Part I
“Hereafter, when they come to model Heaven
And calculate the Stars [planets], how they will wield
The mighty frame, how build, unbuild, contrive
To save appearances, how gird the Sphere
With Centric and Eccentric scribbled over,
Cycle and Epicycle, Orb in Orb.”
John Milton (1667)1
A Universe that can be Counted on
Ancient astronomers must have looked out at the bright beacons of Mars and Venus with a sense of wonder and awe. These celestial vagabonds did not move with the stars. They crossed the sky in a regular pattern that might be used to predict when and where they would next appear. Our ancestors called them planetes, the ancient Greek word for “wanderers.” The ordered motion of the planets was surely set in place by some great power,2 and when astronomers tried to describe their wandering movements science began.
As described by the Nobel-prize winning physicist, Robert Millikan, astronomy explains: “A Universe that knows no caprice, a Universe that behaves in a knowable and predictable way, a Universe that can be counted on; in a word, a God who works through law.”3
The geometrical models that were constructed to describe the planetary movements depended upon one’s perspective. About 2000 years ago, the Greco-Egyptian astronomer Claudius Ptolemaeus, provided a complex model involving circular motions in an Earth-centered Universe, which was the best description available for about 1400 years. Then the Polish astronomer Nicolaus Copernicus questioned the Ptolemaic model and set the Earth in motion around the Sun.
In the following century, Galileo Galilei brought the Heavens down to Earth by using the newly invented telescope to find otherwise unseen mountains and valleys on the Moon, a star-filled Milky Way, and four moons circling around Jupiter. Galileo’s contemporary Johannes Kepler removed the “perfect” circle from consideration of the planetary motions, and replaced it with elongated paths around the Sun. He discovered laws that would provide the foundation of Isaac Newton’s theory of universal gravitation.
Pure, Everlasting, Heavenly Music
In antiquity, it was thought that both the planets and stars move in heavenly circles about a central unmoving Earth. Their circular movement had no beginning or end, and would continue forever without change. After all, the Sun and Moon are circular in shape, and wheels move easily across the Earth’s ground because they are round.
The ancient Greek philosopher and mathematician Pythagoras of Samos has been credited with the idea that there is music in the spacing of the planets, which emit harmonious sounds related to their distances and speeds of motion. The nearest, slower planets were thought to emit a low sound; the distant faster ones produced a high sound.
Both Plato and Aristotle subsequently developed the concept of the music of the spheres. In his Republic, written around 380 BC, Plato advocated circular planetary motions at different uniform speeds in proportion to their distance from the central, spherical Earth.
In his De Caelo (On the Heavens), Plato’s student Aristotle provided a mechanism for the motion by attaching the known planets to seven rotating, crystal-like spheres with a common center, all in counter-rotation to an eighth swift, outermost sphere of stars. Such a stellar sphere would explain why the stars seem to slide across the night sky, and why travelers to new and distant lands see new stars as well as new people.
For Aristotle, the Earth was a place of decay and change, the home of our temporary and impure lives. Natural motions on Earth, as distinguished from forced motions there, travel in straight lines, and that motion always ends. A stone falls straight down and stops, a fire rises straight up and disappears, and every human journey ends. In contrast, the indestructible, pure and eternal planets and stars are in everlasting motion. They seem to last forever and never stop moving.
To the ancient Greeks, the outermost celestial sphere formed the edge of the observable Universe. This sphere contained the fixed stars that remained firmly rooted within the night sky without ever moving with respect to each other. They all moved together as the celestial sphere wheeled around the central Earth once every day. The planets were supposed to move in the opposite direction at a slower pace.
Following Plato’s suggestion, astronomers spent centuries trying to describe the observed planetary movements, their appearances, using circular motion at constant speed around a central Earth, but they never could reproduce the temporary backwards motion of Mars, known as a retrograde, or its faster and slower motions observed during different parts of its path in the sky.
In the second century AD, the Greek mathematical astronomer Claudius Ptolemaeus created a geometrical model that could “save the appearances” presented by the planets. Ptolemy, as he is known, worked in the fine library at Alexandria, Egypt, where he was able to consult the work of previous astronomers. He showed that the observed planetary movements could be described by a system of moving circles in motion around the Earth, like the gears of some fantastic cosmic machine. Each planet was supposed to move with constant speed on a small circle, or epicycle, while the center of the epicycle revolved on a larger circle whose center was displaced from the Earth. A planet in uniform circular motion about a center slightly offset from the Earth would appear to a terrestrial observer to be moving with varying speed, faster when it is closest to Earth and slower when further away.
