Astronomy in the Modern Times
author Paul Boșcu, April 2017

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The fifteenth century in Europe was remarkable in that two great intellectual movements began to sweep across the continent almost simultaneously: the Renaissance and free scientific inquiry—particularly astronomy.

The Renaissance contributed to the growth of new ideas in that it encouraged art, literature, architecture, and exploration. This led to technological developments and the invention of such things as the mariner's compass (the magnetic compass). Ultimately these technological developments led to the astronomical telescope.

A few writers on astronomy are worth mentioning, not because they contributed to the Copernican revolution that was to come but because they kept alive the flow of new ideas. Among them were Celio Calcagnini, Johannes de Monte Regio, George Rohrbach, Girolamo Fracastoro, and Giovanni Battista Amiri.

One of the founding fathers of modern astronomy, Nicolaus Copernicus, made waves for his rejection of the Earth as the literal center of the universe. Based on an elegant theoretical model of the geometry of the solar system and the motions of the planets, he eventually came up with the idea that the Sun was at the center of the solar system, not the Earth. Copernicus first presented his heliocentric theory in a preliminary thesis that was never published. He later expounded upon this thesis in a work called De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), which wasn’t published until 1543, the year of his death.

Copernicus, deeply concerned about his commitments to his church and his devotion to the Pope, was very reluctant to publish his heliocentric theory, even though he was strongly urged to do so by some church dignitaries themselves. Most people think that Copernicus delayed publishing his ideas because he was afraid to go against the powerful religious forces of the day — then again, he could also have just feared looking foolish.

Copernicus had started his Italian schooling at the University of Bologna, where he studied with the astronomer Domenico Maria de Novara, who was a very careful observer. Before leaving Italy for the first time Copernicus spent a year at the University of Rome, where he gave a course on mathematics. When Copernicus returned to Italy he went to Padua where he continued his studies of law, mathematics, and medicine, receiving a degree of Doctor of Canon Law. By the time he left Italy he was a master of theology and knew the classics thoroughly; he had also mastered all the mathematics and the astronomy known at that time.

When Copernicus returned to his canonry duties in Ermland, he was delighted by the leisure he had to pursue his astronomical studies and by the small demands on his time made by his clerical commitments. Copernicus, untrained an observer as he was, discovered many celestial phenomena that are greatly simplified by a heliocentric solar system, and so he decided to devote the rest of his life to formulating a heliocentric system that would be acceptable to everyone, even to the Pope. He was driven by the conviction that if one accepted, that the earth and all the other planets revolve around the sun, the astronomy of the solar system would be simplified.

Nicolaus Copernicus was born in Thorn on the Vistula. He was educated as an Aristotelian and, in his early years, accepted the Ptolemaic model of the solar system, as taught at the University of Cracow by the outstanding authority on astronomy, Albert Brudzew (Brudzewski), who had written the first of a series of commentaries on the outstanding book on planetary motions by Rohrbach.

Whether Brudzewski had imbued Copernicus with doubt about Ptolemy's theory is not clear, but Copernicus' thinking about the motions of the earth and the planets was influenced much more by his travels in Italy than by his studies at Cracow. When Copernicus returned home from Cracow, his maternal uncle, Lucas Watzenrode, Bishop of Ermland, made him a canon of the Church in the Cathedral of Frauenburg. Watzenrode insisted, however, that his nephew spend time at various Italian universities before assuming the canonry.

In his dedication to Pope Paul III at the beginning of his great book, Copernicus remarks that he was prompted to develop a new model of the solar system by the inadequacies and inconsistencies he found in the Ptolemaic solar system. In his dedication to Pope Paul III, Copernicus includes a passionate and poetic panegyric to the sun: "How could the light [the sun] be given a better place to illuminate the whole temple of God? The Greeks called the Sun the guide and soul of the world; Sophocles spoke of it as the All-seeing One; Trismegistus held it to be the visible embodiment of God. Now let us place it upon a royal throne, let it in truth guide the circling family of planets, including the Earth. What a picture—so simple, so clear, so beautiful."

One of the cardinals in Rome gave a lecture to the Pope on Copernicus' heliocentric theory, and sent his secretary to Frauenburg to obtain copies of Copernicus' proof that the earth revolves around the sun. In a letter to Copernicus he stated "If you fulfill this wish of mine you will learn how deeply concerned I am of your fame, and how I endeavor to win recognition of your deed. I have closed you in my heart." This letter was equivalent to an official sanction from the Church because the cardinal was its chief censor. This was followed by the encouragement from the Bishop in Copernicus' diocese that Copernicus' book be published as a duty to the world.

After its appearance, De revolutionibus became the astronomy textbook of choice, quickly displacing Ptolemy's Almagest. The most remarkable thing about this tale was that the acceptance of the motion of the earth, as Copernicus wove it into his heliocentric theory over a period of some 30 years, overthrew a 1600- year-old tract that had enthralled the greatest minds for centuries.

The best was yet to come, for Copernicus had opened the floodgates to a vast flow of new discoveries and concepts that revealed an incredibly pent up desire among intellectual leaders to throw off the theological and scholastic chains that had bound humanity for centuries.

Taking all of the pertinent things into account we must place Copernicus' achievement on a very high level even though his importance to astronomy is often downgraded because his detractors argue that he made very few observations. This in itself is a testament to the greatness of his achievement. It is one thing to be forced to a particular conclusion by incontestable observations and quite another to construct a correct theoretical model on the basis of pure thought, as Copernicus had done in concluding that the heliocentric model of the solar system is superior intellectually and aesthetically to the Ptolemaic system in every way.

We must not suppose that the Copernican doctrine was the concern of astronomers and astrologers only. Indeed, it left its imprint on philosophy, physics, art, literature, and humanism, in general. Scholasticism was dead and the only thing that stood in the way of Copernicanism was theology—Protestantism as well as Catholicism. In spite of this dangerous roadblock to the advance of the new ideas, their growing popularity could not be denied.

Tycho Brahe, the last and greatest of all naked-eye observers, was a Danish noble. He studied at the University of Copenhagen. He is known for his very accurate astronomical observations. Tycho had studied the stars so assiduously that he knew by heart the positions of all the visible stars in the sky. His uncle sent him to Germany to complete his studies, and his fame grew across Europe as a young, energetic astronomer. It did not take much to convince Tycho about the need for precise observations because he had pursued the practice of very accurate observing over long periods of time.

Tycho Brahe, the last and greatest of all naked-eye observers, was born in the 16th century in Knudstrup, then a province of Denmark, His father had been governor of Helsingborg and his uncle was a country squire and a vice admiral. Tycho was adopted and raised by his childless uncle who planned to steer his nephew into a career of law, statesmanship, or diplomacy, to uphold the honor and noble name of the Brahe family. But Tycho would have none of that and early in life became devoted to astronomy.

If Tycho had remained in Copenhagen, it is doubtful that he would have become sufficiently acquainted with Copernicus' work to have been influenced by his thinking. But Tycho's uncle decided, after Tycho had spent three years at Copenhagen, that his nephew should travel to a foreign country and, accordingly, sent him to Leipzig, supervised by a young tutor. Undeterred by the tutor in any way from pursuing his astronomical observations, Tycho continued his studies at the Universities of Wittenberg, Rostock, Basel, and Augsburg, until his twenty-sixth year. By this time he had become famous on the continent as the young, brilliant nonpareil Danish astronomer.

He was sent to the University of Copenhagen to study philosophy and rhetoric, but he turned completely away from these studies at the end of his first year in Copenhagen when he watched a partial eclipse of the sun, which had been previously announced. To Tycho it was a divine revelation that one could know the motions of the celestial bodies with such accuracy that one could then predict the exact time of a solar eclipse. He decided then that he would devote his life to acquiring that kind of divinity. This was a fortuitous choice for the immediate future of astronomy.

A young, brilliant French mathematician Pierre de la Ramee, or Petrus Ramus, a professor of philosophy and rhetoric at the College Royale at Paris, convinced Brahe about the truth of Copernicus’ theories. De la Ramee spoke passionately about the need for a young man like Tycho to start from scratch and construct a correct mathematical theory of the orbits of the planets (earth included) around the sun that was based on a large number of the positions of the planets. This, as we shall see, Kepler did later with Tycho's precise observations.

So careful an observer did Brahe become that he discovered serious errors in the Alfonsine tables of the planets and the Ptolemaic tables that the German astronomer Erasmus Reinhold had prepared and published to correct the Alfonsine tables.

The Copernican model of the solar system disturbed Brahe for he reacted to it with great ambivalence: on the one hand, he was greatly attracted to it for its simplicity and elegance; on the other hand, he was repelled by the concept of a moving earth. He rejected that part of Copernicus' theory because, he correctly argued, "if the earth is moving in a circle around the sun, I [Tycho] should see the stars shift back and forth once a year and since I do not observe the stars doing that, I reject the motion of the earth." Tycho's argument and reasoning are correct; the stars do indeed appear to shift back and forth, which is how we measure stellar distances today—the so-called method of stellar parallaxes. Tycho's mistake was in his assumption that he could detect and measure this apparent shifting of the stars.

Not to be left behind completely by the rapid advance of the Copernicans, Tycho finally struck upon a new system now known as the Tychonic system which permitted him to keep the earth fixed and yet to accept the Copernican principle that the planets revolve around the sun. In the Tychonic system the earth is still fixed at the center of the solar system, but with the other planets revolving around the sun, which, in turn, is revolving around the earth.

Tycho had gained great fame at an early age, becoming so famous by the age of 26 years for his brilliant and accurate observations that the King of Denmark, Frederick II, invited hint to come back to Denmark to become the court astrologer. Because astrology in those days was in vogue among the nobility and Tycho himself was passionately devoted to it, he accepted the king's offer. Frederick was so pleased with Tycho that he offered him the island of Hven as the site for an observatory. Tycho accepted this offer and initiated the construction of the first and one of the most famous observatories in the history of astronomy—Uraniborg, or "City in the Sky".

Financed by Frederick's treasury, Brahe's observatory was constructed like a vast fortress, with underground dungeons, which he held as a threat over workers who failed to share his passion for accurate observing, which was all that mattered to him.

Urania was equipped with the best naked-eye instruments Tycho could design, including huge equatorial armillary spheres, quadrants, sextants, and celestial globes. These instruments ultimately ended up in the Jesuit observatory in Peking after Brahe was expelled from his island castle because he refused to obey the commands of the new young King Christian IV, who inherited the Danish crown when his father, Frederick, died.

When Christian IV, the new Danish king, deprived Tycho of the observatory and the benefits, Tycho accepted the invitation of the Holy Roman Emperor Rudolph II to come to Bohemia as the royal astronomer. There he was given an estate and castle at Benatky, near Prague. With a stipend of 3000 ducats, Tycho built another, much less pretentious observatory, and laid the basis for his collaboration with Kepler, which began in 1600, a year before Tycho died.

Brahe died in Prague. His wife and children were treated as nobility at the imperial court. They never had been at the Danish court.

The last 18 months of Brahe's life were perhaps his most productive— not because of what he himself did in that highly dramatic year and a half—but because of the work of his assistant, Johannes Kepler. In fact, it would not be too farfetched to suggest that Kepler's labors were anything less than the "redemption of Tycho Brahe."

Tycho knew that, without Kepler, the Tychonic system could never be placed on a sound mathematical base, and Kepler knew that all his attempts to establish the truth of the Copernican system would be in vain without Tycho's highly accurate observations of the planets, particularly those of Mars. Kepler believed that if he could fit Tycho's data for Mars into a circular orbit, he could prove the correctness of the Copernican heliocentric model of the solar system.

Tycho contributed two important discoveries to the understanding of two astronomical phenomena that were observed at that time. Tycho, on a walk near his home, suddenly saw a very bright star, near the constellation of Cassiopeia. As Tycho followed it, night after night, it began to fade. We know now that Tycho had observed a supernova, which is still called the 1572 Tycho nova. Tycho discussed the great comet of 1577 and conclusively proved that comets are not atmospheric phenomena but are instead produced in regions beyond the moon.

