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A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD 7.1 Planetary Motion and Gravitation In spite of many common misconceptions, the debate between sun-centered and earth-centered solar system models began long before Copernicus existed. Nearly 2000 years before, Philolaus proposed a sun-centered model of the solar system to counter the popular earth-centered model. Hundreds of years later, Ptolemy proposed an earthcentered model as a compromise; to describe what appears to be not what actually is. In the time of Copernicus, the compromise aspect was forgotten and it was believed Ptolemy believed his model to be factual. Nicholas Copernicus was correct in his assessment, and had data to prove the predicted positions of the planets according to Ptolemy did not match their visual locations in the sky. Tycho Brahe spent 20 years meticulously collecting data on the positions of the planets. Johannes Kepler was able to utilize that data to develop laws that describe the motions of the planets. Galileo Galilei described the motion of falling objects near the earth surface. Isaac Newton developed those descriptions into a mathematical law and linked the force of gravity to the motion of the planets as well. He was able to provide the explanation that was missing from all the recorded observations. It is important to keep in mind that at the time these astronomers knew about only five planets: Mercury, Venus, Mars, Jupiter, and Saturn. Newton’s Law of Universal Gravitation. The force of attraction between any two objects is directly proportional to the product of the two masses and inversely proportional to the square of the radius between them. Fg = G m1 m2 R2 Experiments show that if Fg is measured in Newtons, the masses are measured in kg and R in meters, G has the value of 6.67 x 10-11 Nm2/kg2. Kepler’s First Law: Law of Ellipses. Every planet moves about the sun in an elliptical orbit (near circular, ovals) with the sun at one focus. This law allows for a description of the planet’s orbit; namely the semi-major axis, the eccentricity, and the period of orbit. The semi-major axis, a, is the average distance of the planet from the sun (the textbook uses r). The eccentricity, e, defines the flatness of the oval. The period of orbit, T, is the time for one complete orbit of the planet around the sun. Combining this with Newton’s Law of Universal Gravitation, and the distance at any point in the orbit could be determined: r = 42 a4 1 . 2 G mo T (1 + e cos) Kepler’s Second Law: Law of Equal Areas: A line drawn from the sun to a planet will sweep out equal areas of space in equal times. = constant = a2 t T This indicates that the planet speeds up as it approaches perihelion (the closest point in its orbit) and slows down as it approaches aphelion (the farthest point in its orbit), and can be used to calculate , the angular displacement of the planet from perihelion. Kepler’s Third Law: Law of Harmony: The ratio of the cube of the average orbital radius to the square of its period is a constant. a3 = Kepler’s Constant = G mo T2 42 Kepler applied his laws to the planets. Galileo observed that Kepler’s Laws could be applied to the moons orbiting Jupiter. Newton proved that Kepler’s Laws could be applied to any object orbiting a star, planet, or moon. Kepler’s Third Law can be used between any two objects orbiting the same central object. Kepler’s Law of Harmony can be restated a13 = a23 T12 T22 A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD 7.2 Using the Law of Universal Gravitation For any satellite in a low-earth, near-circular orbit, the force of gravity is the centripetal force that keeps the satellite in orbit. This allows for the calculation of the period of the orbit and the speed of the satellite. First, the speed: Fg = Fc G mo ms = ms v2 a2 a v = G mo √ a Next, the period: Fg = Fc G mo ms = ms 42 a a2 T2 T = 2 a3 . √ G mo Notice that neither the speed of the satellite, nor the period of orbit depend on the mass of the satellite. Another quantity that can be obtained from Newton’s Law of Universal Gravitation is the value of the gravitational field strength. Gravity pulls between any two objects. How one object is affected in the presence of gravity is determined by the strength of the pull of gravity on the object. This strength depends on the distance the object is from the center of gravity. Fg = m2 g = G m1 m2 r2 g = G m1 r2 Yes, another term for the gravitational field strength is the acceleration due to gravity. Near the earth’s surface, g = 9.80 m/s2. Another application of gravitation is the study of the tides. Ocean tides are the result of the difference in the pull of gravity from one side of the earth to the other. The side of the earth closer to the moon is pulled harder on by gravity from