With this complex arrangement, Ptolemy was able to use circles upon circles to reproduce and predict the apparent motions of the planets with remarkable accuracy. He succeeded so well that his model was still being used to predict the locations of the planets in the sky more than a thousand years after his death.
Then, in the mid-16th century, the Polish cleric Mikolaj Kopernik, better known as Nicolaus Copernicus, set the Earth and other planets moving about a stationary, non-moving Sun.
Copernicus’ Vision of Sun-Centered Motion
Nicolaus Copernicus was born on February 19, 1473 in the city of Torún in the Province of Royal Prussia, a region of the Kingdom of Poland. His father was a merchant from the capital Cracow, and his mother, Barbara Watzenrode, was a member of a wealthy and powerful Torún family.
Upon his father’s death, when Copernicus was just 10 years old, his mother’s brother, Lucas Watzenrode, looked after his education and career. At age 19 he matriculated at the University of Cracow, where his studies included astronomy, mathematics, philosophy, physics, and the works of Aristotle and Ptolemy. Four years later, in 1496, Copernicus began a three-year study of law at the University of Bologna, Italy, a prominent European legal institution. Here he learned Papal decisions regarding authority, judgments, rights, and penalties within the jurisdiction of the Church, known as canon law. To round out his education, Copernicus then began a two-year study of medicine at Padua University in Italy, a leading faculty of medicine.
In 1503, at the age of 30, Copernicus returned home to join the staff of his Uncle Lucas, now the Catholic Bishop of Varmia, which was an area covering about five thousand square kilometers in the far northeast, Baltic coast of Poland, near Gdansk. He spent the next seven years as companion, secretary, and personal physician to his uncle, taking part in administrative, ecclesiastic, economic, and political duties that benefited from his education in canon law.
Before the end of 1510, Copernicus left service with his Bishop-Uncle, and moved to take up duties as the Canon of the Cathedral at Frombork. This town is located at the Vistula Lagoon on the Baltic Sea, far from the centers of European society, and it is in this remote location that the isolated genius would reside for most of his remaining 33 years. His life ended on May 24, 1543 at the age of 70, without ever being married or having children.
In Copernicus’ day, just about everyone thought that the Sun and stars were eternally wheeling about the immobile Earth, the center of the Universe. It certainly looked like the Sun was moving around the Earth and across the sky, and even in modern times people still say that the Sun rises and sets, to clock our daily rhythm. The distant stars were similarly thought to revolve around the Earth, and that was why they were seen moving across the dark night sky. Copernicus’ great insight was to place the Earth and other planets in uniform, circular motion around a central, stationary Sun.4
In the opening remarks of his Commentariolus, or Little Commentary, circulated around 1510, Copernicus stated that the heavenly bodies move with uniform speed in a “perfect” circle, as Plato and Aristotle had proposed. He then examined Ptolemy’s widely used planetary theories in which a planet moves on a small circle around a bigger one, but not really at uniform speed around any circle’s center. It only appears in uniform motion when viewed from outside the circle’s center, at an “equant” point chosen for that purpose.
Although Ptolemy’s theory was good enough to predict planetary motions and positions, Copernicus commented that: “A theory of this sort seemed neither sufficiently absolute, or complete enough, nor sufficiently pleasing to the mind,” and he therefore sought a more reasonable arrangement of circles that would “explain all the observed irregularities in planetary motion while keeping everything moving uniformly about its proper center, as required by the principle of perfect motion.”5 He accomplished this by setting the Earth free to revolve about the Sun, which became the immovable center of the Universe.
The Earth became just one planet among five others. They all whirled around the Sun, the source of our light and warmth. It was the daily rotation of the Earth that made the Sun apparently move across the daytime sky and the stars swing by at night.
In Copernicus’ Sun-centered model, the Earth and the five other planets visible to the unaided eye swung in the same direction, in uniform circular motion with a period of revolution that increased with the planet’s distance from the Sun. In order of increasing distance, they are Mercury, Venus, Earth, Mars, Jupiter and Saturn. [The more distant planets Uranus and Neptune were not discovered until 1781 and 1846, respectively, and that required the use of the telescope that was not invented until the early 1600s.]