Far brighter than Venus, the star overwhelmed Tycho for he had never seen such a luminous non planetary object. Knowing the positions of all the visible stars, Tycho could only conclude that a new star had suddenly been created. Not believing his own eyes, he called upon all his neighbors to confirm his vision, which they did. This star was so bright that some people could see it during the day. Other astronomers had also seen it.

In those days the concept of a nova or supernova was not known and so the Tycho nova produced enormous excitement throughout Europe and confirmed the popular belief that Tycho was the supreme astronomer of his day. The wonder this celestial phenomenon produced stemmed from the belief that all changes observed in the sky were produced by the earth's atmosphere in accordance with Aristotelian philosophy and with the Scriptures.

Historians, through reading Pliny's Natural History, and astronomers knew that Hipparchus had recorded the appearance of a supernova in the year 125 BC but that was before the Christian era and, as a result, did not disturb the theologians of Tycho's time. Tycho considered this apparition as evidence of God's handiwork—the creation of a new star. To commemorate this occurrence, he published his first book De Stella Nova, in which he gave a detailed description of his observations of the nova, giving its exact position and an accurate description of the variations in its brightness from night to night. This book assured his everlasting fame.

By careful measurements of its change of position during the night and from night to night Brahe proved conclusively that comets come in from distances "at least six times as far as the moon." This, too, was in direct conflict with the Scriptures and Aristotelianism, which, during the Middle Ages, had prevented any serious study of comets.

Some attempts, particularly by Regiomontamus in Niirnberg, were made in the fifteenth century to measure the distance of some comets, but without success, because astronomical instruments were very crude in those days.

Tycho even attempted to calculate the orbit around the sun of the 1577 comet, but the best he could do was to conclude that the comet moved around the sun in a circle larger than the orbit of Venus. Tycho, of course, emphasized in his second book that the orbit of the comet fit nicely in his (the Tychonic system) model of the solar system. This book, widely distributed, popularized the Tychonic system.

Outstanding among all the Copemicans was the Italian philosopher and Dominican monk Giordano Bruno, who proposed the truly revolutionary idea that every star in the sky is a sun and that the universe extends infinitely in all directions so that no center of the universe exists. Bruno paid with his life for these ideas, being burned at the stake by the Inquisition as a heretic.

Bruno was thus the founder of modem philosophy, as first developed by Benedict Spinoza, who was greatly influenced by Bruno.

Many powerful church leaders in the Protestant and Catholic countries vigorously fought the spread of the Copernican doctrine. Martin Luther in Germany, for example, denounced the Copernicans as "scoundrels" and labeled Copernicus as "the fool [who] will upset the whole science of astronomy" and defy the "Holy Scripture [which] shows that it was the sun and not the earth which Joshua ordered to stand still."

The philosopher Philipp Melanchthon, a scholar and religious reformer, strongly supported Luther's condemnation of the Copernicans. Indeed, even before the publication of De Revolutionibus, Melanchthon wrote to a correspondent that "wise rulers should suppress such unbridled license of mind".

A Copernican, Kepler was was particularly driven to find relations among what, to others, appeared to be disparate, unrelated concepts. He did not believe in coincidences in nature. Throughout his life Kepler sought the law or laws that bind the solar system together and determine the geometry of the orbits and the dynamics of planets. He was Tycho Brahe’s disciple. His greatest achievement is discovering a set of laws of planetary motion, describing the motions of the planets around the sun. That the planets move in elliptical orbits is one of the most remarkable discoveries in the history of science.

Kepler was born on in the township of Weil (called Weil der Stadt), Wurtemberg. He described his grandfather Sibald as "remarkably arrogant and proudly dressed … short-tempered and obstinate . . . and licentious, eloquent, but ignorant" He predicted that his father, who deserted the family periodically, was "doomed to a bad end," picturing him as "vicious, inflexible, quarrelsome," and cruel to his family. He described himself as constantly ill, suffering from all kinds of diseases. In 1586, he wrote about himself "that man [Kepler] has in every way a doglike nature. In this man there are two opposite tendencies: always to regret any wasted time and always to waste it willingly."

He joined Tycho at the Castle of Benatky as his "official collaborator." A year later when Tycho died, Kepler was appointed to succeed him as imperial mathematician. With Brahe's observations of the planetary positions to hand, Kepler began his monumental work on the nature of the planetary orbits. The work lasted for 30 years and was completed with his discovery of his third law of planetary motion, which he called the "harmonic law."

He studied theology at the University of Tubingen, where Michael Mastlin, the outstanding scholar and astronomer of the time, introduced him to the Copernican heliocentric theory, with which Kepler was immediately enthralled. He had intended to enter the Protestant church as a Lutheran minister but was repelled by the narrow-minded spirit then prevalent among Lutheran theologians. He was therefore very happy to accept the post of "provincial mathematician" of Styria, which had extensive Protestant estates but was ruled by a Catholic Hapsburg prince.

When Kepler began his planetary research his target was Mars because the motion of Mars, as seen from the earth, is more irregular than that of any of the other known planets. Kepler knew that if he could "conquer the recalcitrant Mars" the other planets would be easy. He described Mars as the key to the mystery of the planetary orbits. In his usual flowery language he wrote that "Mars alone enables us to penetrate the secrets of astronomy which otherwise would remain forever hidden from us." Since no one before his time had discovered the true orbit of Mars he considered Mars as the "mighty victor of human inquisitiveness, who mocked all the devices of astronomers."

To solve the Martian problem Kepler first had to use the method of trigonometric parallaxes to calculate the distance of Mars from the sun for each distance of Mars from the Earth as given by Tycho. This is now known as the "Kepler problem." This may be described simply as the method a surveyor uses to find distances by triangulation. Kepler succeeded in deducing the orbit of Mars around the sun.

Kepler's work came to Tycho Brahe's attention and convinced Tycho that Kepler was a brilliant astronomer and just the kind of imaginative scientist he needed to prove the validity of the Tychonic model of the solar system. He therefore planned to make Kepler a member of his observatory. Kepler was quite enthusiastic about the prospect of working with Tycho.

Kepler published his first two laws in his magnum opus with the grand title: The New Astronomy Based on Causation or a Physics of the Sky Derived from the Investigations of the Motions of Mars Founded on the Observations of the Noble Tycho Brake. Kepler's book contains a complete description of Kepler's first two laws. This book launched Kepler into great public esteem and popularity. As its author, he became the uncontested astronomical authority and the "first astronomer" of Europe, recognized by poets, mathematicians, and other astronomers, including Galileo, as the greatest scientist of the age.

Astronomers after Copernicus continued his work, but none did so more faithfully than Galileo Galilei. An Italian astronomer, mathematician, physicist, and all-around scientist, Galileo was one of the first scientists to provide a mathematical description for the laws of nature. He also contributed significantly to society’s understanding of the physics of motion. Galileo designed enhanced telescopes (think of ’em as the Hubble Space Telescope of the Renaissance period) that were the most powerful of the day. That allowed him to perform the most-detailed astronomical observations of the time, including a study of Jupiter’s moons.

By using his telescopes, Galileo was able to identify lunar topography, observe the phases of Venus, and make detailed notes about stars and their positions over time. His studies also convinced him that the geocentric theory of planetary orbit was wrong, and he expressed vocal support for the heliocentric theory espoused by Copernicus. However, the Catholic Church persecuted him for teaching these beliefs and committed him to house arrest toward the end of his life.

Like Kepler, Galileo began as a mathematician, starting his mathematical career at the age of 25 when he was appointed to the chair of mathematics at the University of Pisa. Though miserably paid, he was content to remain there for about 3 years because he had the leisure time to pursue his interests in mathematics and physics. During his few years at Pisa, Galileo turned to his true interest—the nature of motion and the motions of freely falling bodies. These investigations led him to the discovery or, more appropriately, to the founding of the modem science of dynamics.

From Pisa Galileo went to Padua where he spent 18 years as professor of mathematics at the University of Padua. In addition to mathematics, he also taught astronomy there but devoted most of his spare time to constructing and studying the mechanics of such devices as pendula, metronomes, and the hydrostatic balance. His treatises on such instruments which he circulated and his lectures brought him to the attention of the outstanding scholars of the day.

Galileo pursued his interests in physics. During this period of his life he discovered one of the most remarkable laws in nature: all bodies starting from rest at the same point (the same height) above the surface of the earth fall with exactly the same speed in a vacuum regardless of their weights. Galileo did not state this as a natural law because he did not have the law of gravity (which Newton discovered later) to guide him. He simply stated it as an observation, after watching different bodies fall to the ground from the same height (from the top of the leaning tower of Pisa, it is said).

The turning point in Galileo's pursuit of science and in the study of astronomy occurred in 1609 when he learned that a Dutch lensmaker (optician) Johann Lippershey had constructed a telescope. After reading the description of the instrument, Galileo built one himself, which was the first astronomical telescope. It did not take Galileo long to go from the description of the Lippershey telescope to the construction of his own model, which consisted of two lenses mounted in a long tube.

The basic optical principle of the telescope is quite simple. The lens mounted at the front end of the tube is called the "objective" of the telescope. It refracts (bends) the rays of light from a star so that they converge to a point near the rear end of the tube, thus forming an image of the star, or of any distant object. Since this image is very small, a second lens called an "eyepiece" is introduced at the rear of the tube to magnify the image. The objective (the front lens) is convex (both surfaces bulge out) but the "eyepiece" (the back lens) may be convex or concave (both surfaces curve in). Galileo constructed a telescope with a convex objective (an absolute requirement) and with a concave eyepiece; in modern telescopes the eyepieces are convex.

Galileo was also the first to discover gaseous nebulae in our galaxy, noting that they are distributed in regions outside the Milky Way and that a close inspection of these nebulae reveals the presence of stars within them. Galileo was particularly struck by the Orion nebula in which he found 21 stare and the Praesepe nebula in which he counted "40 starlets."

Galileo’s main concern, after he built his telescope, was to inform the public of his great astronomical discoveries, and he began by inviting the Venetian Senate to look through his "spyglass" from the tower of St. Marco. By that time he had built a 9-power telescope and its effect on the senators was spectacular. The Senate immediately doubled his salary and made his professorship at Padua permanent. His next step was to publish the first of his books, The Starry Messenger, which revolutionized the study of astronomy. He dedicated his book to Duke Cosimo II De Medici, his sponsor, whom Galileo tutored during childhood.

In Galileo's book, we see the revolution that made astronomy accessible to more than the few devotees such as Tycho Brahe who had developed the special aptitudes and patience that are required for the naked-eye study of celestial bodies and placed it in the hands of all who could construct or buy telescopes. In addition, the gap that existed between the observational and theoretical astronomers before Galileo was eliminated, As we have already noted, Copernicus was not an observer nor was Kepler. Thus Galileo was the first astronomer who combined observation and theory.

Observing the sky every night, he soon discovered the difference between the fixed stars and those he called the Medicean stars (the moons of Jupiter) which do not remain fixed but, as he noted, revolve around Jupiter, This was the first clear statement in the story of astronomy that the fixed stars constitute a celestial system quite distinct from the system of planets and satellites.

The frontispiece of the book read: “ Revealing great, unusual and remarkable spectacles, opening these to the consideration of every man, and especially of philosophers and astronomers; as Observed by Galileo Galilei, Gentleman of Florence, Professor of Mathematics in the University of Padua With the Aid of a Spyglass lately invented by him, in the surface of the Moon, in innumerable Fixed Stars, in nebulae and Above all in FOUR PLANETS swiftly moving about Jupiter at differing distances and periods and known to no one before the author recently perceived them and decided that they should be named THE MEDICEAN STARS, VENICE 1610.”