the moon than the far side of the earth. This causes the earth to stretch slightly in the direction of the moon. As the earth rotates into this stretchy bulge, the water level rises, since water is affected by the pull differential more than the solid earth. This is called high tide. It is noticed when the moon is directly overhead. When the moon sets in the west there is low tide. About five hours forty-seven and one-half minutes later, high tide occurs again, followed by low tide when the moon rises in the east. The cycle repeats. Even though the sun is larger than the moon, even though the sun’s gravitational pull on the earth is greater than the moon’s, the affects of the moon’s pull on the tides is greater than the sun’s. Remember, the tides are caused by the difference in the pull of gravity from one side of the earth to the other, not by the size of the pull of gravity on the earth. The moon is much closer than the sun. The difference in the pull of gravity from one side of the earth to the other would be greater than the difference in the pull of gravity from the sun. The sun has an affect on the tides as well. The combination of pulls between the two objects can be complex. When the sun, moon, and the earth are inline, the differential pulls combine producing higher than average high tides and lower than average low tides. These tides are known as Spring Tides. They occur during the phase of the moon known as the New Moon phase and the Full moon phase. When the moon is positioned directly overhead and the sun is either rising in the east, or setting in the west, their differential pulls almost cancel each other, producing lower than average high tides, and higher than average low tides. These are called neap tides. They occur during the First Quarter and the Third Quarter moon phases. It is possible for the tension at the top of the circle to equal zero. In that case, ac = g. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Origins of Astronomy Origins of Constellations Archeology has shed light on the earliest astronomical practices. Actual physical evidence of these practices date back as far as 30,000 B.C. and are scattered all over Europe and the Commonwealth of Soviet States. By using these calendars and observing the relative positions of the sun, stars, and other wandering stars called planets, observers were able to identify and label certain regions of the nighttime sky. Nomadic hunters and gatherers needed to know when migratory birds would arrive and when berries would ripen. Women needed to know in what season their child would be born and when their next menstrual period would occur. Farmers needed to predict seasonal changes to know when to plant and harvest, when to send livestock into the field, and when to shelter them. Observers tracked the path of the sun through the stars. This path was called the ecliptic. Such knowledge required cumulative day counts and knowledge of seasons best derived from sky phenomena. In villages where records were kept, opportunities were made to discover seasonal and annual cycles and events. Organized observations of this kind were made throughout the world around 4000 – 3000 B.C. Observations mad on a single night revealed that stars slowly spun around point in the northern sky. This point was called the North Celestial Pole. Its opposing point was called the South Celestial Pole. The constellations surrounding these points were called circumpolar constellations. They were used to identify the locations of the celestial poles. Observations of the sun’s motion relative to other features of the sky would help date the exact number of days in a year. Further observations of weather patterns can divide the year into four distinct seasons. Observations of the moon’s motion would help determine the exact number of days in a “moon”, a lunar cycle which eventually became known as a month. As early as 2800 B.C., massive stone or wood structures were constructed as calendars and so oriented as to clock the sun’s motion as it traversed the sky. The path the sun moved through the stars was called the ecliptic. Observers tracked the paths of the planets through the stars. These paths followed closely to the ecliptic and passed through certain groups of stars that stretched across the sky. Many patterns were recognized within these stars. Those patterns were called constellations. These patterns were said to resemble animals, so this band of constellations became known as the zodiac. Other constellations were used to identify the location of the line that circled the sky exactly midway between the two poles. This line was called the celestial equator. Constellations have been used as early as 2600 B.C. as navigational aids and for teaching navigation for locating the celestial poles and celestial equator, and for tracking the seasons by identifying the zodiac. They were not often used for storytelling or for entertainment purposes as many might believe. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Origins of Astrology In villages where records were kept of seasons, annual cycles and events, priest-astrologers kept track of these changes by recording their observations and announced when to plant crops, when to harvest, or when certain events would occur. A philosophical error sprang up with the announcement rituals in these societies. They mistook these events as being controlled by the motions, rather than being tracked by the motions. These observatories then became temples and the ceremonies developed into religious rituals. Some villages containing these observatories/ temples include Stonehenge in England, c. 2500 B.C.; Woodhenge near St. Louis, c. 2000 B.C.; the Temple of Amen-Ra at Karnak in Egypt, c. 1400 B.C.; Casa Grande in Arizona; and the Myan ruins in the Yucatan. year of 346.62 days. This provides an opportunity for an eclipse every 173.31 days, repeating the entire cycle every 18.6 years. Thales was not as precise with his calculations. He calculated the entire cycle at 19 years and was most noted for being able to predict the next solar eclipse. He called his prediction the Saros Cycle. Records From Other Cultures The MYAN calendar system had two parts. The first was a 365-day cycle of the Sun. The second was a 260 day cycle called the Myan Sacred Round. This was a list of names for the days based on the notion of an eclipse year. 2 Myan Sacred Rounds = 3 Saros Cycles 2 (260 days) = 3 (173.31 days) Origins of Greek Thought (Science) In INDIA, the astronomical practices dated back to 1500 B.C. The first known astronomy text appeared around 600 B.C. Other texts from around A.D. 450 used Greek computational methods, indicating an influence of Greek thought. As these priest-astrologers continued to record and preserve their observations, certain philosophers (lovers of wisdom) benefited from those records. One such philosopher, Thales in 580 B.C., used records dating back to 711 B.C. to discover a periodic cycle of eclipses. CHINESE astronomers left records of predicting eclipses long before 1000 B.C., and lists of mysterious “guest stars” – nova – recorded from 100 B.C. and still used today. Texts from 120 B.C. described concepts similar to modern theories on space and time and a revolving earth. Several simultaneous cycles had to be in place to produce an eclipse. The 29.531 day lunar revolution with respect to the sun, in addition to the 365.242199 day revolution of the earth around the sun, combined with the 18.6 year regression of the moon’s orbit allows two specific points in the moon’s orbit to line up with the sun. “All time that has passed from antiquity until now is called chou; all space in every direction is called yü.” The moon’s orbit is tilted 5° to the plane of the earth’s orbit. This causes the moon’s orbit to intersect with the earth’s orbit at two opposing points, called nodes. The combination of the three aforementioned cycles causes these points to align with the sun every 173.31 days, yielding an eclipse “The earth is constantly in motion, never stopping, but men do not know it; they are people sitting in a huge boat with the windows closed. The boat moves, but those inside feel nothing. HEBREW writers wrote “He spreads out the northern skies over empty space; He suspends the earth over nothing,” and “The earth is turned as clay under the seal,” and “He sits enthroned above the circle of the earth. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Early Greek Astronomy With the rise of the Greek civilization came the development of different ways of looking at the world. The Greeks noticed cycles within the motions of the heavens and sought answers to explain these motions. The records they used were from the priest-astrologers of Egypt, Babylonia, and the surrounding regions. Ionian School (pre-Socrates) THALES (640-545 B.C.) developed the Saros Cycle and predicted the eclipse of 580 B.C. He motivated more Greek thinkers to look at the world in terms of tractable, physical ideas. ANAXIMANDER (611-547 B.C.) was the first to speculate on the relative distances to the Sun, Moon, and stars from Earth. He coined the term “Celesial Sphere, referring to the encompassing dome surrounding the earth on which the stars are placed. He argued that the earth was at the center of that sphere and that all matter is an eternal substance. ANAXIMENES (c. 528 B.C) did little more than to write in agreement with Anaximander. PARMENIDES (510-450 B.C.) argued for a static, non-changing world in which our senses were misleading. Reason, to him, was the only reality. His doctrines strongly influenced Plato. HERACLITUS (535-475 B.C.) rejected Parmenides’ doctrine of a unitary, static reality. He maintained that everything was changing and wisdom consisted of seeking to understand the dynamic principle that unified the diversity of nature. XENOPHANES (c. 500 B.C.) was a monotheist who rejected the Homeric mythology and Greek religions. ZENO of ELENA (c. 450 B.C.) developed many paradoxes regarding motion. Pythagorean School PYTHAGORAS (540-470 B.C.) studied under the Ionians, developed his own school of thought and established a school and religious order in southern Italy. His doctrines strongly influenced Parmenides. He developed geometry and advanced geometric principles and proposed that the earth was spherical. PHILOLAUS (c. 450 B.C.) agreed with Pythagoras in regard to a spherical earth, but, since fire was the basis of all matter, and since the sun was the brightest object in the heavens, he placed the sun at the center of Anaximander’s Celestial Sphere. Any apparent motion in the heavensa was therefore due to the motion of the earth. He also proposed a counter-earth called Antichthon. ANAXAGORAS (500-420 B.C.) deduced the true nature of eclipses to be the blockage of sunlight by either the earth on the moon or the moon on the earth. From the shadow of the earth on the moon, he speculated that the earth was round and that the sun was much larger than all of Greece. For that, he was banished from Athens. EUDOXUS (408-355 B.C.) represented the motion of the planets with combinations of rotating spheres. Each sphere pivoted at two points on opposing sides of the next inner sphere. The innermost sphere carried the planet. His system required 27 spheres (1 for the sun, 1 for the moon, 1 for the stars, 3 for the earth, and 3 for each planet. Recall that at that time only 5 planets were known.) DEMOCRITUS (c. 400 B.C.) attributed the faint glow of the Milky Way to a mass of unresolved stars. CALLIPPUS (c. 350 B.C.) refined Eudoxus’ scheme by adding seven more spheres. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Sophists From 500 to 300 B.C the Sophists were itinerant experts on various subjects. They were not a clearly defined school, but they did have certain common interests. Their educational program centered around the belief that virtue can be taught. They taught relativistic ideas on truth, morality, and ethics. They taught atheism, but profess agnosticism. They were accused of lacking morality, or even a basis for their beliefs, other than their own desires. Their school soon died out. Athenian School SOCRATES (469-399 B.C.) diverted philosophy from the physical realm of the Ionians to the ethical realm. His insistence upon thorough, critical analyses of ethical concepts marked the beginning of logic. His “Socratic Method” of teaching was by eliciting answers from others to reveal inconsistencies in their opinions – a method particularly effective against the Sophists. PLATO (429-347 B.C.) established an academy c. 385 B.C. His idealism and religion affected his teaching greatly and continue even to this day. He insisted that the earth-centered view of the universe was correct and therefore disagreed with the Pythagoreans. His reasoning was basically religious and was influenced by Parmenides. He gave Sophists a bad name as tricksters, interested in money and prestige more than truth. ARISTOTLE (384-322 B.C.) wrote over 400 books on every branch of learning. He agreed with the Ionians’ and with Plato’s view of an earthcentered universe. His reasoning was more realistic than idealistic. If the earth moved around the sun, a slight shift in stellar positions would be noticed. Since no shift was seen, the earth must be at the center. He viewed the earth’s shadows from lunar eclipses and concluded that the earth was round. He proved that by watching a boat sail over the ocean and disappear. He had a library and a museum at Athens, given to him by Alexander the Great. Later Greek Astronomy When Alexander the Great conquered Egypt, a library was established at Alexandria (c. 322 B.C.). It housed all of the works of every great philosopher discussed earlier and then some. In addition, it included much of the observations of the astrologerpriests. These were, however, copies of copies of translations of copies of the originals. At this library, there also evolved a school of thought. Alexandrian School ARISTARCHUS of SAMOS (310-230 B.C.) was the first to calculate and quantify the distances and sizes of the earth, moon, sun, and the Celestial Sphere. Knowing those sizes, he rejected the earthcentered view of the universe. He was sharply criticized for three reasons: 1) His view no longer held earth as divinely different from any other planet and, thus, the divinity of the universe was threatened. (Plato’s students were against it.) 2) The stellar parallax referred to by Aristotle was not observed. Though