chapter 3 astronomy

deferent

_____________- In the Ptolemaic model of the Solar System, the large circle around Earth along which the center of an epicycle moved.

geosynchronous satellite

1a A ______________ ____________ orbits eastward with the rotation of Earth and remains above a fixed spot on the equator, which is ideal for communications and weather satellites.

not, parallax, object, different, distorting, constellations, small

1a Ancient astronomers believed that Earth did ____ move because they saw no __________, the apparent motion of an __________ because of the motion of the observer. To demonstrate parallax, close one eye and cover a distant object with your thumb held at arm's length. Switch eyes, and your thumb appears to shift position as shown at left. If Earth moves, ancient astronomers reasoned, you should see the sky from _________ locations at different times of the year, and you should see parallax ______________ the shapes of the ________________. They saw no parallax, so they concluded Earth could not move. Actually, the parallax of the stars is too ______ to see with the unaided eye.

straight line, continuously accelerate, curved orbit

1b According to Newton's first law of motion, the Moon should follow a ___________ _______ and leave Earth forever. Because it follows a curve, Newton knew that some force must ______________ ______________ it toward Earth, gravity. Every second the Moon moves 1020 m (3350 ft) eastward and falls about 1.4 mm (1/18 in.) toward Earth. The combination of these motions produces the Moon's ___________ _______. The Moon is falling all the time.

gravity, miss, free fall, each other, mutual, center of mass, closer, massive

1c Astronauts in orbit around Earth feel weightless, but they are not—to use a term from old science fiction movies—"beyond Earth's gravity." Like the Moon, the astronauts are accelerated toward Earth by Earth's __________, but they travel fast enough along their orbits that they continually "_______ the Earth." They are literally falling around Earth. Inside or outside a spacecraft, astronauts feel weightless because they and their spacecraft are falling at the same rate. Rather than saying they are weightless, you should more accurately say they are in ________ _______. 2 To be accurate you should not say that an object orbits Earth. Rather, the two objects orbit ______ _______. Gravitation is ___________, and if Earth pulls on the Moon, the Moon pulls on Earth. The two bodies revolve around their common __________ ____ ______, the balance point of the system. 2a Two bodies of different mass balance at their center of mass, which is located ____________ to the more ______________ object. As the two objects orbit each other, they revolve around their common center of mass as shown at right. The center of mass of the Earth-Moon system lies only 4670 km (2900 mi) from the center of Earth—inside Earth. As the Moon orbits the center of mass on one side, Earth swings around the center of mass on the opposite side.

Planetary motion, wanderer, stop, westward, retrograde motion, gears

2 _______________ __________ was a big problem for ancient astronomers. In fact, the word planet comes from the Greek word for "_____________," referring to the eastward motion of the planets against the background of the fixed stars. The planets did not, however, move at a constant rate, and they could occasionally ________ and move _______________ for a few months before resuming their eastward motion. This backward motion is called _________________ ______________. (retrograde motion of planets is an optical illusion created when earth passes slower moving planets further out in orbit) 2a Simple uniform circular motion centered on Earth could not explain retrograde motion, so ancient astronomers combined uniformly rotating circles much like __________ in a machine to try to reproduce the motion of the planets.

repeating, escape velocity, open orbit, lowest, farthest, highest, closest, perigee

3 Closed orbits are __________ cycles. The Moon and artificial satellites orbit Earth in closed orbits. Below, the cannonball could follow an elliptical or a circular Closed orbits. If the cannonball travels at the velocity needed to leave Earth permanently, called ___________ ____________, it will enter an _______ ______. An open orbit does not return the cannonball to Earth; it will escape. 3a As described by Kepler's second law, an object in an elliptical orbit has its _____________ velocity when it is _____________ from Earth (apogee), and its _____________ velocity when it is _________ to Earth (perigee). _____________ must be above Earth's atmosphere, or friction will rob the satellite of energy and it will quickly fall back to Earth.