Galileo dedicated The Starry Messenger to "The Most Serene Cosimo II De Medici" in the very flowery language that Galileo used in his pursuit of powerful public figures and patrons who might support his scientific ventures. Unlike Kepler, Galileo was never loathe to compliment those who could help him. Thus in his dedication to Cosimo de Medici he emphasized that he named the four satellites that he observed circling Jupiter "the Medicean Stars" in honor of the Medici family.

The language of Galileo's dedication speaks volumes about his own personality: “Indeed, the maker of the stars himself has seemed by clear indications to direct that I assign these new planets Your Highness' famous name in preference to all others. For just as these stars, like children worthy of their sire, never leave the side of Jupiter by any appreciable distance, so as, indeed, who does not know clemency, kindness of heart, gentleness of manner, splendor of royal blood, nobility in public affairs, and excellency of authority and rule have all fixed their abode and habitation in Your Highness. And who, I ask once more, does not know that all these virtues emanate from the benign star of Jupiter next after God as the source of all things good.”

One can hardly treat The Starry Messenger as a book because it consisted of no more than 27 pages; it is thus a treatise or a pamphlet. Each of the discoveries announced in it could quite easily have been expanded into a thick tome, but Galileo was so astonished and overwhelmed by his discoveries that he could not resist the intense pressure to publish them immediately and receive his due credits and rewards before anyone else could do so.

Galileo's book was as much a journal of his discoveries and was presumably written in the order in which the discoveries were made. First, he discussed the surface of the moon. Galileo's description of the stars as revealed by the telescope followed this discussion of the moon. He then went on to report that the Milky Way is not a nebulous gaseous structure like smoke but consists of innumerable "points of light" which he correctly interpreted as individual stars at such great distances that they appear faint.

A student at Padua, Baldassarre Capra, published in Latin, Galileo's description (written in the Tuscan dialect) of the compass and claimed it as his own. Galileo was so enraged at this attempted theft that he wrote A Defense Against the Calumnies and Impostures of Baldessarre Capra. Galileo brought a legal action against Capra, which he won, and so Capra's book was banned. Galileo's writings brought him fame throughout Europe and he was sought out by students everywhere.

Here Galileo, accusing Capra of plagiarism and theft, exhibited his great skill as a polemicist; he used this skill extensively in all his future literary works.

Galileo was somewhat secretive about his important discoveries such as the law of falling bodies, the concept of inertia, and the laws of projectiles. He communicated these ideas, as well as his cosmological concepts, only to those persons like Kepler, who, he knew would accept them or, at the very least, consider them with an open mind. The two corresponded regularly. Galileo first learned of Kepler through a common friend, Paulus Amberger, who delivered Kepler's book, Cosmic Mystery, to Galileo. Kepler, in a letter to his teacher, Maestlin, states that he had sent a copy of his book "to a mathematician Galileus Galileus, as he signs himself."

In spite of Galileo's complete acceptance of the Copernican doctrine, he was loathe to publicize it, not because of his fear of persecution by the Church but because of his fear of ridicule. This fear is indicated in the final lines of the substantive part of this letter to Kepler where Galileo expresses his reluctance as follows: “I have written [conscripsi] many arguments in support of him [Copernicus] and in refutation of the opposite view, with which, however, so far I have not dared into the public light, frightened by the fate of Copernicus himself, our teacher, who, though he acquired immortal fame with some, is yet to an infinitude of others (for such is the number of fools) an object of ridicule and derision, I would certainly dare to publish my reflections at once if more people like you existed; as they don't, I shall refrain from doing so.” In a reply to this letter, Kepler exhorts Galileo to help spread the Copernican truth and not to fear the scorn of the ignorant, presenting himself as an example of one who prefers "the most acrimonious criticism of a single enlightened man to the unreasoned applause of the common crowd."

Seeking the approbation of his science peers and recognizing Kepler as "the Imperial Mathematician" of Europe, Galileo wanted, above all, Kepler's praise and so he requested the Tuscan ambassador to Prague, Julian de Medici, to inform Kepler verbally of his astronomical telescope and of his discoveries. Kepler's response was immediate and wrote his support in the form of an open letter which appeared in the form of a scientific pamphlet which he titled "Conversations with the Star Messenger," which was printed in Prague and in Florence in Italian. In his most glowing language, Kepler exhorted the public to recognize Galileo's great discoveries.

Referring to The Starry Messenger, Kepler wrote that "it offered a very important and wonderful revelation to astronomers and philosophers, inviting all adherents of true philosophy and truth to contemplate matters of greatest import. Who can remain silent in the face of such a message? Who does not overflow with the love of the divine?"

To emphasize his support of Galileo, Kepler wrote to him that "in the battle against the ill-tempered reactionaries, who reject everything that is unknown as unbelievable, who reject everything that departs from the beaten track of Aristotle as a desecration ... I accept your claims as true, without being able to add my own observations."

Galileo was under attack by the Aristotelians and clerics who saw his doctrines as a direct threat to their power and positions. They therefore turned to the Bible to find arguments against his support of the Copernican cosmology. Galileo was very skillful in demolishing the arguments of his opponents, but he could not defend himself from arrest and trial by the Roman Inquisition. This was preceded by the publication of Galileo's last great work, The Dialogue on the Two Chief Systems of the World. This was the first book of popular science ever written. Only with Galileo's death in 1643 did the struggle between science and religion end.

Galileo was clever enough to see that he could defeat his attackers only by showing first that the Bible cannot and, indeed, should not be used as a measure of the truth of scientific enquiries and, second, that none of his own discoveries conflicted with the Bible.

The Dialogue on the Two Chief Systems of the World was a layman's encyclopedia of all of Galileo's discoveries and his explanation of the natural phenomena they represented. Here he boldly defended the Copernican system and the doctrine of the motion of the Earth around the sun.

The persecution of Galileo by the Church marked the last unsuccessful gasp of the clerics' efforts to prevent the flowering of the new science brought forth by the works of Copernicus, Kepler, and Galileo. Ultimately these new ideas swept aside the increasingly obsolete objections voiced by their critics. Although the Church was not happy to lose its primacy in matters relating to the description of creation, there was increasingly little to be done about it.

Various monarchs, in the tradition of King Frederick II of Denmark who funded Brahe's observatory Urania, and Emperor Rudolf II of Bohemia who funded Brahe's observatory at Benathky, began to encourage and fund astronomical research and the construction of observatories and telescopes in their countries. Most notable among these was Louis XIV (the "Sun King") of France, who established the French Academy of Sciences. The French Academy of Sciences attracted scientists from all over the world, among them astronomers such as Johannes Hevelius of Danzig, Giovanni Cassini of Bologna, Olaus Roemer of Denmark, and Christian Huygens of Holland.

With the great publicity that followed Galileo's exploits with his telescope, it was quite natural that members of the French Academy and other astronomers should concentrate on constructing larger and larger telescopes, with the hope of increasing their magnifying power and thereby seeing the images produced by these telescopes in greater detail.

The French Academy met in a baroque palace, which would have remained just that if its future director Giovanni Cassini had not insisted that it also serve as an observatory to accommodate Cassini's telescope. But he could not convince Louis XIV to go to the additional expense of altering the palace, so its desired functions had to be pursued outside the palace, where Cassini set up his instruments and made his observations.

Giovanni Cassini’s greatest discovery was that the "handles" that Galileo observed around Saturn do not form a continuous structure but consist of a set of rings separated from each other by gaps, Cassini discovered the largest of these divisions, called the "Cassini division." Today we know, from space probes, that the rings contain many such divisions. Cassini also measured Jupiter's period of rotation (about 10 hours), discovered the dark band across Jupiter's equator, and found four other Jovian moons which are much fainter than the four moons Galileo had discovered.

During this pre-Newtonian period advances in astronomy remained in the realm of observation and measurement, with very little time or effort devoted to theory, that is, to the understanding or explanation of celestial phenomena in terms of bask laws or principles. But the observations and measurements became more sophisticated and accurate. Thus the French Academy set as one of its goals the accurate determination of the circumference of the Earth, which, as we have already mentioned, Eratosthenes had done in about 250 BC.

Johannes Hevelius of Danzig was particularly interested in the moon and constructed one of the first private observatories to study the lunar surface; he produced more than a hundred prints of its surface which he had engraved on copper plates. Hevelius also studied sunspots, cataloged many stars, discovered four comets, recorded the phases of Saturn,and was one of the first to observe the transit of Mercury across the face of the sun.

The known distance of the sun from the earth and the eclipses of Jupiter's moons enabled Olaus Roemer to measure, for the first time, the speed of light. The determination of the nature of light and, particularly, the measurement of its speed, had eluded scientists for thousands of years. Roemer greatly increased the usefulness of the telescope as an instrument for measuring and cataloging the positions of celestial bodies by anchoring the telescope to the floor of an observatory in such a way that it could be rotated only along the meridian (the north-south circle). This circle thus became known as the "meridian circle."

Christian Huygens was the youngest member of the Academy but he contributed greatly to all branches of science, particularly to the wave theory of light. He spent only a few years at the French Academy, and then returned to Holland.

Isaac Newton was the dominant figure of 17th and early 18th century physical astronomy England under Newton, became the center of research not only in experimental science (physics) but also, owing to Newton's great mathematical powers, in theoretical physics. This primacy, of course, influenced the development of astronomy enormously. Here, however, we consider primarily his contributions to astronomy. His contributions to the optics of the telescope led to great improvements in telescope construction and in the quality of the images produced by telescopes. He also formulated 3 fundamental laws of motion.

Newton's contributions to astronomy were not limited to his theoretical work, as manifested by his laws, for his work in optics led to the discovery of the spectroscope and to the introduction of the reflecting telescope.

Though not a spectacular classroom student during his boyhood, Newton was always performing all sorts of simple experiments on things all around him to satisfy his curiosity about "how things worked." His boyhood fancies gave way to great and profound ideas after he had enrolled at Cambridge at the age of 18. Newton completed his bachelor's degree in 1665 when he was ready to astound the world of science and mathematics with the announcement of his many simultaneous discoveries.

Newton made a number of theoretical and experimental discoveries that many consider to be the greatest intellectual accomplishment of all time. Among his greatest discoveries were his summing of infinite series, representing binomials as series (e.g. the binomial theorem), trigonometry, the differential calculus (the fluxions), the "theory of colors," the integral calculus, the law of gravity, and the laws of motion.

In the first edition of his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) he stated that "the whole burden of philosophy [natural laws] seems to consist in this—from the phenomena of motions to investigating the forces of nature and from these forces to demonstrate the other phenomena." This immediately presents to us the revolutionary nature of Newton's departure from the Aristotelian approach to the study and the nature of motion. Newton did not differentiate between "heavy" and "light" bodies, stating that the way all bodies move depends on the forces acting on these bodies.

Newton noted that the motions of the moon and the planets deviate from rectilinear motion and concluded that some kind of force acts on these bodies which emanates from the Earth (in the case of the moon) and from the sun (in the case of the planets). With these ideas slowly maturing in his mind, Newton was about to formulate his three laws of motion which launched astronomy from guesswork and speculation to being a precise science.

Galileo's concept of inertia (mass) as that property of a body which causes the body to persist in its state of motion (rest or uniform motion in a straight line) unless prevented from doing so by some external agency. Newton accepted this hypothesis as a law of nature and called the external agency "force." This, indeed, became Newton's first law of motion. This led him to a profound insight into the motion of the moon around the earth and the motions of the planets around the sun.

The second law of motion explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the "changes" expressed in the second law are most accurately defined in differential forms. The third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force on object A. Notice that the forces are exerted on different objects.

To evaluate the full impact of Newton's work on astronomy is difficult, if not impossible, but we are not off the mark if we say that Newton ushered in the rise of modern astronomy. His discoveries in mathematics, physics, and optics were incredible stimuli to the rapid development of theoretical astronomy, observational astronomy, and to the construction of observatories, either as adjuncts to universities or as independent national institutions.