As Copernicus noticed, the further a planet is from the Sun, the longer it takes the planet to complete a circuit around the Sun. This vision is conveyed in this extract from his Revolutions: “In no other way do we find a wonderful commensurability and a sure harmonious connection between the size of the orbit and the planet’s period of revolution.”6 [Copernicus used the relative planetary distances from the Sun expressed in terms of the Earth’s mean distance, the “common measure” of the Universe, but no one knew its precise value for an additional three centuries.]
How do the Planets Move?
So who was right? Does the Earth move around the Sun, or is the opposite true? There was no definitive observational test at the time.
Both Ptolemy’s Earth-centered motion and Copernicus’ Sun-centered one provided different explanations for the temporary backwards motion that had been observed for Mars (Fig. 1.1). It apparently looped back in the wrong direction for weeks at a time, seemingly disrupting its uniform progress across the night sky. The planet gradually came to a stop in its eastward motion, moved toward the west, and then turned around again and resumed moving toward the east. Jupiter and Saturn also displayed such a temporary reversed motion in the westward “retrograde” direction before continuing on in the eastward “prograde” direction.
Fig. 1.1. Retrograde loops This photograph shows the apparent movements of the planets against the background stars. Mars, Jupiter and Saturn appear to stop in their orbits, then reverse direction before continuing on — a phenomenon called retrograde motion by modern astronomers. (Courtesy of Erich Lessing/Magnum.)
In Ptolemy’s Earth-centered model, combinations of uniform circular motions explained these looping, retrograde paths of the planets. As mentioned in Copernicus’ Little Commentary, and emphasized in his Revolutions, the apparent backwards motions can instead be explained by the uniform motion of the Earth and other planets at different speeds around the Sun.
In Copernicus’ interpretation, planets moving at a slower speed than the Earth would sometimes appear to move ahead of Earth, and sometimes fall behind. During the relatively short time that the Earth overtakes one of these planets, that planet appears to be moving backward. Moreover, this explained why the size of the retrogrades differs for Saturn, Jupiter, and Mars, and one could confidently predict when their apparent motion would come to a halt and turn around, and for how long they would seem to move in the wrong direction.
Sun-centered planetary motion did provide natural explanations for other planetary observations. If the orbit of Venus lies inside that of Earth and closer to the Sun, it would account for the fact that Venus never appears to venture very far ahead or behind the Sun. An orbit around the Sun might also be adopted to explain the observed track of Venus’ motion, which twists and turns in the sky and does not appear to move in a circle around the Earth. In the Sun-centered Copernican model, the orbits of Mars, Jupiter and Saturn lie outside that of the Earth, which explains why they are visible throughout the night.
Nevertheless, when it came to describing and predicting observed planetary motions, Copernicus’ Sun-centered model was neither more accurate nor simpler than Ptolemy’s Earth-centered one. They were both only approximate accounts of observations. Copernicus was forced to adopt multiple circles to explain the apparent variations in the planetary motions, just as Ptolemy did, and the only major simplification of Copernicus’ model was that descriptions of the motions of the Sun and stars were no longer needed. Their movement could be eliminated under the assumption that the Earth rotated daily upon its axis.
In their day, both the Ptolemaic and Copernican models had aspects that critics found hard to believe. In Ptolemy’s theory the enormous Sun had to travel around the smaller Earth once each day, and the distant stars had to wheel overhead more rapidly than the Sun every single day. Copernicus found an explanation for the apparent motions of both the Sun and stars, by replacing them with the rotation of the Earth, but his theory strained credibility by placing the stars at a considerably greater distance than had previously been assumed.
If the Earth moved in a great orbit around the Sun, then the stars would have to be very much farther away than the width of the Earth’s path. Otherwise, the nearby stars would show a slight change in position when observed from opposite sides of our planet’s orbit, which had never been seen. The fact that no such change had been recorded was indeed used as an argument against the Sun-centered hypothesis from the time of Aristotle on.
The slight change in the apparent positions of nearby stars remained undetected for three centuries after Copernicus’ death. Before 1838 there wasn’t any definite proof that the Earth moves around the Sun.7 And it was not until 1852 that the rotation of the Earth was conclusively demonstrated using Foucault’s famous swinging pendulum.8
Copernicus never did present a vigorous defense of the Earth’s motion around the Sun, and at the time it was thought to be no more than a conjecture or unproven hypothesis that might be convenient for astronomical calculations and predictions. Planetary movement about a central, unmoving Earth continued to be the favored world-view for about a century after Copernicus’ death, and it wasn’t until around 1700 that his idea became widely accepted. In the meantime, Galileo had used the newly invented telescope to bring the Heavens down to Earth, and the Earth into the Heavens, and in 1633, the Catholic Church had summoned Galileo before a Holy Inquisition for supporting Sun-centered planetary motion.