Claudius Ptolemy, epicycle, deferent, approximate, off center, epicycle, equant, epicycles

3 Uniformly rotating circles were key elements of ancient astronomy. ___________ ___________ created a mathematical model of the Aristotelian universe in which the planet followed a small circle called the __________ that slid around a larger circle called the _____________. By adjusting the size and rate of rotation of the circles, he could _______________ the retrograde motion of a planet. See illustration at right. To adjust the speed of the planet, Ptolemy supposed that Earth was slightly ___ ____________ and that the center of the _______ moved such that it appeared to move at a constant rate as seen from the point called the _____________. To further adjust his model, Ptolemy added small _______________ (not shown here) riding on top of larger epicycles, producing a highly complex model. (https://www.youtube.com/watch?v=utH-GHH1FT8)

first principles, examination, reexamined, circular, constant, motionless, center, backward, planets

3-1a Aristotle's Universe Philosophers of the ancient world attempted to deduce truth about the Universe by reasoning from _______ ____________. A first principle was something that seemed obviously true to everyone and supposedly needed no further _____________. That may strike you as peculiar; modern thinkers tend to observe how things work and then from that evidence make principles and conclusions that can always be ______________. Before the Renaissance, however, reasoning from evidence (which you might call "scientific thinking") was not widespread. Study Concept Art 3A, "The Ancient Universe," and notice three important ideas: 1) Ancient philosophers and astronomers accepted without question—as first principles— that heavenly objects must move on __________ paths at ___________ speeds, and that the Earth was _____________ at the __________ of the Universe. Although a few ancient writers mentioned the possibility that Earth might move, most of them did so in order to point out how that idea was "obviously" wrong. 2) As viewed by you from Earth, the planets seem to follow complicated paths in the sky, including episodes of "__________" motion that are difficult to explain in terms of motion on circular paths at constant speeds. 3) Finally, you can see how Ptolemy created an elaborate geometrical and mathematical model to explain details of the observed motions of the ____________ while assuming Earth was motionless at the center of the Universe.

Nicolaus Copernicus, heavens, earth, christian, heresy

3-2 NICOLAUS COPERNICUS ______________ ______________ (originally, Mikolaj Kopernik) was born in 1473 in what is now Poland (Figure 3-1). At the time of his birth—and throughout his life—astronomy was based on Ptolemy's model of Aristotle's universe. In spite of many revisions, the Ptolemaic model was still a poor predictor of planet positions, but because of the authority of Aristotle, widely accepted. Moreover, because in Aristotle's philosophy the most perfect region was in the ____________ and the most imperfect region was at ___________'s center, the classical geocentric universe model matched the commonly held ___________ view of the geometry of heaven and hell. Anyone who criticized Aristotle's model of the Universe was thereby also challenging belief in the locations of heaven and hell, risking at least criticism and perhaps a serious charge of _________ with a possible death penalty. (Nicolaus Copernicus (Latinized version of his birth name, Mikolaj Kopernik) pursued a lifetime career in the Church, but he was also a talented mathematician and astronomer. His work triggered a revolution in human thought)

church, hesitated, Sun, heliocentric, detailed model, 1514

3-2a Copernicus's Model Copernicus was associated with the Roman Catholic ____________ throughout his life. His uncle, by whom he was raised and educated, was a bishop. After studying medicine and Church law in some of the major universities in Europe, Copernicus became a Church employee, serving as secretary and personal physician to his powerful uncle for 15 years and moving into quarters in the cathedral after his uncle died. Because of this connection to the Church and his fear of persecution, he _____________ to publish his revolutionary ideas that challenged the Ptolemaic model and, indirectly, belief in heaven and hell. What were these revolutionary ideas? Copernicus believed that the _______ and not Earth was the center of the Universe and that Earth rotated on its axis and revolved around the Sun. Copernicus apparently began doubting Ptolemy's geocentric model during his college days. A _____________ universe model (Sun centered, from the Greek word for Sun, helios) had been discussed occasionally before Copernicus's time, but Copernicus was the first person to produce a ____________ ______________ with substantial justifying arguments. Sometime before _______, Copernicus wrote a short pamphlet summarizing his model and distributed it in handwritten form while he worked on his book.

Copernican Revolution

Although astronomers throughout Europe read and admired De Revolutionibus and found Copernicus's astronomical observations and mathematics to have great value, few astronomers believed, at first, that the Sun actually was the center of the Solar System and that Earth moved. How the Copernican hypothesis was gradually recognized as correct has been called the _____________ ________________, because it was not just the adoption of a new idea but a total change in the way astronomers and the rest of humanity thought about the place of Earth.