Newton's discovery of the differential calculus and its enormous usefulness in expressing in manageable mathematical forms (differential equations) the motions of bodies acted on by forces, loosed a veritable torrent of activity in the mathematical analysis of the dynamics of the solar system and stellar systems. These studies were no longer the exclusive domain of astronomers for they were open to anyone who knew some calculus and knew how to apply it to dynamical analysis.

Observational astronomy, observatories, and telescopes grew and evolved together. Naturally, considering Newton's great influence, we can understand why England led in these developments. The first great national observatory at Greenwich, founded by King Charles II, has been in the forefront of astronomical research for more than 300 years. At the same time the office of the Astronomer Royal and the Royal Astronomical Society were established, John Flamsteed was appointed the first Astronomer Royal. He was followed by Edmund Halley, famous for his discovery of the comet named for him.

The continental countries quickly followed England's lead, constructing telescopes and observatories of their own. But England had an additional motivation that contributed to the rapid construction of observatories: the Royal Navy's need for accurate navigational instruments and techniques. As the leading maritime European power at the time of Newton, with commercial interests all over the world, England's devotion to astronomy and to the Greenwich observatory was prompted, in part, by its search for an accurate navigational technology based on accurate observations of the positions of groups of well-known stars.

The Newtonian principles (the laws of motion and the law of gravity) and the calculus beckoned physicists and mathematicians, as well as theoretical astronomers, to the pursuit of theoretical astronomy. The emphasis in those early days was on the study of planetary motions and on attempts to deduce them mathematically from Newton's laws.

As the first Astronomer Royal, John Flamsteed laid the foundation for the vast scientific structure that we now call observational or positional astronomy, which deals primarily with measuring accurately the positions of stars. Flamsteed showed, by comparing the positions of the same stars over time, that the stars are not fixed but move about the evening sky. This discovery stemmed from later observations that the positions of the stars had changed. Flamsteed himself had measured the positions of about 3000 stars.

Newton's contribution to astronomy went far beyond his discoveries of the laws of motion and gravity because he changed the whole spirit and tenor of the study of celestial bodies and even of space and time. This was a giant step away from the Galilean era. After Newton, no one dared to challenge scientific doctrine or discoveries, no matter how far they departed from religious doctrine or scholasticism.

Edmund Halley improved on John Flamsteed's observations of stellar positions, becoming the first astronomer to demonstrate that "fixed stars" are not fixed but move with respect to each other and with respect to the solar system. Before becoming the Astronomer Royal, he went to the Island of St. Helena to catalog stars visible only in the southern latitudes. In his ocean journeys he discovered that his magnetic compass did not always point due north and from that observation deduced that the north magnetic pole does not coincide with the geographic North Pole. Halley also studied comets.

From a comparison of his measured positions of stars with those of Flamsteed, Halley proved by direct observations a conclusion he had already drawn from a comparison of ancient astronomical manuscripts listing stellar positions with those that his contemporaries were preparing using the best instruments then available—that the stars are actually moving objects. In particular, he found that Sirius, Aldebaran, and Arcturus had shifted from their positions listed by Aristarchus.

Halley decided to apply Newton's laws to the motions of comets and proved that the comets he studied were, like the planets, moving in elliptical orbits around the sun. He applied his analysis of comets, in particular, to the famous comet that appeared in 1687 and which now bears his name, correctly calculating its period as 76 years, from which he deduced that the same comet had appeared in 1066,1531, and 1607, He went on to predict that it would reappear in 1758, as it did.

By comparing the times of occurrence of ancient eclipses with the time of occurrence of similar eclipses in the 17th century, Haley deduced that the length of the day had increased since biblical times and that the moon's distance from the earth had increased, while at the same time, its speed in its orbit around the earth had decreased.

Halley was a devoted disciple of Newton and advanced his ideas and theories whenever and wherever he could. Concerned that the Newtonian truths might be lost, he persuaded Newton to write his famous Principia which Hailey published at his own expense.

Halley also oversaw the physical production of the book and spent many hours reviewing its proofs. Indeed, it may be said that Newton's Principia, perhaps the single most influential scientific work of all time, would never have seen the light of day had it not been for Halley's insistence that Newton expound his revolutionary ideas about motion and gravity.

James Bradley, who took over management of the Greenwich Observatory front Halley, was also a follower of Newton. His great contribution to observational astronomy was his insistence on the need for accuracy in such observations. He pointed out that such stellar observations are affected by certain properties of the Earth.

If the Earth were not rotating or revolving around the sun but were a perfect sphere with no atmosphere, then the observed position of a star would be its accurate position relative to the earth. But the earth's atmosphere and its various motions introduce errors in the observations. These errors arise from the refraction of the light from the star by the Earth's atmosphere, the aberration of starlight stemming from the Earth's motion around the sun, and the shift of the Earth's north celestial pole owing to what we now call the precession of the equinoxes.

Bradley calculated the speed of the Earth in its orbit to be 1/10000 times the speed of light. He then calculated the circumference of the Earth's orbit and, thus, the radius of the Earth's orbit. Taking all of these discoveries into account we may say that Bradley was the father of precision in observational astronomy.

Not all of Newton's contemporaries worshipped him as devotedly as Halley and Bradley. Robert Hooke was one of the those who even went so far as to claim (unjustly) prior discovery of some of Newton's discoveries. He even claimed that he had prior knowledge of the law of gravity, but he could point to nothing that he had written or said that can be taken as a formulation of the law. Although a brilliant researcher Hooke's work did not advance astronomy to any great extent, even though he was a fervent supporter of it.

Hooke was a very ingenious experimenter with a brilliant mind who dabbled in many things including philosophy. He made some important discoveries in the structure and properties of matter, including Hooke's law of the elasticity of solids: the amount by which a solid can be stretched in a given direction is proportional to the force acting on the body in that direction. This law is generally expressed by the statement that "strain is proportional to stress."

Although Hooke's discoveries had no direct bearing on astronomy, they convinced others that careful experimentation and measurements reveal laws of nature. Robert Boyle was a contemporary of Newton, for example, who stands high in the ranks of such experimenters.

Christian Huygens proposed the wave theory of light, which marked him as one of the outstanding physicists of all time. Not only was Huygens an excellent mathematician and physicist, but he was also a very good astronomer. He developed a new method of grinding and polishing lenses which produced more accurate and better lenses.

He also designed a new type of eyepiece for telescopes so that he achieved sharper optical definition, leading him to the discovery of a satellite of Saturn and to a more accurate description of Saturn's rings than had been possible previously. The wave theory of light (called physical optics) enables us to understand better the formation of images in telescopes.

Turning away from Newton's immediate contemporaries we come to Thomas Wright, who may be called the father of galactic astronomy. As a sailor he had ample time to study the heavens, particularly the Milky Way or galaxy. Many observers before Wright had discovered that as one turned toward the Milky Way the number of stars concentrated in a given area of the sky increased. But Wright was the first to suggest that the stars in the Milky Way form a single system shaped like a lens, thick at the center and thin at the edges.

Wright concluded, very boldly, that the stars do not form a spherical system but rather a somewhat flattened system. His only error was his assumption that our solar system is at the center of this system.

As astronomers discovered in the modern astronomical era we are far from the center—indeed, our solar system is at the edge of the galaxy, some 30,000 light years from its center. This same idea was promulgated some years later by the German philosopher Immanuel Kant in his book General Natural History and Theory of the Heavens. Kant went so far as to suggest that many galaxies like ours exist in the universe, each consisting of numerous stars. We may consider this prediction as marking the beginning of modern cosmology.

Leonhard Euler was probably the most productive mathematician of the 18th century. In his work on the lunar theory Euler laid the mathematical foundation for almost all future work that dealt with orbital theory. In particular, he initiated the theory of "successive approximation" and the theory of "perturbations," which encompass more than astronomical problems. Among his astronomical treatises we note his work on celestial mechanics, which stemmed from his analysis of the motions of the planets and comets. He discovered the “Euler equation”, an extension of Newton’s work.

Newton obtained Kepler's laws (elliptical orbits) with very little effort, but he could not solve the general three-body problem, which deals with three mass points interacting gravitationally. Euler confronted this problem, which has still not been solved, in his treatment of the lunar problem, the three bodies in this case being the Earth, the moon, and the sun.

The Euler equation is really a set of equations which Euler deduced by the application of a new branch of calculus called "the calculus of variations" which is useful and, indeed, indispensable in every branch of science. Euler also developed a set of equations, again an extension of Newton's laws of motion, to describe the motions of rigid bodies. These equations are indispensable in the study of the rotation of bodies such as the earth, the sun, and the planets.

Joseph Louis Lagrange is most famous for his "Mecanique Analytique" in which he extended Euler's dynamical equations in a form which is still used extensively in physics and astronomy. For the first time the concept of energy was introduced (specifically in the study of the motions of the planets).

Lagrange pointed out that Newton's laws need not be introduced specifically; one can replace them by introducing a quantity that is now known as the Lagrangian of a system of bodies. The "Lagrangian" consists of two kinds of energy of a body: the kinetic energy and the potential energy.

With the aid of Lagrange's equation we can then show, as Lagrange did, that only if the total energy of a body, revolving around another one gravitationally, is negative, can the two bodies stay bound to each other. The orbit is then an ellipse. If the total energy is zero, the orbit is a parabola and the two bodies cannot stay together. If the total energy is positive, the orbit is a hyperbola and, again, the bodies fly apart. Since the orbit of any one of the planets in the solar system is closed, the planet remains attached to the sun; its total energy is thus negative.

The introduction of the energy concept in dynamics led to the principle of conservation of energy, the first of a series of conservation principles which are extremely important in astronomy. This principle tells us that the total energy of a planet moving around the sun must remain constant.

Lagrange's final contribution to astronomical theory dealt with the stability of the planetary system. Although the gravitational interactions of the planets among themselves are negligible compared to the overall solar gravitational action, one might expect these interplanetary interactions to be cumulative and, ultimately, after millions of years, to destroy the planetary order. But, as Lagrange proved, this is not so; the perturbations produce small periodic changes in the planetary orbits, but the planets always remain near mean positions which define their orbits. The solar system is, accordingly, highly stable.

Alexis Claude Clairaut, having published his first mathematical paper, The Differential Geometry of Space Curves, at the age of 18, he was elected to the French Academy by the time he entered the university. Interested as he was in space geometry, he turned his attention to the shape of the Earth, which he analyzed in his book The Theory of the Shape of the Earth. Clairaut proved that, owing to its rotation, the Earth is not a sphere but an ellipsoid, flattened at its poles. Clairaut achieved another success when he confirmed, by detailed calculations, Halley's prediction that Jupiter's gravitational pull on Halley's comet delays its periodic return.

Clairaut showed that the Earth's shape is determined by its surface gravity, which depends both on its ellipticity and on its internal constitution. As the Earth's rotation produces a centrifugal force on its surface, the Earth's shape at any point on its surface depends on how large this "centrifugal force" is compared to the force of gravity at that point. Clairaut derived the formula for the oblateness of the Earth (the flattening at its poles) in terms of its surface gravity. This must be credited as one of the great successes of gravitational theory.

Clairaut had predicted that the comet would return in the early part of 1759, somewhat later than one might have expected. It returned on March 13, 1759, a month earlier than Clairaut's calculations had predicted. This was a remarkable achievement when one considers the almost primitive level of mathematical calculations in those days.

Clairaut's scientific enterprises are associated with the activities of another famous mathematician, Pierre de Maupertuis. Though Maupertuis did not contribute much to astronomy, he discovered a remarkable principle which made him famous. This principle, known as the "principle of least action," states that a certain entity called "action" associated with the motion of a particle or a group of particles must be a minimum along the actual path of the particle. According to this point of view, a planet moves along an ellipse because its action along the ellipse is smaller than along any other path.

This remarkable minimal principle has expanded enormously since it was first proposed by de Maupertuis in its simple form.