Heavenly Things Never Seen Before
Galileo Galilei was born in Pisa, Italy in 1564, and died at the age of 77 at his home in Arcetri within the hills surrounding Firenze (Florence), Italy. His long life included acclaim and fame, condemnation and house arrest, and emotional extremes ranging from passion to despair. He was ambitious and gregarious, proud and humble, religious and independent minded, and both humorous and sarcastic.
After years of study and teaching in Pisa, Galileo was appointed by the Venetian Senate to the vacant Chair of Mathematics at the University of Padua near Venice, where he taught geometry, mechanics and astronomy for 18 years, from 1592 to 1610. As Galileo would later claim, these were the best years of his life, filled with novel ideas, alert colleagues, new friends, and his beautiful Venetian mistress Marina Gamba. The colorful Galileo was also a notorious lover of good wine, which he called “light held together by moisture.”9
Galileo was already middle aged when the telescope, or spyglass as it was first called, was invented.10 When he heard of the device that brought faraway things nearby, Galileo promptly built improved versions of it and anticipated its military advantages for defense of Venice, a walled city beside the sea.11
When Galileo demonstrated his telescope to the Venetian senators, and gave them one as a gift, he was awarded by a substantial increase in salary and granted lifelong tenure at Padua. The inquisitive professor then turned one of his telescopes toward the sky, and revealed things never seen before.12
In Galileo’s time, many astronomers supposed that the Milky Way was composed of a misty, nebulous substance, but his spyglass showed that it instead consists of a multitude of stars that cannot be seen with the unaided eye. He also turned his telescope to the Moon and was able to resolve features that otherwise remained blurred or unseen. Chains of lofty mountains, deep valleys, and round craters were discovered on the Moon’s surface. It is pockmarked, cracked, and molded into high and low places, just like the Earth.
Then in January 1610, the innovative Galileo made another startling discovery that further diminished the central specialness of the Earth. When directing his telescope at the nearly full Moon, Galileo must have naturally moved his spyglass just a little to look at Jupiter, which was then located just above the Moon and the next brightest object in the sky. Perhaps for the first time in history, he observed a planet not as a point, but as a round disk. Moreover, near Jupiter he saw three unresolved objects all in a straight line passing through the planet’s disk. The three companions were detected on the next night, and at first he thought they were stars. But one of them disappeared the next two nights, and then reappeared. On the following night, Galileo for the first time saw four objects near the planet Jupiter (Fig. 1.2).13
Galileo became convinced that he was seeing four moons that revolved about Jupiter the way our Moon moves around the Earth. They accompanied Jupiter in its motion across the sky, and traveled regularly around the planet at different distances and speeds.
Fig. 1.2. Moons of Jupiter Some of Galileo Galilei’s observations of the “Medicean stars”, which were drawn in his Sidereus Nuncius of 1610. They are lined up on each side of Jupiter and change apparent position while orbiting the planet.
No one had predicted the possible existence of moons orbiting any other object than the Earth, and the Jovian moons conclusively showed for the first time that the Earth is not the only center of heavenly motion.
As Galileo subsequently demonstrated, the orbital periods of the Jovian moons increase with their distance from Jupiter, from 42 hours to half a month, which meant that the closer moons systematically move faster around the planet than the more distant ones.
Every possible evening Galileo recorded the positions of Jupiter’s moons, while also writing a report of his pioneering discoveries with the telescope and publishing it in March 1610. The short book, Sidereus Nuncius or The Sidereal Messenger, is one of the most fascinating and lively books in astronomy.14
Sidereus Nuncius was written in Latin to make Galileo’s results accessible to international scholars, and the result was overwhelming. All of Europe was abuzz with excitement over this treatise about previously unseen features on the Moon and new moons that circle Jupiter. These were incredible discoveries, and anyone who heard about them must have been captivated by the wonder of it all. There were hidden things out there that no one had ever seen before.
Barely ten months after Galileo’s book was published, the English poet John Donne captured the essence of the discoveries, writing:
“Man hath weaved out a net, and this net thrown
Upon the Heavens, and now they are his own.”15
Under Galileo’s telescopic scrutiny, the Moon, Sun, and planets suddenly became physical objects with irregularities, spots, and moons of their own. They were no longer the “perfect” heavenly jewels imagined by Aristotle. Heaven had been brought down to Earth and the Earth up into Heaven. The Earth could no longer be considered the center of all heavenly motion, for Jupiter had moons that revolved around that planet rather than the Earth. Galileo also opened the skies to vast numbers of stars that could only be seen with a telescope.