a lack of parallax was explained, that did not matter. (Aristotle’s students were against it) 3) It wasn’t detailed enough. ERATOSTHENES (276-195 B.C.) was the first to measure (not just calculate) the size of the earth. HIPPARCHUS of RHODES (160-127 B.C.) was the original “Rhodes Scholar”. He invented and developed trigonometry, allowing for more extensive and systematic observations. He devised a system of categorizing brightness that is still used today and catalogued over 850 stars by position and brightness. Like Aristarchus, he calculated distances to the sun and moon. His calculations were more precise, though still far from correct. He was also the first to observe the precession of the poles and explained this by using eccentric circles as orbits. This led him to conclude that the sun-centered view of the universe was correct. To avoid criticism, he also explained the precession from an earthcentered view using epicycles and deferents. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Later Greek Astronomy Alexandrian School CLAUDIUS PTOLEMY (c. A.D. 150) expanded the catalogue started by Hipparchus to 1022 stars. He agreed with the conclusion of Hipparchus of a sun-centered universe. To avoid the same criticism, he proposed a cosmology that was of a model of what was seen rather than what actually was. His model placed the earth in the center of the celestial sphere with all the planets, the sun and the moon orbiting the earth on epicycles and deferents. To be more accurate than Hipparchus, the epicycles were eccentric with the earth located at one of the equants. His work was contained in 13 volumes called “The Mathematical Collection”, which became known in Arabic as “AlMagiste”, or “The Greatest.” HYPATIA (A.D. 375-415) was a mathematician and the last of the great librarians at Alexandria. She wrote a commentary on Ptolemy’s works and also invented some astronomical and navigational devices. Medieval Astronomy In western Europe, the works of the Greeks were all but forgotten. Much of the ideas of Plato found their way into the theology of the early Christian church and eventually into the tenets of the Roman Catholic Church. PANTAEUS (c. 200) an early church leader, he received pressure from followers of Ptolemy to accept their philosophy. He declined. CLEMENT of ROME (c. 200) another early church leader and head of the school at Alexandria. In his writings the influence of Greek philosophy was prominent, especially the teachings of Plato. He sought to synthesize Christianity and Greek philosophy. He failed and the Ptolemists ousted him after only two years of service. ORIGEN (c. ???) His works on theology, science, and philosophy numbered in the six thousands. ANATHASIUS (293-373) rose to a position of leadership in Alexandria and, after his defense of Christ over Arianism at the Council of Nicea, he became bishop of Alexandria. His writings were also influenced by Plato and influenced Jerome. JEROME (345-420) a writer against heresies. He interpreted and accepted church doctrine. Through his writings, the influence of Plato and Plato’s earth-centered view of the cosmos found its way into the dogma of the Roman Catholic Church. He was pressured into acceptance in large parts by the student of Ptolemy. As the Greek civilization declined, and Rome captured Egypt, interest in science died out. In A.D. 640, the Romans destroyed the library before the Muslims captured Alexandria. Most of the documents were lost. A few of them were spared and translated into Arabic and Aramaic and studied by Arabs. Although they made new and better observations, they made no advancements in explanations or ideas. MUHAMMAD al BATTANI (c. 900) compiled tables of the positions of the sun, moon, and planets. He predicted eclipses and recalculated the rate of precession first noticed by Hipparchus. IBN JUNIS (c. 1000) kept more complete records. With the destruction of Alexandria, the works of Plato and Aristotle were lost until the crusades forced the Muslims out of Spain. By 1130 complete manuscripts of at least one of Aristotle’s books were known and all 13 volumes of Arabic translations of Ptolemy’s Al-Magiste were found. These works reinforced the Church dogma handed down through Jerome. They also sparked a new interest in science and technology. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Astronomy in the Middle Ages Astronomy In The Scientific Revolution Arab astronomers introduced the Ptolemaic model of the solar system to European Astronomers. By A.D. 1130 all 13 volumes of AlMagiste were translated into Latin. European astronomers took the model to be what is and not what is seen. By the 1200’s European astronomers realized that further adjustments were needed for the Ptolemaic model. In 1252 King Alfonso X of Castile supported a ten year project to calculate predicted planetary positions. The results were called the Alfonsine Tables, which became the basis for planetary predictions for the next three centuries. NICOLAS COPERNICUS (1473-1543) analyzed planetary motions by various methods. In 1504 he observed a conjunction between all five known planets, the sun and moon in the constellation Cancer. He noted their positions departed drastically from the predictions of the Alfonsine Tablets. Applying Occam’s Razor, he realized that the universe would be simpler and predictions would be easier if the sun were placed at the center of the Celestial Sphere. 1. He placed the Sun at the center of the Celestial Sphere. 2. He placed the planets in their correct order from the Sun. 3. He placed the stars at such a great distance from the sun that the distance from the sun to any planet was negligible in comparison. WILLIAM of OCCAM (c. 1340) was an English scholar and philosopher who enunciated a principle applicable to all branches of science and philosophy, “Multiplicity ought not be posited without necessity.” – a.k.a. Occam’s Razor. More simply stated, among competing theories, the simplest, the one requiring the fewest assumptions and modifications in order to fit the observations if the best theory. PURBACH (1423-1461) revised the Ptolemaic model using 61 separate deferents and epicycles. JEROME FRACASTER (c. 1538) introduced another revision using 79 separate deferents and epicycles. His theory contradicted many theologians and scholars. Turmoil and controversy erupted thereafter. The debate became violent. Copernicus died years later of natural causes on the very day the first copy of his book “On the Revolution of Celestial Orbs was presented to him. MICHAEL SERVETUS (c. 1533) agreed adamantly with Copernicus and violently against the church. He was burned at the stake by Protestant and Catholic Scholars and theologians. GIORDANO BRUNO (1548-1600) vigorously defended the theories of Copernicus against the academies. He added that the stars were worlds like our sun and might have planets orbiting them. He too was burned at the stake. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Astronomy In The Scientific Revolution TYCHO BRAHE (1546-1601) built the first “modern” European observatory named “Uraniborg”, or “Sky Castle”, near Copenhagen. Based upon his naked-eye observations, He catalogued nearly 800 stars, their positions and relative brightness. He noted many errors in the Alfonsine Tables (1562). He viewed a nova (new star) for 16 months (1572-1573). It outshone Venus for many weeks. It had no parallax shift, which meant it was part of the Celestial Sphere. He catalogued the precise positions of each planet for twenty years (1576-1596). He viewed no parallax for seven comets (1577, 1580, 1582, 1585, 1590, 1593, and 1596). He devised a compromise between the cosmologies of Ptolemy and Copernicus. 1. Earth was at the center of the Celestial Sphere. (He truly believed it was too big to move and he was a follower of Aristotelian philosophy.) 2. Both the Sun and Moon orbited the earth. 3. The planets orbited the Sun in order: Mercury, Venus, Mars, Jupiter, and Saturn. Tycho was hired by King Frederick II of Denmark to make these observations for the purpose of making astrological forecasts. When the King died, the new King, King Christian IV, could not stand Tycho’s arrogance or extravagance. He withdrew Tycho’s funding. Tycho was forced to move to Prague where he studied his observations under the funding of Emperor Rudolf until he died. JOHANES KEPLER (1571-1630) was a learned theologian, mathematician and astrologer. He learned of Copernicus’ theory and was certain that planetary motions were governed by hidden regularities. He went to Prague to work with Tycho Brahe, attempting to find a satisfactory solution to the problem of planetary motion – a solution that was compatible with Tycho’s observations. Only after Tycho’s death was he able to gain access to the data. He succeeded Tycho as mathematician/ astrologer to Emperor Rudolf. Eventually, he stumbled upon the cosmology that He summarized into His three laws. 1. Law of Ellipses. Every planet moves about the sun in an elliptical orbit with the sun positioned at one focus. 2. Law of Equal Areas: A line drawn from the sun to a planet will sweep out equal areas of space in equal times. 