The attention of the French circle of astronomers and mathematicians now shifted to Pierre-Simon Laplace, whom we may consider as the father of cosmogony. He wrote a history of astronomy, Exposition du Système du Monde. First attracted to the dynamics of the solar system, he progressed from an analysis of the perturbations of the planets, proving that the solar system is highly stable, to his magnum opus, the origin of the solar system, based on his "nebular hypothesis" of the origin of stars. Laplace's boldness knew no bounds for he promulgated what we must accept as the first statement of a unified theory of science.

It was only natural for mathematicians, philosophers, physicists, and theologians to turn to cosmogony (which deals with the origin of the cosmos) and cosmology (which deals with the evolution of the cosmos) with the acceptance of Newtonian gravitation as the basis of the dynamics which governs the entire universe.

In promulgating his nebular hypothesis of the origin of the solar system, Laplace went far beyond anything that had been done with Newtonian dynamics up to that time. This required boldness of thought and great mathematical skill, both of which Laplace had in abundance.

The nebular hypothesis was not entirely original with Laplace. The German philosopher Immanuel Kant had proposed a similar idea, as had the Swedish scientist Emanuel Swedenborg. The difference between Laplace's proposal and those of Kant and Swedenborg is that Laplace's work, still extant, was developed in a rigorous mathematical way whereas Kant and Swedenborg did nothing more than propose their speculative ideas.

The nebular hypothesis was not immediately accepted by Laplace's contemporaries because the mathematical skills required to show in detail just how the sun and planets in the solar system took their present shapes and sizes, and why the planets move in orbits that are spaced in a fairly regular pattern around the sun, were not available.

Though accepted quite readily in its early years, the nebular hypothesis lost favor in time, but it regained favor in the 20th century and today, though still presenting very challenging problems, it is universally accepted as the only viable theory of the birth of stars and planets.

Laplace’s statement of a unified theory of science,expressed in his own words it must have shocked the 18th century intelligentsia, in spite of their acceptance of their age as the "age of reason," for it was a direct acceptance of what we would now call "mechanical materialism," which Laplace stated as follows: “An intelligence which, for a given instant, knew all the forces by which nature is animated, and the respective positions of the beings which compose it, and which, besides, was large enough to submit these data to analysis, would embrace in the same formula the motions of the largest bodies in the universe, and those of the lightest atoms: nothing would be uncertain to it, and the future as well as the past would be present to its eyes. Human mind offers a feeble sketch of this intelligence to the perfection which it has been able to give to Astronomy.”

To the late 18th and early 19th century observational astronomers, making meaningful observations beyond the solar system meant constructing large telescopes and large observatories to house them. In this resurgence of observational astronomy, the lead, under the direction of the British astronomer, Sir William Herschel, was taken by England. He constructed the largest telescope up to that date. Charismatic and friendly, he was became famous for the discovery of the planet Uranus. Outside our solar system Herschel studied binary stars and star clusters.

In 1757 a 19-year-old musician from Hannover, Germany, settled in England as a music teacher and organist. Coming from a highly cultured and gifted German-Jewish family of musicians and having won a prestigious prize for his organ playing, William Herschel, at the age of 36, became the music master at Bath and a popular conductor. Although he had become a respected composer, he was devoting more and more of his time to astronomy. He began by setting up an observational program. Buying small telescopes he transformed his house into part observatory and part music studio.

From the study of binary stars Herschel went on to the study of groups of stars called stellar clusters, consisting of stars that move together through space, relative to the sun, like a gravitationally bound system. He first discovered triplet systems of stars, then quartets, and finally groups (clusters) consisting of dozens of stars. The Pleiades are a very striking example of such a cluster. Seven stars in this cluster are visible to the naked eye, but even with a small pair of binoculars one can pick up some 50 stars in this cluster.

Because only very small telescopes were available commercially, he decided to construct a large telescope for his own use. This entailed setting up a forge and an optical shop for polishing and testing metal mirrors. He became so proficient at polishing mirrors for telescopes that he began to construct telescopes for sale.

Having married into a wealthy family, his wife's income made it possible for Herschel to fulfill his greatest desire: to construct the largest telescope ever built. This telescope became the sensation of the day and attracted visitors from all parts of England. These visitors enjoyed not only the view of the telescope but also the charm of Herschel himself.

A great teacher and lecturer, Herschel was described by those who heard him as a "delightful, extremely modest man, for all his vast knowledge; candid as a child, delicately tactful and considerate; he makes everything extremely clear . . . and puts over his own ideas with indescribable charm. He knows the history of all the heavenly bodies to the furthermost boundaries of the Galaxy."

Although Herschel became world famous owing to his discovery of the seventh planet Uranus, astronomers do not consider that to be a discovery of basic astronomical importance. Anyone who had surveyed the sky with a large telescope as patiently and as assiduously as Herschel had, would have, in time, picked up Uranus.

Herschel's well-deserved reputation as an innovative astronomer rests on his stellar work, the new observational techniques he introduced, and the types of celestial objects on which he concentrated: nebulae, stellar clusters, and double stars. He studied double stars because he was convinced, and wanted to prove, that many double stars (two stars that appear to be close together) are, indeed, gravitationally bound to each other and thus form what astronomers call a "binary system."

Herschel began to study distant galaxies and, quite correctly, proposed that they are all "island universes" like the Milky Way. This was the beginning of rational cosmology, the attempt by astronomers to understand and describe the structure and manifestations of the entire universe in terms of Newton's laws. Observing the galaxies distributed throughout the space that was observable to him at the time, he reasoned correctly that they could not be fixed or suspended in space. The mutual force of gravity would cause them to move together, ultimately collapsing into a single sphere of matter. This would be the end of the universe.

Herschel paid considerable attention to the stars in the Milky Way and the structure of the Milky Way. He spent hours cataloging the stars in the solar neighborhood, noting how the stellar population increased dramatically as he turned his telescope toward the Milky Way itself. Using statistical methods he drew the first diagram of the Milky Way, showing it as an elongated ellipsoidal structure, thick at the center and thinning out at the edges.

He was the first astronomer to use the light year (the distance light travels in one year—about 6 trillion miles) consistently as an astronomical yardstick.

Caroline Herschel became William's observing assistant, spending many hours peering through the best and largest of his telescopes. Devoting herself to searching for comets, at her brother's suggestion, she became the first female astronomer. In all, she discovered eight comets, adding to the fame of the Herschel family.

Unable to perform all the activities required by his extensive program, Herschel brought his sister, Caroline, and brother, Alexander, over from Germany to live with him and help him in all his projects. Caroline became his assistant in astronomy and Alexander his commercial assistant.

William Herschel's influence on astronomy particularly on stimulating observational astronomy, was immeasurable, for he attracted the wealthy amateurs. The most famous such "wealthy amateur" was William Parsons, the third earl of Rosse in Ireland, who, in 1845, built the largest telescope of that time for his own use. Rosse is most famous for having detected and sketched the detailed spiral structure of what he called the "Whirlpool Nebula" (now known as the M51 galaxy).

His sketch shows a concentrated "core" or "nucleus" with spiral arms emanating from the core, and also a smaller "satellite galaxy" connected to the "whirlpool" by an extension of the outermost spiral arm.

While ever larger telescopes were being constructed by wealthy amateurs, a new technology—astronomical photography burst upon the world in 1870 and was to have as great an effect on 19th century astronomy as Galileo's telescope had on 17th century astronomy. The advent of photography freed observational astronomy from its dependence on the uncertainty of the observer's naked eye.

In photography we need not rely on the interpretation of the image formed on the retina of the observer's eye. It supplies the certainty of a photographic record that all observers can accept as an "objective truth," If one photograph of a celestial object does not suffice, many photographs can be taken and compared with each other.

The Austrian physicist Christian Doppler discovered that the color (wavelength) of the light from the source changed slightly if the source was moving toward him or receding from him as compared to the wavelength if the source was not moving. He explained this effect—known as the Doppler effect— by reasoning that if a source of light and observer are approaching each other, the waves of light are crowded together so that the observer finds the wavelengths shortened and the light is therefore bluer. If, on the other hand, the observer and source are receding from each other, the waves are stretched out (wavelengths are longer) and the light is redder.

For astronomy this was one of the most important discoveries of the 19th century. The Doppler effect is expressed by a simple algebraic formula. As an early example of the usefulness of this simple formula in astronomy, we note that the British astronomer William Higgins discovered that the spectral lines of Sirius are shifted toward the violet (wavelengths are shortened) indicating that Sirius is approaching us.

Photography very quickly permitted astronomers to measure stellar brightnesses and, from these measurements, to determine stellar luminosities very accurately. Photographic astronomy, for the first time, permitted astronomers to introduce a precise magnitude scale of brightness. This was done by the British astronomer Norman Pogson.

Pogson applied photometric measurements to determine by how much the brightness of stars of a given magnitude as proposed or defined by Hipparchus and Ptolemy differ from the brightness of stars assigned to a different magnitude.

Astronomers became interested in Mars owing to the announcement by the Italian astronomer Giovanni Schiaparelli that he had observed very long straight furrows or ravines which he called "canali" on the Martian surface. This word was unfortunately translated as "canals"— artifacts of intelligent beings. Since Schiaparelli was a highly respected astronomer his statement about "canali" on Mars was misinterpreted and blown up by the media out of all proportion. His "canali" became true canals (ie., artificial) in newspapers all over the world. This produced a Martian craze with observatories devoting themselves almost entirely to the study of Mars.

Schiaparelli had also observed the white polar caps of Mars which change with the Martian seasons, which one would naturally expect if the Martian polar caps were frozen water. This added fuel to the popular excitement about "intelligent life" on Mars, for it was argued that the canals had been constructed to bring water from the polar caps to the arid equatorial regions. And so the debate about life on Mars continued until well into the 20th century.

No one today doubts that physics and astronomy are interrelated and contribute to each other in very significant ways. But only in the last half of the nineteenth century was the indispensability of physics to astronomy clearly recognized.

For more than a century after Newton's great work, physics was pretty much limited to gravitational dynamics, and its greatest application was to the motions of celestial bodies, particularly those in the solar system. But this restricted role of physics changed dramatically in the last half of the nineteenth century with the discovery of the electromagnetic theory of light. From that time on, astronomy became increasingly dependent on physics. Indeed, the branch of astronomy that arose from the intimacy between physics and astronomy, now called "astrophysics," could not have emerged from Newtonian physics alone.

Benjamin Franklin discovered electric current. Observations and qualitative experiments with electric charges finally led to the branch of physics called electrostatics, the main goal of which, in the late 18th and early 19th century, was to introduce precision and quantitative methods in the study of electric charge. The first step in this heroic and revolutionary work was taken by the French physicist and engineer Charles Augustin de Coulomb who discovered what we now call Coulomb's law of force between electric charges.

With all of these discoveries about electric charges and magnetic poles, no one had the faintest notion that electricity and magnetism are related. This relationship was discovered accidentally by Danish physicist Hans Oersted while he was lecturing on electricity to a class at the University of Copenhagen. This was the beginning of the science of electromagnetism and electromagnetic technology, both of which were to play very important roles in astronomy.

Michael Faraday was thoroughly devoted to the concept of symmetry in nature, and he was convinced that the electricity-magnetism relationship discovered by Oersted is a two-way street. Being a tenacious experimentalist, it did not take Faraday long to discover that if a magnet is moved in and out of a loop of wire (an electrical conductor) an electric current flows in the loop. This is called electromagnetic induction. Thus Faraday completed the electric-magnetic symmetry circle that Oersted had begun.

Another important development in theoretical physics became the basis for astrophysics. This was thermodynamics, which grew out of the work of a group of brilliant scientists: Julius Mayer and Rudolf Julius Clausius in Germany, Nicolas Sadi Carnot in France, and William Thomson, first Baron Kelvin in England. Mayer's work led to the development of the science of thermodynamics, the mastery of which is absolutely essential to me understanding of stellar structure.

Astrophysics became increasingly more dependent on physics and physicists. Most important in this development were the contributions of the British physicist James Clerk Maxwell, who was the founder of the electromagnetic theory of light, and the Austrian theoretical physicist Ludwig Boltzmann. Boltzmann contributed greatly to the development of what is now called "statistical mechanics," which is the application of probability theory and statistical methods to the analysis and the understanding of phenomena involving extremely large numbers of particles (atoms and molecules), as in the interiors of stars.