De Revolutionibus Orbium Coelestium, 1530, 1542, center, faster, overtakes, steadily, westward, loop, angle, orbital planes, separate

3-2b De Revolutionibus Copernicus's book ___ ___________________ ____________ _____________ (On the Revolutions of Celestial Spheres) was essentially finished by about ________. He hesitated to publish, although other astronomers, and even church officials concerned about reform of the calendar, knew about his work, sought his advice, and looked forward to the book's publication. In _________ Copernicus finally sent the manuscript for De Revolutionibus off to be printed. He died in 1543 before the printing was completed. The most important idea in the book was that the Sun was the _________ of the Universe. That single innovation had an impressive consequence—the retrograde motion of the planets was immediately explained in a straightforward way without the epicycles that Ptolemy used. In Copernicus's model, which you can see in Figure 3-3, Earth moves _______ along its orbit than the planets that lie farther from the Sun. Consequently, Earth periodically ____________ and passes these planets. Imagine that you are a runner on a track moving along an inside lane. Runners well ahead of you appear to be moving forward relative to background scenery. As you overtake and pass slower runners in outside lanes, they fall behind, seeming to move backward for a few moments relative to the scenery. The same thing happens as Earth passes a planet such as Mars. Although Mars moves __________ along its orbit, as seen from Earth it seems to slow to a stop and move ____________ (retrograde) relative to the background stars as Earth passes it (Figure 3-2). Because the planets' orbits do not lie in precisely the same plane, a planet does not resume its eastward motion in precisely the same path it followed earlier. Instead, it describes a ________ with a shape depending on the ______________ between the two __________ __________. (figure 3-2- Earth and Mars are shown at equal intervals to show that as Earth overtakes Mars (a-c), Mars appears to slow its eastward motion. As Earth passes Mars (d), Mars appears to move westward. As Earth draws ahead of Mars (e-g), Mars resumes its eastward motion against the background stars.) ((a) The Copernican universe, as reproduced in his book De Revolutionibus. Earth and all the known planets revolve in ____________ circular orbits about the Sun (Sol) at the center. The outermost sphere carries the immobile stars of the celestial sphere. Notice the orbit of the Moon around Earth (Terra). (b) The model is simple not only in the arrangement of the planets but also in their motions. Orbital velocities (blue arrows) decrease from that of Mercury, the fastest, to that of Saturn, the slowest.)

planetary motion

3-3 TYCHO BRAHE, JOHANNES KEPLER, AND PLANETARY MOTION As astronomers struggled to understand the place of Earth, they also faced the problem of ___________ __________. How exactly do the planets move? That problem was solved by a nobleman who built a fabulous observatory and a poor commoner with a talent for mathematics.

Tycho Brahe, geocentric, Sun

3-3a Tycho Brahe The Danish nobleman _________ _________ is remembered in part for wearing false noses to hide a dueling scar from his college days (Figure 3-4). He was reportedly very proud of his noble station, so his disfigurement probably did little to improve his lordly disposition. (Tycho Brahe was, during his lifetime, the most famous astronomer in the world. Tycho's model of the Universe retained the first principles of classical astronomy; it was ______________ with the Sun and the Moon revolving around Earth, but the planets revolved around the _______. All motion was along circular paths)

Johannes Kepler, copernican hypothesis, The Forerunner of Dissertations on the Universe,

3-3b Johannes Kepler No scientist could have been more different from Tycho Brahe than was _____________ ___________. He was born in 1571, the oldest of six children in a poor family living in what is now southwest Germany. His father, who fought as a mercenary soldier for whomever could afford his fees, eventually disappeared. Kepler's mother was apparently an unpleasant and unpopular woman. She was accused of witchcraft in her later years, and Kepler defended her (successfully) in a trial that dragged on for 3 years. Kepler himself had poor health, even as a child, so it is surprising that he did well in school, winning promotion to a Latin school and eventually a scholarship to the university at Tübingen, where he studied to become a Lutheran pastor. While still a college student, Kepler had become a believer in the _____________ ___________. During his last year of study, Kepler accepted a teaching job in the town of Graz, in what is now Austria, which allowed him to continue his studies in mathematics and astronomy. By 1596, the same year Tycho arrived in Prague, Kepler had learned enough to publish a book called ____ ________________ ____ _______________ ___ _____ ___________, Containing the Mystery of the Universe. The book is more commonly known by an abbreviation of its original Latin title: Mysterium Cosmographicum (Figure 3-5). (a) Johannes Kepler was Tycho Brahe's successor. (b) This diagram, based on one drawn by Kepler, shows how he believed the sizes of the celestial spheres carrying the outer three planets—Saturn, Jupiter, and Mars—are determined by spacers (blue) consisting of two of the five regular solids. Inside the sphere of Mars, the remaining regular solids separated the spheres of Earth, Venus, and Mercury (not shown in this drawing). The Sun lay at the very center of this Copernican universe based on geometrical spacers. (c) The five regular solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, the only shapes with all faces of equal sizes and all equal angles between the faces.)