The enthusiastic Galileo continued with his amazing telescopic discoveries that included the phases and variations in apparent size of Venus. To preserve his priority before being sure of his findings, Galileo circulated the results as Latin anagrams, or successions of scrambled Latin letters. Within a few months, when he had confirmed the findings, he then sent his correspondents the unscrambled solutions, which when translated into English read: The mother of Loves [Venus] emulates the shapes of Cynthia [the Moon].
Venus goes through a complete sequence of Moon-like phases, varying from a thin crescent to a round disk (Fig. 1.3), which meant that “Venus revolves about the Sun.”16 [In the Ptolemaic system the epicycle of Venus always lay between the Earth and the Sun, so if the planet shined by reflected sunlight and orbits the Earth it could never show a full phase.] Nevertheless, this did not prove that the Earth revolves around the Sun.
Fig. 1.3. Venus The planet Venus changes in both the amount of sunlight it reflects and in its apparent size. (Lowell Observatory photographs.)
Under scrutiny with his telescope, Galileo also found that Saturn did not always seem to be perfectly round but elongated. When explained and translated, his anagram read: I have observed the highest planet [Saturn] to be triple-bodied. The blurry objects that Galileo saw on each side of Saturn in 1610 disappeared two years later, when Galileo wondered if the planet “had devoured her children.” The paradox of Saturn’s disappearing appendages wasn’t resolved until 1656 when the Dutch astronomer Christiaan Huygens realized that their geometry suggested a narrow ring.
Galileo’s telescope also indicated that the apparent perfection of the Sun is an illusion. To most of us, the Sun looks like a faultless, white-hot globe, round, smooth and without a blemish, but detailed scrutiny indicates that dark, ephemeral spots, called sunspots, deface the apparently serene face of the Sun. Although Chinese observers had previously noticed the largest sunspots, which can be seen without a telescope, Galileo was one of the first to use a telescope to see smaller sunspots and determine how they came into view, underwent transformations, and disappeared from sight.
The sunspots were always changing shape, and remained visible for hours to weeks before apparently moving back inside the Sun. Altogether, they demonstrated that the Sun was not the unblemished and unchanging heavenly object described by the ancients, but instead: “In that part of the sky which deserves to be considered the most pure and serene of all — I mean in the very face of the Sun, these innumerable multitudes of dense, obscure, and foggy materials are discovered to be produced and dissolved continually in brief periods.”17 By observing a single, long-lived spot, Galileo even demonstrated that the Sun is spinning in space, and turning around once every month or so.
These studies of the motions of moons and planets, as well as his investigations of regular pendulum movements on the Earth, led Galileo to realize the universality of all movements, whether they be in a straight line or rounded into a circular or parabolic trajectory.
Galileo’s Lifelong Faith and Inquisition
For centuries, Galileo’s disputes with the Roman Catholic Church have symbolized defiance of authority and freedom from religious suppression. Nevertheless, he had an indestructible faith, retained strong belief in God throughout his life, and did not intend to undermine prevailing spiritual beliefs. Galileo remained a good Catholic and was committed to the Church throughout his life. He also never criticized the importance of the Holy Bible, just interpretations of some of its passages.
When he discovered new features on the Moon and the four largest moons of Jupiter, in 1610, the devout Galileo wrote to the Tuscan court: “I infinitely render grace to God that it has pleased him to make me alone the first observer of an admirable thing, kept hidden all these ages,”18 and in 1613, in his third Letter on Sunspots, he included: “Whatever the course of our lives, we should receive them as the highest gift from the hand of God…. Indeed, we should accept misfortune not only in thanks, but in infinite gratitude to Providence, which by such means detaches us from an excessive love for earthly things and elevates our minds to the celestial and Divine.”19
Galileo nevertheless believed that the Earth and everything on it were spinning, swift moving through space, and circling the Sun like all the other planetary wanderers. This thought was downright discomforting to powerful clergy who noted that the Bible indicates that the Sun moves and the Earth stands still, not the other way around.