James Clerk Maxwell developed a general formula from which one can calculate the numbers of particles in each velocity range (e.g., the numbers moving twice as fast as the average or one third as fast, etc.). This formula is known as the "Maxwell distribution" of velocities. The important parameter in this formula, as one expects, is the temperature. The importance of this formula for stellar structure (astrophysics) is fairly obvious, for only if we know how fast atoms in a star are moving about at any point can we determine the amount of stellar mass that must be present to keep the atoms from dispersing into space.

The final years of the 19th century saw the coming of age of astronomy as a scientific discipline in its own right and not merely as a branch of physics. This recognition by the science community and the academic community has been marked by the introduction of independent astronomy departments and astronomy faculties throughout the world.

The status of a university and of a college increased in the eyes of most people if the institution had a separate astronomy department. This status was further advanced with the construction of great observatories. In the United States most of the observatories were named after the universities with which they were associated.

In addition to the academic observatories, most countries constructed and financed national observatories. Thus in the United States we have the United States Naval Observatory in Washington, DC, which is not a research observatory but instead a service observatory which issues The American Ephemeris and Nautical Almanac each year, which provides important and useful information not only for the general public and the military but also for astronomers. In England, the Royal Greenwich Observatory performs the same functions.

During this period astronomy was also greatly advanced by the introduction of astronomical journals open to all astronomers and physicists who could submit original papers for publication. Thus the Royal Astronomical Society founded the Monthly Notices, B.A. Gould founded the Astronomical Journal now published by the American Astronomical Society; George E. Hale and James E.K. Keeler founded the Astrophysical Journal. In 1919, the International Astronomical Union (IAU) was founded to coordinate astronomical research in all countries.

Gustav Kirchhoff's law of radiation, states that the rate at which a body radiates energy at a given temperature and frequency (color) equals the rate at which it absorbs radiation at that frequency multiplied by the rate at which a perfect blackbody at the same temperature absorbs such radiation.

The importance of this law in studying the properties of radiation is that we can calculate the rate any body radiates from the rate at which it absorbs and the rate of emission of a black body. For that reason physicists were greatly interested, near the end of the 19th century, in discovering the mathematical formula for blackbody radiation (radiation emitted by a perfect blackbody). This kind of radiation (now called cosmic background radiation) fills all of space.

As the 19th century drew to a close, physicists faced the 20h century with a sense of great confidence, for it appeared to them that all that was left for physicists and astronomers to do was a kind of mopping up operation. With Newtonian dynamics, including Newtonian gravity, and the Maxwellian electromagnetic theory of light, everything in nature that one could think of seemed to be covered. And yet at this very time new experimental discoveries and two new theories were about to burst upon the science community.

The experimental work that was to revolutionize the science of matter dealt with the discovery of the basic electric charges that constitute matter. These experiments were performed with what is called a Crookes tube named after Sir William Crookes, a British chemist and physicist, who directed the meteorological work at the Radcliffe Observatory at Oxford. The Crookes tube is a device for producing what we now call cathode rays so that the Crookes tube is what we now call a cathode ray tube. Such tubes are the image-producing devices in all television sets.

With the discovery of the electron and proton, physicists now pointed the way to unraveling the mystery of the spectral lines by constructing a model of the atom with equal numbers of electrons and protons arranged in each atom to obtain an electrically neutral structure.

The X-ray tubes (which produce X rays) are an extension of the Crookes tube, which are made of glass and contain air or some other gas at very low pressure (about one ten thousandth of normal atmospheric pressure). This is called a Crookes vacuum. Sir Joseph John Thomson, the British experimental physicist and probably the outstanding scientist of his day, was the leader in this research. He correctly interpreted the stream of cathode ray particles as a stream of the basic (elementary) negatively electrically charged particles that constitute one of the electrically charged particles in matter. He called these particles "electrons".

While this exciting experimental work on the structure of matter was being pursued, experimental and theoretical work (theories) dealing with the behavior of light and of radiation, in general, was at the point of revealing two amazing facets of nature. One of these discoveries is associated with Max Planck and the other with Albert Einstein.

Planck's discovery introduced the constant h (Planck's constant of action) into the laws of nature and Einstein's theory introduced the speed of light c into the natural laws. These two constants together with G, the universal constant of gravity, are basic to an understanding of physics and astronomy, particularly astrophysics and cosmology.

All this experimental work pointed to an entirely new approach to the study of stars. After all, if solid matter consists of atoms of various kinds, then this must also be true of stars. The question that arose, of course, was whether observers on the earth could determine the chemical (atomic) nature of stars from an analysis of the light coming from the stars. Joseph von Fraunhofer had already answered this question in the affirmative by his discovery and analysis of the dark lines in the stellar spectra.

Einstein went on to make another important contribution to the development of the quantum theory by insisting that the quantum concept must be applied to all physical phenomena, and, in particular, to the various atomic and molecular processes in the universe. This philosophy led the Danish physicist Niels Bohr to his quantum model of the atom which brought all of physics, chemistry, and astronomy to their present states.

Albert Einstein presented the theory of relativity in two steps: the special theory of relativity first appeared in one of Einstein's three famous papers that were published that year in Annalen der physik. The great importance of these three papers may be gauged by their evaluation, many years later, by the Nobel laureate Max Born, who stated that each of these papers opened up a "whole new branch of physics." The second step in the presentation of the theory of relativity appeared as the general theory of relativity.

The theory of relativity deals with the question of the invariance (the constancy) of the laws of nature as these laws are stated by observers in different frames of reference. The word "different" here refers to the state of motion of the frame of reference. Einstein's theory of relativity goes beyond the invariants of pure mathematics and deals with the invariants and the relativity of the laws of nature and how these laws are to be formulated so that they are the same in all frames of reference. But the concept of invariance refers not to different frames of reference that are at rest with respect to the phenomena being studied but instead frames of reference that are moving with respect to such phenomena and with respect to each other.

If we limit ourselves to frames moving with constant velocity (called inertial frames) we have what Einstein called the "special theory of relativity." The special theory rests on the basic assumption that the laws of nature (of physics) must be "invariant" to a transformation from one inertial frame of reference to any other inertial frame. Because no absolute frame of reference exists in the universe, only relative motion has any physical meaning. This principle of invariance provides us with a very powerful analytical tool which can separate the false statements from the truth about the universe.

Einstein argued that the speed of light is the same for all observers and that the concept of the ether as an absolute frame of rest in the universe must be rejected. Einstein went further to point out that the constancy of the speed of light means that we must also discard the Newtonian-Galilean concept of absolute space and absolute time.

Einstein, knowing that the special theory of relativity is not the final chapter in the story of space, time and matter, spent a decade completing this story in his construction of the general theory of relativity, which is probably the single greatest and boldest creation of the human mind, for it merged physics and geometry.

Some of the most important advances in modern-day astronomy spring from the general theory of relativity. The radiation emitted from an atom in a strong gravitational field as on the surface of a "white dwarf," a very dense, small, but massive sphere, sends out light that is redder than the light it sends out when it is not in a strong gravitational field. The reason for this is that a vibrating atom is essentially a clock and therefore vibrates more slowly in a strong gravitational field than in a region of low gravity. This reddening effect, called the "Einstein red shift," is important in finding the radii of white dwarfs and other very dense stars.

A third effect predicted by Einstein's general theory of relativity is the bending of the path of a ray of light passing close to a massive body, such as the sun. Einstein announced his general theory of relativity during World War 1 and Karl Schwarzschild presented the first solution of Einstein's equations for a point source of gravity like the sun or for any other star. But not until 1919, when a British expedition led by the British astrophysicist Sir Arthur Eddington, observed a total eclipse of the sun in West Africa, was actual proof of this predicted effect obtained.

The announcement of the success of Einstein's general theory of relativity struck the world like a thunderbolt for it placed Einstein with Newton as the preeminent scientists of all time. Suddenly the name Einstein became a household word, while his theory of relativity remained a great mystery, mentioned with reverence and awe but much too esoteric to be understood except by a few chosen ones. Since then the cloak of mystery that surrounded this theory has been swept away and, if properly taught, it can be understood by high school students.

The two great nonclassical physical theories, the quantum theory and the theory of relativity, that led to the nuclear model of the atom, also led to astrophysics, and to a rational cosmology. Astronomy began to change from a discipline concerned with the study of the positions, the motions, and the clustering of stars to the study of the structure of stars, to "astrophysics," which is the application of the laws of physics to the analysis of stellar structure. The aim here was, and still is, to lay down the blueprint for the theoretical structure of a model of a star.

Because stars differ considerably in their physical features, a single stellar model cannot describe all kinds of stars. Astronomers, clearly recognizing this, understood the need to find those common physical characteristics that can be represented by a single stellar model. To this end they began to classify stars into groups with the idea that all the stars in a single group can be described by a single stellar model. Thus they reasoned they could construct a correct model of the sun and that that model would describe all stars like the sun.

Astronomers had been aware of the color differences among the visible stars (Sirius is called a white star whereas Betelgeuse, in Orion, is a red star, and the sun itself is a yellow star). Of course, in designating the color of a star as definite, such as red or blue, we do not mean that the star emits light of only that color; we mean that it is the dominant color in its emitted radiation. Although the sun is said to be a "yellow" star, it emits all colors, including the infrared and ultraviolet. The importance of the dominant color is that it is directly related to the absolute (kelvin) temperature of the star's surface (photosphere). This enables us, then, to correlate the spectra of stars to their colors.

The discovery of the spectral classification of stars was the first step in the study of astrophysics (the physics of stellar interiors) and ultimately, in the study of the birth, evolution, and death of stars. The second step after stellar spectral classification was the discovery of important physical differences among stars belonging to the same spectral class. This discovery required the development of an optical technology that enabled astronomers to assign large numbers of stars to their appropriate spectral classes almost at a glance.

Astronomers quickly discovered differences among stars in the same spectral class. These differences were first discovered by the Danish astronomer E. Hertzsprung. He discovered that the cooler yellow and red stars can themselves be divided into distinct groups: those that are intrinsically faint (low luminosity) and those that are intrinsically bright (large luminosity or small absolute magnitudes). Hertzsprung called the low luminosity stars "dwarfs" and large luminosity stars "giants." Thus the sun and Capella belong to the same spectral class (they are both G-type stars) but Capella, called a giant, is about 100 times as luminous as the sun.

This work begun by Hertzsprung was later extended by the Princeton University astronomer Henry Morris Russell, who extended these ideas to the hotter stars such as the A-type B-type stars. These discoveries of Hertzsprung and Russell were finally summarized in what today is called the Hertzsprung-Russell (H-R) diagram.

Sir Arthur Eddington published a series of basic papers which initiated modern astrophysics. Eddington may properly be called the father of astrophysics. His most important contribution was his demonstration that in most stars (such as the sun) the heat is transported by radiation and that convection may play a role close to the center of the star and in its outer envelope.

By accepting radiation as the dominant mechanism for stellar heat transport, astrophysicists were on their way to constructing acceptable stellar models and, in particular, solar models. But they could do this only if they could write down the proper equations to describe the transport of radiation through the stellar interior. This required some additional knowledge about the resistance of the stellar gaseous medium to the flow of radiation.

Eddington pointed out that at the high temperatures in stellar interiors all the electrons are stripped away from their nuclei so that the stellar material is essentially what physicists call a "plasma"—a medium of freely moving positive and negative electrical charges. Eddington made one more important contribution, pointing out that most of the stellar plasma consists of electrons, protons, helium nuclei, and only traces of heavy nuclei—no more than about 3 percent. Eddington's great contributions are summarized in his book The Internal Constitution of Stars, the first modern book on astrophysics and still a standard text.