ellipse, foci, constant

3-3c Kepler's Three Laws of Planetary Motion Although Kepler dabbled in the philosophical arguments of the day, he was a mathematician, and his triumph was the solution of the problem of the motion of the planets. The key to his solution was the _________. An ellipse is a figure drawn around two points, called the ______, in such a way that the distance from one focus to any point on the ellipse and back to the other focus equals a ________. This makes it easy to draw ellipses with two thumbtacks and a loop of string. Press the thumbtacks into a board, hook the string about the tacks, and place a pencil in the loop. As you can see in Figure 3-6a, if you keep the string taut as you move the pencil, it traces out an ellipse. (The geometry of elliptical orbits. (a) Drawing an ellipse with two tacks and a loop of string. (b) The semi-major axis, a, is half of the longest diameter. (c) Kepler's second law is demonstrated by a planet that moves from A to B in one month and from A' to B' in the same amount of time. The two blue sectors have the same area.)

telescope, build, observe, apply, moon, shadows, four, galilean moons

3-4a Telescopic Observations It was the __________ that drove Galileo to publicly defend the heliocentric model. Galileo did not invent the telescope. It was apparently invented around 1608 by lens makers in Holland. Galileo, hearing descriptions in the fall of 1609, was able to _____ working telescopes in his laboratory. Galileo was also not the first person to look at the sky through a telescope, but he was the first person to ______ the sky carefully and ______ his observations to the main theoretical problem of the day—the place of Earth. What Galileo saw through his telescopes was so amazing he rushed a small book into print, Sidereus Nuncius (The Starry Messenger). In that book he reported two major discoveries about the Solar System. First, the ______ was not perfect. It had mountains and valleys on its surface, and Galileo used the _______ to calculate the height of the mountains. Aristotle's philosophy held that the Moon was perfect, but Galileo showed that it was not only imperfect but was even a world like Earth. Second, Galileo's telescope revealed ____ new "planets" circling Jupiter, planets that we know today as the ________ _____ of Jupiter, shown in Figure 3-8.

cease, 1632, aristotle, ptolemy, debate, ridicule

3-4b Dialogo and Trial In 1623 Galileo's friend Cardinal Barberini became pope, taking the name Urban VIII. Galileo went to Rome in an attempt to have the 1616 order to _____ debate lifted. Although that attempt was unsuccessful, Galileo began to write a massive defense of Copernicus's model, completing it in 1629. After some delay, Galileo's book was approved by both the local censor in Florence and the head censor of the Vatican in Rome. It was printed in ______. Called Dialogo Sopra i Due Massimi Sistemi del Mondo (Dialogue Concerning the Two Chief World Systems), it confronts the ancient astronomy of _______ and _______ with the Copernican model. Galileo wrote the book as a _______ among three friends. Salviati is a swift-tongued defender of Copernicus; Sagredo is intelligent but largely uninformed; Simplicio is a dim-witted defender of Ptolemy. The book was a clear defense of Copernicus, and, either intentionally or unintentionally, Galileo exposed the pope's authority to _______. Urban VIII was fond of arguing that, as God was omnipotent, God could construct the Universe in any form while making it appear to humans to have a different form, and thus its true nature could not be deduced by mere observation. Galileo placed the pope's argument in the mouth of Simplicio. The pope took offense and ordered Galileo to face the Inquisition.

religious, observations, contradicted, modern science

3-4c Two Ways to Understand the World Galileo was tried and condemned on a charge you might call a technicality. Why then is his trial so important that historians have studied it for almost four centuries? Why have some of the world's greatest authors, including Bertolt Brecht, written about Galileo's trial? Why in 1992 did a commission established by Pope John Paul II report that the Inquisition had erred in condemning Galileo? To understand the trial, you must recognize that it was the result of a conflict between two ways of understanding the Universe. Since the Middle Ages, European scholars had taught that the only path to true understanding was through ________ faith. St. Augustine (354-430) wrote "Credo ut intelligam," which can be translated as, "Believe in order to understand." Galileo and other scientists of the Renaissance, however, used their own ___________ as evidence to try to understand the Universe; when their observations __________ religious authorities, they assumed their observations of reality were correct. (See How Do We Know?.) Galileo paraphrased Cardinal Baronius in saying, "The Bible tells us how to go to heaven, not how the heavens go." The significance of Galileo's trial is about the birth of _______ _______ as a new way to understand the Universe.