3. Law of Harmony: The ratio of the cube of the average orbital radius to the square of its period is a constant. a3 = Kepler’s Constant T2 A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Astronomy In The Scientific Revolution GALILEO GALILEI (1564-1642) established himself as a brilliant scientific investigator. He agreed with much of Aristotle’s principles of mechanics and set out to prove them experimentally. He devised many experiments in mechanics, optics and astronomy. The latter got him into trouble with his fellow scholars, as did the fact that he wrote his findings in Italian and not Latin. This made Him popular outside the normal university circles. He did not invent the telescope, but was the first to turn it’s use toward the stars, revealing proof that other objects did not revolve around the earth and that heavenly objects were not perfect, unmarred spheres. His many observations included: Viewing 4 moons orbiting Jupiter. Viewing “ears” on Saturn, later viewed as rings by Huygens in 1655. Viewing phases of Venus and Mercury, just like the Moon. Viewing lines on Mars. Viewing depressions and mountains on the Moon. Viewing blemishes on the sun (sunspots) and noticing them to move across the face of the sun. He offered many scholars the opportunity to see for themselves. Many refused; many claimed to see nothing; many claimed the telescope to be valueless because, “the Greeks had not invented it.” Galileo was forbidden to “hold or defend” the views of Copernicus by the decree of 1616. He found favor with the Pope, Pope Urban VIII. He was ordered to stand trial in 1633 before the Inquisition for failure to comply with the decree – even though he did comply. He was sentenced to prison, but the Pope commuted the sentence to a house arrest, where Galileo died in 1642. COMMON FACTS ABOUT THE TRIAL OF GALILEO: 1. Galileo was forced to recant his testimony despite his observations, arguments, and evidence. 2. Theologians were involved in this decision. 3. The works of Copernicus, Kepler, and Galileo were placed on the list of forbidden books, the Index Liborium Prohibitorium. 4. One of the arguments against Galileo and Copernicus was that their teachings were contrary to the Bible. NOT SO COMMON FACTS ON RECORD: 1. Arguments against Galileo were four-fold: 2. Theologians of that day and the scholars of that day were one in the same. They are not to be confused with the church officials or leaders. Since the major universities and academies were owned by the Catholic Church, much of the work of the universities fell under the administration of the church. Many debates and disputes were therefore settled by the church officials. 3. Church dogma was mainly dictated by these theologians and scholars, who based their arguments on the teachings of Aristotle and traditions. 4. Records do indicate that many scholars, theologians, and church leaders sided with Galileo and Copernicus. In 1400’s, for example, Cardinal Nicholas deCasa argued that the Bible did not teach an earth-centered cosmology. 5. The Bible itself was banned by the Catholic Church and placed on the Index Liborium Prohibitorium by the Councils of Valencia (1229), Toulouse (1229), Terragona (1234), and Trent (1563). All favored the reading of the Bible by common folk. 6. Some records indicate the trial of Galileo was a sham, used to cover up a much larger embarrassment of doctrine or scandal. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Astronomy In The Scientific Revolution Astronomy in the Renaissance ISAAC NEWTON (1643-1727) formulated the basic laws of modern mechanics and showed them to be universal. He proved that they applied to motions of celestial objects as well as objects on the earth. He began with a few universally accepted principles postulated by Aristotle and developed them into three fundamental laws of mechanics. He then applied these laws to the laws proposed by Kepler and the motions of the orbits of the moons of Jupiter seen by Galileo. He then proved these motions had to exist as a consequence of his laws. He then developed the mathematical concept behind the only force that could hold these moons in their orbit, gravity. EDMUND HALLEY (1656-1742) greatly extended Newton’s studies to the motions of comets. In 1705 he published calculations relating to 24 comet orbits. Three in particular he noted were so similar they had to come from the same comet. He predicted that the comet would return in 1758. The telescope is by now a commonly used tool for astronomers. His three laws of motion, and his law of gravity united the works of Galileo and Kepler and proved that Copernicus and Philolaus must be correct (except no one remembered Philolaus by this time). Although his results were published in 1687, at the age of 44, he had completed much of these by 1667, at the age of 24. Newton is often considered to be “the greatest genius that ever lived”. By the time of his death in 1727, the solar system was conceived essentially as it is viewed today, lacking only the discovery of the three outer planets – Uranus, Neptune, and Pluto? and what about Cedna? There was still much development needed for the rest of the universe. ALEXIS CLAIRAUT (c. ???) used Halley’s data to predict the comet’s position upon its return. GEORGE PALITZSCH (c. 