Eddington described astrophysics as an "intellectual delving machine," for it permits us to probe deep into stellar interiors and to explain their superficial appearances as the consequence of their internal structures. All of this by properly applying the basic physical laws to the behavior of atoms and radiation at temperatures of millions of degrees. This is one of science's great successes.

While Eddington was laying down the foundations of modern astrophysics, his British contemporary, Sir James Jeans, like Eddington an excellent theoretical physicist as well as an astronomer, was extending the domain in which physics and astrophysics overlap so that one could justifiably speak of "astrophysics" as a field of study in its own right with physics as important to it as astronomy. Jeans was best known as a physicist for his theoretical contribution to our understanding of the laws of radiation.

These contributions and his astrophysical researches are described in his book Astronomy and Cosmogony, which goes beyond astrophysics and discusses such diverse astronomical fields as galaxies, the evolution of stars, stellar formations, stellar rotation, and the fission of stars.

The lack of knowledge about nuclear energy, which Eddington had suggested as a source of the sun's power, held up the development of astrophysics for some 20 years. The door to solving the stellar energy problem was opened by the discovery of the neutron by the British physicist James Chadwick. Up to that time the structure of the atomic nucleus was a deep mystery.

Because the neutron has zero electric charge we can add to or remove neutrons from nuclei without altering the chemical properties of their atoms, which are determined by the electric charges on their nuclei (their external electrons). Thus neutrons account for atomic isotopes (atoms with the same chemical properties but with different atomic weights).

The existence of the neutron leads us to the existence of another particle, called the neutrino, which plays an important role in physics and astronomy—particularly in the generation of nuclear energy. The neutrino was introduced in 1930 by the theoretical physicist Wolfgang Pauli to account for problems associated with the decay of certain radioactive nuclei that decay by emitting electrons, which are called beta rays.

The British experimentalist Sir Ernest Rutherford, who had worked extensively with radioactive atoms (nuclei), was the first to distinguish among the different components of the radiation emitted by such nuclei, calling them alpha, beta, and gamma rays. He identified alpha rays as positively charged particles with the same mass as the helium nucleus and then identified them as helium nuclei. He identified the gamma rays as very high energy photons (electromagnetic particles of very high frequencies) and identified the beta particles as high energy electrons.

The gamma rays and alpha particles presented no problems at the time of their discovery but the beta rays (electrons) presented a very serious problem which Pauli solved by proposing the neutrino. Pauli proposed the concept of the emission of another kind of particle with the electron in the beta decay of any beta-radioactive nucleus. This companion particle of the electron was named the neutrino because it is electrically neutral and, therefore, difficult to detect. Indeed, it was not detected until 1957.

The neutrino was used to explain some nuclear reactions of the sun that did not appear to conserve energy. Solar neutrinos have been detected. This chain of reactions for the generation of energy in the cores of main sequence stars like the sun was first investigated by Hans Bethe and C.F. von Weizsäcker. Bethe, however, was the first to distinguish between the energy producing nuclear cycle in stars on the lower part of the main sequence and those, like Rigel, on the upper part of the main sequence which are hundreds of times more luminous than the sun.

The H-R Diagram is a is a graphical tool that astronomers use to classify stars according to their luminosity, spectral type, color, temperature and evolutionary stage. That the various branches in the H-R diagram of the distribution of stars point to stellar evolution was first proposed by Henry Norris Russell.

Russell argued that all stars begin as cool luminous red giants (owing to slow gravitational collapse) at the extreme right end of the giant branch in the H-R diagram. To account for the constant luminosity of the giants in the giant branch of the H-R diagram Russell suggested that the young giants continue to contract gravitationally, becoming hotter and smaller, with these two changes in the structure and thermodynamics of the giants to help their luminosities remain constant.

To account for the main sequence stars, Russell continued his evolution theory in the same vein, with one very important change: he suggested that the stars, instead of remaining huge spheres of gas on reaching the main sequence, solidified and moved down the main sequence as they cooled off. However appealing this Russell scenario may be, it is fatally flawed and untenable because the luminosities of stars on the main sequence cannot, even fractionally, be accounted for by a cooling off process. But Russell proposed this evolutionary scheme before the era of nuclear physics. We now know that all stars are governed by the law of gases.

Because we cannot watch individual stars evolve owing to their long lifespans, we must resort to observations of groups of stars which were born together but which evolved at different rates owing to their different masses so that each such group consists of stars in different stages of evolution. Where are such groups to be found? They are scattered throughout our galaxy and are called "local" or "galactic" clusters of stars, which we know must have been born together from the same primordial galactic cloud of gas and dust because they are moving together in the same direction in the galaxy.

These local (galactic) stellar clusters, consisting of population I (solar type) stars, are, ideal laboratories for testing the stellar evolutionary theories of the astrophysicists. Because all the stars in such a cluster started their stellar lives with the same chemical composition, they are all equally old now and any differences among them are a measure of the differences in their rates of evolution which in turn could have arisen only from their mass differences.

The analysis of the relationship of the age of a cluster to the shape and position of its H~R evolutionary diagram track was just the beginning of the observational feature of the theory of the evolution of stars from the zero age main sequence branch of the H-R diagram to the giant and supergiant H-R branches. The theoretical aspect of this phase of astronomy was initiated and developed by the Princeton astrophysicist Martin Schwarzschild, the son of the German cosmologist and astrophysicist, Karl Schwarzschild. This work was developed to its fullest extent by Professor Icko Iben of the University of Illinois.

Without going into any of the details and complexities we can see in a general way that stars must evolve away from the main sequence. Their chemistries change more or less rapidly because the ratio of their hydrogen to helium abundances change continuously as they generate and release nuclear energy.

The astrophysics of the evolution of the supergiant stars explains the presence, in galaxies, of stars that are really pulsating. Such stars, now called "cepheid variables," were named after the typical star in this category, alpha-cephei, first properly labeled as a regular variable in 1784 by J. Goodricke. In 1912 the Harvard astronomer Henrietta Leavitt, studying the cepheid variables in the Magellanic clouds, discovered the famous period-luminosity law of cepheids which states that the luminosity of a cepheid variable is proportional to its pulsation period; the more slowly it pulsates, the greater its luminosity. This is physically reasonable.

The larger a cepheid variable, the more luminous it is and the larger it is, and the more slowly it pulsates (like a swinging pendulum, a long pendulum oscillates more slowly than a short one). The evolutionary paths of giant stars take them into an unstable region in the H-R diagram where they must pulsate as they pass through this region. Thus astrophysicists verified theoretically the existence of cepheid variables.

The discovery of the cepheid period luminosity law opened up a new and very exciting branch of astronomy: the probing of the depths of space—particularly the distances of the most distant galaxies. All one has to do now to find the distance of a galaxy is to pick out a cepheid variable in the galaxy and measure its pulsation period, which can be done very accurately. From that measurement the luminosity of the cepheid can be found from the period-luminosity law. From this luminosity and the cepheid's observed brightness, the distance of this cepheid and, hence, of its galaxy can be found. Our own galaxy was beginning to be studied in depth with new technologies.

The precise distribution of the stars and the sun's position in this distribution was not fully and correctly described until the Harvard astronomer Harlow Shapley completed his investigation of the distribution of globular stellar clusters with respect to the Milky Way. Globular clusters are large spherical distributions containing tens of thousands (up to a few hundred thousand) of stars forming a spherical halo or shell around the Milky Way. That they do not lie in our galaxy (ie., in the plane of the Milky Way) is indicated by our ability to see them at great distances at an angle to the plane of the Milky Way.

Harlow Shapley tried to determine the distance of the center of the galaxy from our solar system. He concluded that the center of the globular cluster halo and hence of the Milky Way is about 30,000 light years away in the direction of the constellation of Sagittarius. These deductions were later confirmed completely by direct observations of radiation (radio waves) from the center of the galaxy but these observations required radio telescopes.

With the discovery that the globular clusters are in the nature of a "boundary" around the galaxy, astronomers were quick to see that the dimensions of this boundary can be used to measure the size of the galaxy. It was found to be about 100,000 light years in diameter as measured in the plane of the Milky Way. Our galaxy contains about 200 billion stars, ranging from very faint ones to the superluminous ones such as the stars of Orion.

Star count technology led to the discovery of the spiral structure of our galaxy. The star count analysis led astronomers to the conclusion that our galaxy consists of three distinct spiral arms: the "Orion" arm, in which the solar system lies at about 1000 light years from the inner edge, the "Perseus" arm further out from the galactic center than the Orion arm, and an inner arm which passes through the region of Sagittarius and Scorpius.

The detailed study of the galaxy led to the discovery of extragalactic galaxies or the distant "spiral nebulae” as they were originally called. Their discovery led to a considerable controversy as to their nature and as to whether or not they are within our galaxy or far outside it. This controversy was not resolved until their correct distances could be measured. The most beautiful of these spiral nebulae is the Great Nebula in Andromeda (in the direction of the constellation Andromeda) some 2 million light years away.

The study of the distant galaxies was dominated by Edwin P. Hubble who gave up a boxing and a law career to study astronomy. He joined the staff of the Mount Wilson Observatory and, a few years later, became its research director. Hubble's studies convinced him, and in time, all astronomers that the extragalactic galaxies are, indeed, aggregates of stars like our own. During his career Hubble collaborated with Milton Humason.

Hubble’s galactic studies proved to him that the distant galaxies are distributed throughout space the way they are distributed around our galaxy. To him this meant that space and its galactic building blocks would look the same no matter where we were in it. This is direct evidence of Einstein's famous "cosmological principle" which Einstein stated as follows: "aside from random fluctuations which may occur locally, the universe must appear the same for all observers no matter where in the universe they may be."

The study of the distant galaxies led very early in the game to a very important discovery: the galaxies are not universally distributed as individuals, equally spaced from each other as one might have, at first, expected, but they tend to cluster. Hubble expressed this important discovery as follows: “While the large-scale distribution appears to be essentially uniform, the small scale distribution is very appreciably influenced by the well-known tendency to cluster. The phenomena might be rightly represented by an originally uniform distribution from which nebulae have tended to gather about various points until now they are found in all stages from random scattering to groups of various sizes, up to occasional great clusters.”

A careful study of the galaxies within 1 and 2 million light years shows that about 10 galaxies lie within 1 million light years of our galaxy (the closest are the Magellanic star clouds) and that about 10 more lie within 1 to 2 million light years. These 20-odd galaxies constitute what is known as the "local group" of galaxies. Such clusters, some containing hundreds and even thousands of galaxies, are found in all directions in space. Each such cluster is given the name of the constellation in which the cluster appears to lie in the sky.

Hubble published his findings as a paper in the Proceedings of the National Academy of Sciences in which he demonstrated conclusively that the radial velocities (motions away from the sun) of galaxies studied by Milton Humason are proportional to their distances: a galaxy B twice the distance from the sun as a galaxy A is receding from the sun twice as fast as galaxy A.

The content of the Hubble law was published jointly by Hubble and Humason in the Astrophysical Journal, and became (and still remains) the basis of the theory of the expanding universe and the concept of the big bang. Humason extended his spectral analysis to the most distant galaxies that could be observed in 1935, confirming Hubble's law out to galaxies receding at speeds of about 40,000 km/sec.

Because waves tend to spread out, physicists such as Werner Heisenberg discarded the classical idea that electrons can be described as being in a particular position in space. Instead, this concept of localization of action of a particle must be replaced by what has since been called Heisenberg's "uncertainty" or "indeterminacy" principle: if one tries to measure the precise position of a particle one loses all knowledge of its motion and vice versa.

The Heisenberg model pictures an electron in an atom as being simultaneously in all possible Bohr orbits, but not in each with equal probability, in line with Heisenberg's picture of an electron as being spread out. This theory of an atom, which incorporates the uncertainty principle, is called "quantum mechanics". It was developed by Heisenberg, Max Born, Jordan, and Wolfgang Pauli to its greatest extent. The mathematical skills this required placed this technology beyond the use of most physicists.