In a letter written to his friend, the monk Benedetto Castelli, and privately circulated in the closing days of 1613, Galileo stated: “Though Holy Scripture cannot err, nevertheless some of its interpreters and expositors can sometimes err in various ways … when they would base themselves always on the literal meaning of words.”20 As Galileo pointed out, in the 4th century Saint Augustine had already written that the Bible did not need to be interpreted strictly or used to understand the course of the Sun and Moon. To make the point, Galileo quoted in 1615 his contemporary Cardinal Cesare Baronio, who stated that the Bible teaches “how to go to Heaven, not how the Heavens go.”21
After further correspondence, disputes, and intrigue, the Roman Catholic Church decided to take action. In 1616, at the request of Pope Paul V, the cardinals of the Holy Office in Rome examined the Copernican system and found it to be false and contrary to Holy Scripture. Cardinal Roberto Bellarmine, a foremost theologian of his day who was subsequently declared a Saint, had already noted that no one had decisively shown that the Earth moves. “To demonstrate that the appearances can be saved by assuming the Sun is at the center,” he exclaimed, “is not the same thing as to demonstrate that in fact the Sun is at the center and the Earth is in the Heavens.”22 In this the Cardinal was not mistaken, for Galileo had not proved that the Earth moves, and he had not conclusively shown this to be the truth.
There was a temporary change in attitude in 1624, when a new Pope Urban VIII, an admirer of Galileo and his telescope, told him that he saw no harm in his using the Sun-centered system as a tool for astronomical calculations and predictions — even to write about it — as long as he considered it an unproved hypothesis and gave equal treatment to different points of view.
So the tide had apparently turned. Galileo had been given a way out, even felt encouraged, but he refused to compromise, and responded to the friendly gesture with a combative Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems), which compared the relative merits of the Earth-centered Ptolemaic system and the Suncentered Copernican one. In 1630, at the age of 66, Galileo took the finished manuscript to Rome to obtain the approval of the Roman Catholic Church. After some changes suggested by the chief censor and a two-year delay, in part resulting from the spread of the Bubonic Plague into Italy, a thousand printed copies of the Dialogo appeared in Firenze, Italy in 1632.
The book was written in Italian with a combative, funny, and at times poetic style, certain to please Galileo’s friends and to entertain the general public. But he misjudged its likely reception by the Catholic Clergy, and it didn’t help that Galileo adopted a scornful attitude toward those “mental pygmies” who held different views. “Philosophers,” he wrote, “fly alone like eagles, and not in flocks like starlings.”23
It was a definite mistake to put Pope Urban VIII’s words — about human ineptitude in understanding a Universe created by an all-powerful God — in the mouth of Simplicio, an apparent simpleton. The Pontiff thought he was being mocked and became an implacable foe. Other opponents thought that the Biblical truth was being threatened, and that the human-centered, Earth-based view of Creation was endangered.
In an oft-told story, the Inquisition summoned Galileo to Rome in 1633. Sick with all manner of afflictions, including gout, arthritis, kidney stones and hernias, and most likely terrified of what might happen to him, the aging and feeble Galileo recanted his physical and astronomical reasons for conclusively supporting the idea that the Earth moved around the Sun.
But the Cardinal-Inquisitors and Pope Urban VIII could show no mercy, partly because other factors were at play. The “Thirty Years” War against the German Protestants was raging through Europe, and the Pope had been openly censured for not defending the Catholic faith. He thought he could support his religion by condemning Galileo for his views.
Galileo was convicted of challenging the authority of the Church, and forced to read a prepared confession that he “abjured, cursed and detested” his erroneous belief that “the Sun is motionless in the center of the world, and the Earth is not the center and moves.”24 The Dialogo was permanently banned in the Index of Prohibited Books, and after being placed in custody at the palace of the Archbishop of Siena; Galileo was confined to his house in Arcetri, in the hills surrounding Firenze, where he spent his last years. Not until 1992 did Pope John Paul II express regret for how the Galileo affair was handled, and the Catholic Church then declared that theologians of Galileo’s time were mistaken because of their literal interpretations of Sacred Scripture.
However, Galileo was never imprisoned, as in a prison cell. He continued to correspond with and even receive distinguished visitors, and to write his important Two New Sciences. Moreover, his forced confession and house confinement did not shake Galileo’s belief in a Creator God. He remained devout until his death.
In the meantime, Tycho Brahe had obtained accurate observations of the shifting locations of planets, and Johannes Kepler used them to show that the planets move with irregular speed along elliptical orbits centered on the Sun. To Kepler, this was in agreement with God’s Creation of Divine and harmonious planetary motion that played His heavenly music. As a Protestant outside the jurisdiction of Rome, Kepler avoided religious persecution for publishing these “revolutionary” ideas in 1609 and 1619, well before Galileo’s Dialogo of 1632.