optics, laws of motion, nature of gravity, invented calculus, move

3-5a Isaac Newton Galileo died in January 1642. Some 11 months later, on Christmas day 1642, Isaac Newton was born in the English village of Woolsthorpe. Newton's life represented the flowering of the seeds planted by the previous four astronomers in this story, Copernicus, Tycho, Kepler, and Galileo. Newton was a quiet child from a farming family, but his work at school was so impressive that his uncle financed his education at Trinity College, where he studied mathematics and physics. In 1665, plague swept through England, and the colleges were closed. During 1665 and 1666, Newton spent his time back home in Woolsthorpe, thinking and studying. It was during these years that he made most of his scientific discoveries. Among other things, he studied _____, developed three _____ __ _____, probed the _____ __ _____, and _______ _______. The publication of his work in his book Philosophia Naturalis Principia Mathematica, know as the Principa (pronounced prin-KIP-ee-ah), in 1687 placed the fields of physics and astronomy on a new firm base. It is beyond the scope of this book to analyze all of Newton's work, but his laws of motion and gravity had an important impact on the future of astronomy. From his study of the work of Galileo, Kepler, and others, Newton extracted three laws that relate the motion of a body to the forces acting on it (Table 3-2). These laws made it possible to predict exactly how a body would _____ if the forces were known.

moon, planets, Kepler's, falling, misses, velocity, mass, open orbit

3-5b Orbital Motion Newton's laws of motion and gravitation make it possible for you to understand why and how the ______ orbits Earth, the __________ orbit the Sun, and to discover why ____________ laws work. To understand how an object can orbit another object, read Concept Art 3B, "Orbiting Earth." You need to see orbital motion as Newton did. Begin by noticing three important ideas: 1) An object orbiting Earth is actually ____________ (being accelerated) toward Earth's center. An object in a stable orbit continuously ____________ Earth because of its horizontal ____________. 2) Objects orbiting each other actually revolve around their mutual center of ________. 3) Notice the difference between closed orbits and open orbits. If you want to leave Earth never to return, you must give your spaceship a high enough velocity so it will follow an ________ ________

tides, universal, differences, gravitational force, side, closer, pulls, deeper, two high, moon, sun, rotation, orbital motion

3-5c Tides: Gravity in Action Newton understood that gravity is mutual—Earth attracts the Moon, and the Moon attracts Earth—and that means the moon's gravity can explain the ocean ________. But Newton also realized that gravitation is ___________, and that means there is much more to tides than just Earth's oceans. Tides are caused by small ____________________ in ________________ ___________. As Earth and the Moon orbit around each other, they attract each other gravitationally. Because the ________ of Earth toward the Moon is a bit ___________, the Moon ___________ on it more strongly and that pulls up a bulge. Also, the Moon pulls on Earth a bit more than it pulls on Earth's far side and that produces a bulge on the far side (Figure 3-12). The oceans are ____________ in these bulges, and as Earth rotates and carries you into a bulge, you see the tide creeping up the beach. Because there are two bulges, there are _____ _____ tides each day, although the exact pattern of tides at any given locality depends on details such as ocean currents, the shape of the shore, and so forth. (Moon's gravity pulls moreon the near side thanthefar side (NPand SP)) (Tides are produced by small differences in the gravitational force exerted on different parts of an object. The side of Earth nearest the Moon feels a larger force than the side farthest away. Relative to Earth's center, small forces are left over, and they cause the tides. Both the _______ and the __________ produce tides on Earth. Tides can alter both an object's ______________ and __________ __________.)

general laws, predictive, analytical, measure, position, motion, cause and effect, second law, acted on, rational, causes