In those early years of the history of quantum mechanics, that this remarkable theory would rarely be used in studying atomic structure. But then the great Austrian physicist Erwin Schrodinger simplified the mathematics of quantum mechanics by introducing the "wave mechanics" which quickly replaced the "matrix mechanics." Schrodinger reasoned that if the electron is dual (particle and wave together), then all the particle features of an electron should be deducible from the wave representation. But this required the formulation of a wave equation for the electron; Schrodinger discovered this wave equation, now called the Schrodinger wave equation.

This was also the period during which new windows into space were opened, stimulated by the discoveries of new kinds of "rays" coming from all parts of space. In particular, "cosmic rays," first correctly described by the Austrian physicist Victor Hess as emanating from outer space and not from the earth, were among the most intriguing of these new kinds of rays. After a lengthy debate about the nature of these particles everyone agreed that they are very energetic charged particles, primarily protons (intermixed with heavy nuclei) and not electromagnetic rays (e.g., X rays and gamma rays).

The speeds with which these cosmic rays strike the earth indicate that they are produced, in some way or another, by the most energetic processes in the universe, exceeding the energies we can produce in our laboratories by trillions of times.

The study of cosmic rays led astronomers and physicists to the first venture into the construction of a self-consistent cosmology and to the careful study of phenomena not immediately ascribable to the stars or even to the galaxies. The primary question the cosmic rays presented dealt with their vast energies (speeds) which far exceed the energies which stars can generate. Of course, vast energies are released when a giant star collapses to become a supernova but supernovas are rare and are formed in galaxies, whereas cosmic rays come from all regions of space, where no galaxies are found.

Astronomers studying galaxies was the recession of the distant galaxies, which led to the much larger and much more important cosmological study of the beginning and end of the universe. This great discovery began with the cosmic "shaking" discovered by Vesto M. Slipher that the spectral lines of the light from the stars in the galaxy M31 reveal an enormous Doppler shift toward the blue end of the spectrum. Over the next two decades Slipher studied the lines in the spectra of some 40 nebulae, finding that most of the spectral lines are shifted toward the red, meaning that these nebulae are receding from the sun.

The large blue shift means that M31 is approaching the sun at a speed of about 300 km/sec. This is so large compared to the speeds of stars in the solar neighborhood in our galaxy that Slipher decided to check the spectra of other galaxies.

Slipher discovered that the fainter (hence, more distant) the galaxies are, the larger the Doppler shift toward the red end of the spectrum, meaning that all but two of the galaxies studied are receding from us. Most of the extragalactic galaxies are receding from our galaxy at speeds that increase with their distances (the more distant galaxies are receding more rapidly than the nearby ones).

The study of galactic clusters has led to a deeper insight into the importance of the "missing mass" (the dark matter) in the universe. That a great deal more matter is present in each cluster of galaxies is clear if one determines the mass: luminosity ratio in each cluster. Each cluster has much more mass than that amount deduced from the cluster's luminosity.

The German-American astronomer, Fritz Zwicky, was the first to apply a famous theorem in gravitational dynamics to determine the masses of the clusters. This theorem states that a cluster of objects gravitationally bound to each other will remain intact only if the cluster has enough matter in it (enough galaxies) to bind gravitationally any galaxy strongly enough to prevent that galaxy from leaving the cluster.

Jan Oort had become interested in constructing a model of the galaxy. He had analyzed star counts to show that the galaxy may be pictured as consisting of layers of stars lying in planes parallel to the plane of the Milky Way. These planes thin out with increasing distance from the plane of the Milky Way, This led him to the study of the motions of the stars in the galactic solar neighborhood. He concluded that the galaxy is rotating. Oort first theorised the existence of a icy shell of objects that exist in the outermost reaches of the solar system.

Oort reasoned that all the stars in the galaxy are revolving around the center of the galaxy according to Kepler's laws of motions for the motions of the planets around the sun. This means that the stars closer to the center of the galaxy are moving faster than the sun and those more distant stars are moving slower than the sun. Oort verified this relationship by measuring the velocities of stars relative to the sun both between the center of the galaxy and the sun and between the sun and the outer edge of the galaxy. These velocities supported Ms hypothesis which led him to the conclusion that the galaxy is rotating.

But with the development of electromagnetic technology, other windows into space were discovered and used extensively. Radio astronomy was the most important of these new technologies because the optical part of the electromagnetic spectrum (to which the human eye responds) is only a small portion (one octave—from red to violet) of what we might use for peering into space. This goal was realized with the introduction of radio telescopes, which can pick up a much wider range of electromagnetic wavelengths.

If our study of the extragalactic galaxies had depended entirely on optical telescopes we would not be as far advanced as we are in our understanding of the nature, structure, and distribution of these galaxies. Nor would we have as great a knowledge about the much broader subject of the structure, the origin, and, ultimately, the evolution of the universe.

Radio astronomy did not begin as the brainchild of astronomers because they themselves never suspected that radio waves contain vast treasures of astronomical information. Indeed, astronomers at the beginning of the fourth decade of the twentieth century when cosmic electromagnetic waves (radio waves) were first detected, did not even think of astronomical bodies such as stars and galaxies as generators of radio waves.

Communication technicians concerned with improving radio reception knew that terrestrial radio reception was strongly affected during intense solar activity, but they did not, in general, carry this knowledge over to astronomy. One such technician, Karl Jansky who was concerned with improving the radio antennas used for long-range radio communication, discovered that he could not eliminate a persistent background interference (static) or locate the source of the static. He asserted that the unknown, interfering radio source behaves like one of the "fixed stars" which also rise 4 minutes earlier each day. This was the beginning of radio astronomy.

An amateur astronomer and radio ham operator named Grote Reber built the first radio telescope, which was essentially a spherical, concave metal dish with a reflector and an electronic detector, to record the reflected radio waves. Reber built several such radio telescopes to pursue his study of cosmic radio waves, discovering that most of the sources of such waves are discrete, like the stars. After 1942, when radio signals were detected from the sun, astronomers began to study Reber's radio sources in earnest. This was the beginning of radio astronomy and many nations began to build radio telescopes and radio astronomical observatories.

Radio astronomy received a great boost after World War II owing to the rapid development of radar, which is essentially a radio technology in which short wave radio signals are directed to and then reflected from the surfaces of nearby celestial objects such as the moon, the planets, comets, and meteors. One of the most remarkable astronomical discoveries made with radar waves reflected from the planets was that the surface of Venus is very hot.

The astrophysicist Irwin Shapiro of the Harvard-Smithsonian Institute used radar to test the general theory of relativity, according to which a beam is slowed down as it traverses a gravitational field. Shapiro tested this theory by bouncing radar beams (from an earth source) off the various planets and measuring the times of the traversal of these beams from earth to planet and back. The amounts they were delayed corresponded exactly to those reductions in the speed of light that were predicted by the general theory of relativity.

The discovery of the hydrogen 21-centimeter (wavelength) radio line was another remarkable and extremely important event owing to its great usefulness in plotting the hydrogen atoms in our galaxy and in other galaxies. The existence of such a spectral line was first predicted by the Dutch astronomer H.C. van de Hulst during World War 2. This opens up the possibility of studying the galactic core of the Milky Way.

The study of the 21-centimeter line, emitted from different parts of our galaxy, became a new and very important phase of galactic astronomy because it revealed the center of the galaxy, which is not accessible to optical telescopes owing to the opaque dust clouds that cut off our view of the galactic center at a distance of 6000 light years.

The detailed study of the interstellar medium in our galaxy using optical and radio technology has revealed that this interstellar medium contains clouds of dust and gas (now called bright and dark nebulae) and atoms and molecules distributed fairly uniformly throughout the galactic interstellar space.

After world war 2 technological advancements allowed humankind to send artificial satellites, and evan humans into space. This, of course benefited astronomy. Space probes were also used to explore the cosmos. Today, the Hubble telescope offers invaluable information about the universe. Among the more important cosmological probes was the Cosmic Background Explorer (COBE) to determine the temperature of the universe, that is, the absolute (kelvin) temperature of intergalactic space.

Our earth-based telescopes and the orbiting Hubble telescope have not yet revealed how the universe looked when it was formed, but other observations, not of the matter in the universe but of the cosmic background radiation, give us an almost complete picture of the conditions in the universe shortly after the big bang. These observations were made and recorded by a special satellite, the Cosmic Background Radiation Experiment (COBE) designed to detect very weak, long wavelength microwave radiation from all directions. This experiment was successful, proving, conclusively, that a weak background radiation exists, reaching the earth from all directions.

The conclusions drawn from the COBE data are that the cosmic background radiation corresponds exactly to what we would expect if the radiation were coming from a furnace at a temperature about 3 degrees above absolute zero, which is 273 degrees below zero centigrade. With this discovery of the cosmic radiation the big bang became a fact because the cold cosmic background radiation is the cosmic remnant radiation of what, originally, was extremely hot radiation.

The story of the birth of the universe and its evolution from chaos to order, told here, spans some 14 billion years. The big bang theory is the prevailing cosmological model for the formation of the universe. At its simplest, it talks about the universe as we know it starting with a small singularity, then inflating over the next 13.8 billion years to the cosmos that we know today.

Because current instruments don't allow astronomers to peer back at the universe's birth, much of what we understand about the Big Bang Theory comes from mathematical theory and models. Astronomers can, however, see the "echo" of the expansion through a phenomenon known as the cosmic microwave background.

The phrase "Big Bang Theory" has been popular among astrophysicists for decades, but it hit the mainstream in 2007 when a comedy show with the same name premiered on CBS. The show follows the home and academic life of several researchers (including an astrophysicist).

As one contemplates this vast panorama, in which a world of order, symmetry, and intelligent life arose from disorder, as the culmination of a series of natural events, one is struck by the incredible contrast, bordering on what appears to be incompatibility and antagonism, between one realm of nature, life, and the antagonistic realm of the inanimate universe surrounding us.

Another cosmology that was vigorously supported initially by a number of leading cosmologists but is no longer as popular as it was initially, was introduced in the 1970s by the MIT physicist Alan Guth, who was concerned with certain esoteric features of the observable universe that seemed to contradict the big bang cosmology, Guth called his cosmology the "inflationary" universe cosmology. Guth argued that the empty universe expanded initially by many orders of magnitude (a hundred thousand trillion trillion times) thus "supercooling" itself and then releasing vast amounts of energy which became the big bang.

This theory has lost favor because it is just too complex a scenario for nature to have followed. Why could not nature have produced the big bang directly instead of going to the trouble of a vast inflation first and then a big bang? One important feature that we have learned about nature is that it performs its "miracles" minimally, using only as much technology as it needs.

The American Vela satellites were orbited to detect gamma ray flashes as signatures of nuclear bomb explosions because gamma rays are emitted by nuclei. These satellites did, indeed, record such flashes but it soon became clear that these gamma ray bursts were not produced by exploding bombs but were natural phenomena. This was announced in the prestigious Astrophysical Journal, These gamma ray bursts have been studied extensively since then and they have been found to occur throughout the universe.

These bursts may last for several seconds, and if the gamma ray energy released were emitted in the visible part of the spectrum, each such burst would appear brighter than any other object in the sky outside the solar system. If these events are phenomena beyond the Milky Way, each flash consists of an amount of energy equivalent to that emitted by the sun over billions of years.

Another mystery was presented to cosmologists by the discovery of certain radio sources which appeared like ordinary faint stars on photographic plates. But from the careful observations of a group of California astronomers it was discovered that these objects are at vast distances (billions of light years away) and, therefore, cannot be stars. These objects, now called "quasars," are small, compact extremely luminous objects, emitting as much energy per second as ten trillion suns or a few hundred galaxies.

Quasars first caught the attention of astronomers because they are sources of intense radio waves emitting enormous quantities of radio energy even though they appear like ordinary faint Milky Way stars on photographic plates. Because ordinary stars, like the sun, emit only weak radio waves, the discovery of a "star" that is a source of strong radio waves was an exciting event and a source of wonder.