction of Jupiter he could see four small spots of light near the planet. He observed Jupiter every night and discovered that the spots of light changed their positions. He had discovered the four largest moons of Jupiter, namely Io, Europa, Ganymede and Callisto. This in itself produced a problem for the geocentric traditionalists because it brought the number of bodies believed to be orbiting Earth to more than the sacred number seven. Then Galileo turned his telescope to look at Saturn. He discovered two strange companions, one on each side of the planet. What he was observing were the rings of Saturn, but the telescope was not powerful enough to resolve them properly. Over a period of time the companions grew smaller and disappeared, only to return again later in the year (an effect caused by the rings being seen edge on). When he observed the planet Mars he saw that it clearly displayed a disc. However, it was the planet Venus that offered the greatest surprise. Through the telescope Venus showed phases, just like the Moon. This observation more than any of the others convinced Galileo that the Copernican system was right; the phases of Venus exactly matched the motion of the planet around the Sun.

  When Galileo turned his telescope to the stars he got another surprise. The stars still appeared as tiny spots of light—the telescope did not seem to bring them any nearer—but when he looked at the spaces between the stars, more and more stars appeared. When he trained his magic tube on the Milky Way he saw new stars appearing in their hundreds and thousands:

  In order that you may see one or two proofs of the inconceivable manner in which they are crowded together, I have determined to make a case against two star-clusters, that from them as a specimen you may decide about the rest. As my first example I had determined to depict the entire constellation of Orion, but I was so overwhelmed by the vast quantity of stars and by want of time that I have deferred attempting this to another occasion, for there are adjacent to, or scattered among the old stars more than 500 new stars
within the limits of one or two degrees … As a second example I have depicted the six stars in the constellation Taurus, called the Pleiades … near these lie more than forty others invisible to the naked eye, no one of which is more than half a degree off any of the aforesaid six, of these I have noticed only thirty-six in my diagram.

  The universe obviously contained far more stars than anybody had ever imagined. The number of visible stars in the universe seemed to have increased a thousand-fold or more, just by the invention of the telescope. It seemed that it would take a hundred men a lifetime to catalog all of them.

  Getting around the Censors

  Excited by his discoveries, Galileo wrote a small book called the Sidereus Nuncius, or Starry Messenger, in which he described them. The book appeared in print in 1610, and not surprisingly it came in for immediate criticism. The first salvo was fired in 1612 by a Dominican friar called Nicolo Lorini (fl. 1614) and the second in 1614 by another Dominican called Tommaso Caccini (1550–1618). The affair simmered for a few years, until Galileo was summoned to see the pope about his unconventional thoughts. In 1616 he was instructed very clearly to desist from putting forward his view that the Sun lay at the center of the universe. But Galileo knew that he was right. Instead of renouncing his ideas he simply gathered more evidence to support his case. The result was that Galileo’s Sidereus Nuncius was put, along with Copernicus’ De Revolutionibus Orbium Coelestium, on the list of prohibited books.