3-5d Newton's Universe Newton's insight gave the world a new conception of nature. His laws of motion and gravity were __________ __________ that described the motions of all bodies under the action of external forces. In addition, the laws were ________ because they made possible specific calculations of predictions that could be tested by observation. For example, Newton's laws of motion can be used to derive Kepler's third law from the law of gravity. Newton's discoveries remade astronomy into an ___________ science in which astronomers could ___________ the ___________ and ___________ of celestial bodies, calculate the gravitational forces acting on them, and predict their future motion. One of the most often used and least often stated principles of science is __________ ____ __________. You could argue that Newton's __________ ________ of motion was the first clear statement of that principle. Ancient philosophers such as Aristotle believed that objects moved because of innate tendencies; for example, objects made of earth or water had a natural tendency to move toward Earth at the center of the Universe. In contrast, Newton's second law says if an object changes its motion by an acceleration, then it must have been ________ ___ by a force. The principle of cause and effect gives scientists confidence that every effect has a cause. If the Universe were not rational, then you could never expect to discover causes. Newton's second law of motion was arguably the first explicit statement that the behavior of the Universe is _________ and depends on _________. (See "What Are We?")

Mathematical Syntaxis, almagest, mercury, venus, Earth-Sun, telescope

3a Ptolemy's great book _______________ _____________ (about the year 140) contained the details of his model. Islamic astronomers preserved and studied the book through the Middle Ages, and they called it Al Majisti (The Greatest). When the book was found and translated from Arabic to Latin in the 12th century, it became known as _____________. 3b The Ptolemaic model of the Universe shown below was geocentric and based on uniform circular motion. Note that ___________ and ___________ were treated differently from the rest of the planets. The centers of the epicycles of Mercury and Venus had to remain on the ________-________ line as the Sun circled Earth through the year. Equants and smaller epicycles are not shown here. Some versions contained nearly 100 epicycles as generations of astronomers tried to fine-tune the model to better reproduce the motion of the planets. Notice that this modern illustration shows rings around Saturn and sunlight illuminating the globes of the planets, features that could not be known before the invention of the ______________.

heavens, spheres, vary, sizes, locations

Aristotle lived in Greece from the year 384 to 322 BCE. He believed as a first principle that the _________ were perfect. Because the sphere and circle were considered the only perfect geometrical figures, Aristotle also believed that all motion in the perfect heavens must be caused by the rotation of spheres carrying objects around in uniform circular motions. Aristotle's writings became so famous that he was known throughout the Middle Ages as "The Philosopher," and the geocentric universe of nested ___________ that he devised dominated astronomy. His opinions on the nature of Earth and the sky were widely accepted for almost 2000 years. Claudius Ptolemy, a mathematician who lived roughly 500 years after Aristotle, believed in the basic ideas of Aristotle's universe but was interested in practical rather than philosophical questions. For Ptolemy, first principles took second place to accuracy. He set about making an accurate mathematical description of the motions of the planets. Ptolemy weakened the first principles of Aristotle by moving Earth a little off-center in the model and inventing a way to slightly _______ the planets' speeds. This made his model (published around the year 140) a better match to the observed motions. Aristotle's universe, as embodied in the mathematics of Ptolemy's model, dominated ancient astronomy. At first the Ptolemaic model predicted positions of the planets with fair accuracy; but as centuries passed, errors accumulated, and Islamic and later European astronomers had to update the model, adjusting the _________ and ______________ of the circles and changing the rates of motion.

spacing, orbits, motions, mars, ellipse, faster, sun, radius

By modern standards, the book contains almost nothing of value. It begins with a long appreciation of Copernicus's model and then goes on to mystical speculation on the reason for the ________ of the planets' orbits. The second half has one virtue—as Kepler tried to understand planet _______, he demonstrated that he was a talented mathematician and that he had become well versed in astronomy. He sent copies to Tycho and to Galileo, who both recognized Kepler's talent in spite of the mystical parts of the book. Life was unsettled for Kepler in Graz because of the persecution of Protestants in that region, so when Tycho Brahe invited him to Prague in 1600, Kepler went eagerly, ready to work with the famous astronomer. Tycho's sudden death in 1601 left Kepler in a position to use Tycho's extensive records of observations to analyze the ___________ of the planets. Kepler began by studying the motion of ____, trying to deduce from the observations how the planet actually moved. By 1606, he had solved the mystery: The orbit of Mars is an __________, not a circle. Thus, he abandoned the ancient belief in the circular motion of the planets. But the mystery was even more complex. The planets do not move at uniform speeds along their elliptical orbits. Kepler recognized that they move _______ when closer to the _______ and slower when farther away. Thus Kepler abandoned both uniform motion and circular motion and thereby finally solved the problem of planetary motion. Later, he discovered that the period of each planet's orbit is related to that orbit's __________. Kepler published his results in 1609 and 1619 in books called, respectively, Astronomia Nova (New Astronomy) and Harmonices Mundi (The Harmony of the World).