Kepler’s Sacred Mystery and Divine Harmony
Johannes Kepler was born on December 27, 1571 into what was once a prominent Protestant family in the small village of Weil der Stadt in southwest Germany, now part of the Stuttgart region near the Black Forest and the Rhine. [He was therefore just seven years younger than Galileo.]
Johannes had a total of six brothers and sisters. Three died in childhood, two led normal adult lives, and a third Heinrich, was an epileptic misfit. Johannes was himself born premature and almost died from childhood smallpox, which left him with weak vision and crippled hands.
Kepler probably found solace and refuge from such an unhappy beginning in astronomy, mathematics, and religion, which would have drawn his attention away from his everyday life. He was the first in his family to be sent to an elementary school, where he was seen to be an unusual student and was therefore transferred from a German to a Latin school. Since the University of Tübingen was full, Kepler completed his undergraduate work at a preparatory school, and then matriculated at Tübingen with the intent of becoming a Protestant minister.
After qualifying to become a pastor, Kepler took a job as a teacher of mathematics and astronomy at Graz, which is now the second-largest city in Austria after Vienna. While at Graz, Kepler published his Mysterium cosmographicum, or The Sacred Mystery of the Cosmos, where he interpreted the relative sizes of six planetary orbits around the Sun in terms of six spheres with five geometric solids between them. When nested inside each other they could explain the relative sizes of the planetary orbits, in a geometric design that Kepler believed was created by God.
While at Graz, Kepler married Barbara Müller, who was already twice widowed at the age of twenty-three. In 1597 they embarked on a marriage that was just about as unpleasant to Kepler as his childhood, and ended fourteen-years later when Barbara passed away with a disturbed mind.
Meanwhile, after refusing to convert to Catholicism, Kepler and his family were banished from Graz, and traveled to Prague where he began work with the Danish nobleman Tycho Brahe. With royal patronage, Brahe had built an awesome private observatory, Uraniborg, on the island of Hven, where he spent twenty years amassing the long, exact observations required for a good understanding of planetary motion, including especially precise and detailed measurements of the changing location of Mars. This was before the invention of the telescope, and Tycho used ingenious measuring instruments with graduated circles but without any lenses or mirrors to obtain a then incomparable angular positional accuracy of about one minute of arc.
In 1600 Johannes Kepler began his attempts at explaining Tycho’s precise observations of Mars, and kept at the task for nearly 10 years before he could fully account for them. He spent years trying to explain the observations under the assumption that Mars moves in a circle, but the calculations always disagreed with the observations by a frustrating 8 minutes of arc. With extraordinary dedication, endurance and patience, Kepler kept at the task until he found that a non-circular, elliptical orbit could be used to make predictions of Mars’ position in the sky accurate to a few minutes of arc. [Shortly after Tycho’s unexpected death on October 24, 1601, Kepler was appointed imperial mathematician to the Holy Roman Emperor Rudolph II.]
Kepler apparently reached his startling conclusion that Mars moves at a varying speed along an oval trajectory in 1605, but disagreements with Tycho’s heirs prevented publication of this result until 1609, in Astronomia nova seu physica coelestis, the New Astronomy or Celestial Physics.25 It explained the motion of Mars and presented the first two of his now-famous laws of planetary motion. In the first law, Kepler abandoned circular motion, and proposed that all the planets move along an ellipse with the Sun at one of two foci. The term focus was used by Kepler to designate “hearth,” because to him the Sun was at the hearth and heart of the Universe.
His realization that an elliptical orbit would match the observed path of Mars in the sky resembled an epiphany, which Kepler described: “As if I were roused from a dream and saw a new light.”26 He believed that God had guided him towards the problem and its solution, writing: “I believe it was an act of Divine Providence that I arrived just at the time when Longomontanus [Tycho Brahe’s assistant before Kepler] was occupied with Mars. For Mars alone enables us to penetrate the secrets of astronomy which otherwise would remain forever hidden from us.”27
Because observations indicated that Mars moves a little faster when nearest the Sun than when further away, Kepler proposed his second law, known as the law of areas, that specifies such a variation of speed along the orbit. Assuming that the Sun is the source of all planetary motion, Kepler imagined that an invisible line connected the central Sun to each planet. Remembering that Archimedes found a circle’s area by dividing it into a large number of triangles, Kepler imagined that a planet sweeps out triangles as it moves along its elliptical orbit. If triangles with equal areas are swept out in equal time, which is the law of areas, then the planet moves fastest when nearest the Sun (Fig. 1.4).