1758) recorded the sighting of a comet on Christmas Eve and charted its position for several months. This was the same comet predicted by Halley. JOHANN BODE (1747-1826) popularized a relationship between the planets and their distances from the sun. This relationship was initially discovered by Titus of Wittenburg, and was used to predict the locations of other planets. His rule was simple. Starting with a series of 4’s, one for each planet. Add to each four the corresponding number in this series; 0, 3, 6, 12, 24, 48,… and doubling each successive number. Finally divide the numbers by 10. The resulting series of numbers represents the distances from the sun to each planet compared to the distance from the sun to the earth (i.e. distance from earth to the sun is 1). planet number + 1 4 0 4 2 4 3 7 3 4 6 10 4 4 12 16 5 4 24 28 6 4 48 52 7 4 96 100 8 4 192 196 9 4 384 388 10 4 768 772 planet. dist. 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 77.2 planet Mercury Earth Mars Saturn Neptune Pluto name Venus Asteroids Jupiter Uranus Cedna a = 0.4 0.7 1.0 1.5 1.9 5.2 9.3 19.1 39.0 80.0 GIUSEPPE PIAZZI (1746-1826) observed an uncharted star and noticed that it moved among the stars like planets. It was supposed to be at a distance between Mars and Jupiter, which fit Bode’s Rule. It was thought to be the missing planet. A PHYSICS GUIDE FOR… CHAPTER 7 NAME DATE PERIOD Appendix: Historical Developments in Astronomy Astronomy In The Scientific Revolution Modern Astronomy WILLIAM HERSCHEL (c.1780) discovered another object to fit Bode’s Rule. Its orbit was frther out past Saturn. It was called Uranus (March 13, 1781). He also made a star count using the largest telescope at the time and mapped out the shape of the universe, shattering the concept from the Greeks of a Celestial Sphere. The universe, he claimed, was disk-shaped with the stars at varying distances and our sun at the center (1790). He proposed the “Island Universe” hypothesis. J. C. KAPTEYN (c.1910) employed Herschel’s methods of star counting with larger telescopes and more accurate instruments. He was able to increase the size of the universe to about 55,000 ly. CHARLES MESSIER (c. 1781) charted and catalogued 56 star clusters and 47 nebulae (gas clouds). JOHN COUCH ADAMS (c. ???) using minor discrepancies from Bode’s Rule, Newton’s Laws, and the data collected on the orbit of Uranus, he predicted where another planet should be found. GALLE (c. 1850) used Adam’s calculations and located the new planet on September 23, 1846. He named it Neptune. Misc. Many, many other objects have been spotted orbiting the sun. These have been called asteroids. The largest concentration of these lie at a distance between the moon and Jupiter. This belt of asteroids fit the predictions form Bode’s Rule. Another planet has since been discovered out farther than Pluto. It is larger than Pluto, but is considered not to be a planet. It, like Pluto, has been classified as a “dwarf planet” for various reasons. Its name is Cedna. Although Bode’s rule was used to find Pluto, there are many oddities to Pluto’s orbit and it doesn’t fit the predictions as it should. Cedna does. HARLOW SHAPLEY (c. 1920) observed the positions of globular clusters (large spherical groups of stars) and determined that they formed a spherical swarm above and below the galactic disk and that they centered on a point in the direction of the constellation Sagittarius. He concluded that there are objects beyond this galaxy and that this galaxy was about 300,000 ly in diameter and disc shaped. EDWIN HUBBLE (c. 1924) located some cephied variables (certain type of stars that fluctuate in brightness) in some nebulae and calculated their distances to be very far away – too far to be a part of this galaxy. This was proof of objects in the universe that were similar to our own galaxy. The “Island Universe” concept was proven wrong. He also used Doppler shifts to record velocities of many nebulae and identified around 45,000 galaxies other than our own. H.P. ROBERTSON (c. 1925) discovered the relationship between the distance to the galaxies and their Doppler shifts. He concluded the universe was expanding outward from a common center located in the constellation Virgo. The last of the great Greek doctrines – that of a steady-state, an unchanging cosmos – had collapsed. CLYDE TOMBAUGH (c. 1930) – discovered the existence of another planet beyond Neptune. This planet was called Pluto. He used the calculations from Percival Lowell. PLASKETT (c. 1935) using correct dimensions of the galaxy, he was able to construct our current model of our Milky Way galaxy. It is disc shaped, about 100,000 ly in diameter and 20,000 ly thick with arms spiraling out from the center. Our sun is positioned about two-thirds of the way from the center, near the edge of one of the spiral arms.