plato, perfect, sphere, uniform circular motion, Aristotle, imperfect, geocentric universe, 55

CONCEPT ART 3A AN ANCIENT MODEL OF THE UNIVERSE 1 For 2000 years, the minds of astronomers were shackled by a pair of ideas. The Greek philosopher _________ argued that the heavens were ____________. Because the only perfect geometrical shape is a ____________, which carries a point around in a circle as it rotates, and because the only perfect motion is uniform motion, Plato concluded that all motion in the heavens must be made up of combinations of circles turning at uniform rates. This idea was called __________ ____________ ___________. Plato's student _____________ argued that Earth was ______________ and lay at the center of the Universe. Such a model is known as a _______________ _____________. His model contained _____ spheres turning at different rates and at different angles to carry the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn across the sky. Aristotle was known as the greatest philosopher in the ancient world, and for 2000 years his authority chained the minds of astronomers with uniform circular motion and geocentrism. See the model at right.

higher, orbit, circular velocity, 88

CONCEPT ART 3B ORBITS 1 You can understand orbital motion by thinking of a cannonball moving around Earth in a circular path. Imagine a cannon on a high mountain aimed horizontally as shown at right. A little gunpowder gives the cannonball a low velocity, and it doesn't travel very far before falling to Earth. More gunpowder gives the cannonball a ________ velocity, and it travels farther. With enough gunpowder, the cannonball travels so fast it never strikes the ground. Earth's gravity pulls it toward Earth's center, but Earth's surface curves away from it at the same rate it falls. It is in _______. The velocity needed to stay in a circular orbit is called _________ _______. Just above Earth's atmosphere, at an altitude of 200 km, circular velocity is 7790 m/s or about 17,400 miles per hour, and the orbital period is about _____ minutes (A satellite above Earth's atmosphere feels no friction and will fall around Earth indefinitely.Earth satellites eventually fall back to Earth if they orbit too low and experience friction with the upper atmosphere)

tidal bulges

Caused by the gravitational forces of the Moon, and to a lesser extent the Sun

Aristotle, Claudius Ptolemy, substances, center

Ch 3-1 ASTRONOMY BEFORE COPERNICUS To understand why Copernicus's work was so important, you first need to backtrack to ancient Greece and meet the two great authorities of ancient astronomy, the brilliant philosopher ______________ and a later follower of Aristotle's principles, _____________ _____________, whom you first met in Chapter 2 Section 2-1c in the context of measuring the brightness of stars. Recall from Chapter 1 the differences among Solar System, galaxy, and Universe. The early astronomers discussed here didn't know there were other galaxies. They didn't know that we live inside a galaxy. They didn't even know that the stars were other objects like the Sun. They thought the entire Universe consisted of Earth, the Sun, the Moon, and five moving points of light they called planets. Furthermore, they did not know that the planets are composed of _____________ much like Earth's. They imagined that all of this was enclosed inside the celestial sphere that lay just beyond the most distant planet, Saturn. Their entire Universe was quite small, and they imagined that Earth lay at the ________.

16th, Copernicus, Galileo Galilei, Isaac Newton

Chapter 3- The preceding chapters gave you a modern view of Earth. You can now imagine how Earth, the Moon, and the Sun move through space and how that produces the sights you see in the sky. But how did humanity first realize that we live on a planet moving through space? This realization required the revolutionary overthrow of an ancient and honored idea of Earth's place. By the ______ century, many astronomers were becoming uncomfortable with the idea that Earth sat at the center of a spherical Universe. In this chapter, you will discover how an astronomer named _________________ directly challenged that idea, how ______________ ______________ changed the rules of the debate, and how ________ ____________ changed humanity's concept of nature. (See CO 3.) Here you will find answers to four important questions: 1) How did classical philosophers describe Earth's place in the Universe? 2) How did Copernicus revise that ancient concept? 3) Why was Galileo condemned by the Inquisition? 4) How did Isaac Newton change the way people thought about nature and themselves? This chapter is not just about the history of astronomy. As the astronomers of the Renaissance struggled to understand Earth and the heavens, they invented a new way of understanding nature—a way of thinking that is now called science. Every chapter that follows will use the methods that were invented when Copernicus and others grappled with the ancient idea that Earth is the center of the Universe. (Galileo's telescope revealed such things as craters on the Moon, and he explained how that evidence could be used to test the prevailing Earth-centered model of the Universe. He was condemned by the Inquisition in 1633.)