This dependence of a planet’s orbital speed on its distance from the Sun also suggested to Kepler that planetary motion is driven by the Sun, with a motive power that weakens with increasing distance from it. He would eventually show that this weakening applied not only to a single planet along its oval orbit, but also to different planets, with the more distant planets moving about the Sun at slower speeds.
Kepler’s patron, Rudolph II, died in January 1612, and early that year Kepler moved to Linz, Austria, on the Danube, where he served as a teacher at the district school. He then enjoyed nearly two decades of financial security and religious freedom. Already in 1613, at the age of 41, Kepler had begun a second, happier marriage to Susanna Reuttinger, aged 24. Two years later, he successfully defended his mother at her trial for witchcraft and consorting with the Devil. [She used herbs to make potions that she believed had magical powers].
Fig. 1.4. Kepler’s first and second laws The orbit of a planet about the Sun is an ellipse with the Sun at one focus, and the line joining a planet to the Sun sweeps out equal areas in equal times. The planet therefore changes speed in its orbit and moves fastest when closest to the Sun.
In another four years Kepler had written and published his infamous Harmonices mundi, or Harmony of the World, which extends his investigations of Mars to the orbits of the other known planets. It describes what is now known as his third law of planetary motion, in which the squares of the periods of revolution of any two planets about the Sun are proportional to the cubes of their mean distances from the Sun (Fig. 1.5). In Kepler’s own description of this harmonic relation, written in 1618: “[It] agreed so perfectly with the data which my seventeen years of labor on Tycho’s observations had yielded, that I thought at first I was dreaming.”28
Invisible Powers Move the Planets
Kepler thought that the Sun governs the motion of the planets. In the first edition of his Mysterium cosmographicum, published in 1596, he had noticed that the more remote planets move more slowly, suggesting that either the individual soul that moves each planet is less active at greater distances from the Sun or that one moving soul in the central Sun drives the planets with less vigor the further the planet is. In the second edition of the book, published in 1621, Kepler substituted the mechanical word “force” for the magical term “soul.” The Sun’s force, which was responsible for moving the planets around their orbits, was supposed to diminish in strength with increasing distance as the intensity of light does, with the inverse square of the distance. The Sun was, after all, the source of the light that illuminates and warms the Earth.
Fig. 1.5. Kepler’s third law The squares of the orbital periods of the planets increase with the cubes of their distances from the Sun. This relation is shown as a straight line in this logarithmic display; it also applies to Jupiter’s four largest satellites shown in the inset.
What forces keep the planets moving in curved paths about the Sun? It might have something to do with magnetism, whose mysterious unseen force distributes iron filings about a bar magnet. In 1600, William Gilbert, physician to Queen Elizabeth I of England, authored a treatise with the grand title De magnete, magneticisque corporibus, et de magno magnete tellure, translated into English as Concerning Magnetism, Magnetic Bodies, and the Great Magnet Earth. In this work, Gilbert showed that the center of the Earth is itself a great magnet whose lines of force loop out to envelop the planet and explain the orientation of compass needles.
Drawing upon an analogy with the central magnetic source of the Earth, Kepler supposed that an invisible magnetic force emanates from the Sun, pushing the planets through space and controlling their motion. This indicated to him that: “The heavenly machine is a kind of clockwork, insofar as nearly all the manifold motions are caused by a most simple, magnetic, and material force ... given numerical and geometrical expression.”29 The further a planet is from the Sun, the weaker the solar magnetic force and the slower that planet’s motion, as described by Kepler’s harmonic relationship between the orbital period and distance from the Sun.
Kepler incorporated the Trinity of Father, Son, and Holy Spirit into his mystical interpretations of the Universe. The Sun, as God the Father, symbolized God’s motive power emanating out to propel the planets. This invisible power extended throughout all of space, like the Holy Spirit. Supposing that the stars in the heavenly firmament represent Jesus Christ, he then proposed that the Sun, the stars, and the space between them are analogous to the Father, the Son, and the Holy Spirit.
His discoveries became the foundation for Isaac Newton’s proposal that the invisible gravitational force of the Sun grasps the planets and holds them in place. He showed that the pull of gravity is universal, with an unlimited range and capacity to act on all matter, confining the Moon, planets, and comets in their trajectories. This meant that the same physical principles and mathematical laws describe motions everywhere, either up above in the Heavens or down here on Earth.