Galileo Galilei, copernican model, not invent, not condemned,

Chapter 3-4 GALILEO GALILEI ______ ___________ was born in the Italian city of Pisa in 1564 and studied medicine at the university there. His true love, however, was mathematics, and he eventually became professor of mathematics at the university at Padua, where he remained for 18 years. During this time, Galileo seems to have adopted the _________ _______, although he admitted in a 1597 letter to Kepler that he did not support that model publicly, fearing criticism. Most people know two "facts" about Galileo, and both are wrong. Galileo did ____ ________ the telescope, and he was ____ ________ by the Inquisition for believing that Earth moved around the Sun. As you learn about Galileo, you will discover that what was on trial were not just his opinions about the place of Earth but also the methods of science itself.

144, renaissance, Copernican Revolution, Isaac Newton

Chapter 3-5 ISAAC NEWTON, GRAVITY, AND ORBITS The birth of modern astronomy and of modern science dates from the _____ years between the publication of Copernicus's and Newton's chief works (in 1543 and 1687 respectively). The ____________ is commonly taken to be the period approximately between 1350 and 1600, so the 144 years of this story lie at the climax of the European reawakening of learning in all fields (Figure 3-11). >The five astronomers of this story lived at the culmination of the Renaissance: Coperinicus, Tycho Brahe (Tycho's nova- 1572), Galileo (Sidereal messenger- 1610 and Dialogues- 1632), Kepler (Law I and II- 1609 and Law III 1609), Newton (Prinicipia- 1687) telescope invented 1608 The problem of the place of Earth was resolved by the ________ _______, but the problem of planetary motion was only partly solved by Kepler's laws. For the last 10 years of his life, Galileo studied the nature of motion, especially the accelerated motion of falling bodies. Although he made some important progress, he was not able to relate his discoveries about motion to the heavens. That final step was taken by ______ __________.

accurately, uniform circular motion, position, epicycles, elliptical

Copernicus's model was simple and straightforward compared with the multiple off-center circles of the Ptolemaic model. However, De Revolutionibus failed to immediately disprove the geocentric model for one critical reason—the Copernican model could not predict the positions of the planets any more ____________ than the Ptolemaic model could. Although Copernicus proposed a revolutionary idea in making the Solar System heliocentric, he was a classically trained astronomer with great respect for the old concept of uniform circular motion. Copernicus objected to Ptolemy's schemes for moving Earth slightly off-center and varying the speeds of planet motions. That seemed arbitrary and ugly to Copernicus, so he returned to a strong but incorrect belief in ___________ _______________ ____________. Therefore, even though his model put the Sun correctly at the center of the Solar System, it could not accurately predict the ____________ of the planets as seen from Earth. Copernicus even had to reintroduce small ____________ to match minor variations in the motions of the Sun, the Moon, and the planets. Astronomers today recognize those variations as due to the planets' real motions in ______________ orbits (discussed in Section 3-3).

2.14 years, retrograde, east

Every ______ ______, Mars passes through a _____________ loop. Two successive loops are shown here. Each loop occurs further ______ along the ecliptic and has its own shape. (https://www.youtube.com/watch?v=TK9ozJYELR8)

interrogated, Bellarmine, forgery, disobeying, confined

Galileo was _________ by the Inquisition and threatened with torture. He must have thought of Giordano Bruno, a monk who was tried, condemned, and burned at the stake in Rome in 1600 for, among other offenses, supporting Copernicus. However, Galileo's trial did not center on his belief in Copernicus's model. Dialogo had been approved by two censors. Rather, the trial centered on a record of the meeting in 1616 between Galileo and Cardinal _________ that included the statement that Galileo was "not to hold, teach, or defend in any way" the principles of Copernicus. Many historians believe that this document, which was signed neither by Galileo nor by Bellarmine nor by a legal secretary, was a ______, or perhaps a draft that was never used. By this time Bellarmine was dead and could not testify about the meeting or the document. The Inquisition condemned Galileo not for heresy but for ________ the orders given him in 1616. In 1633, at the age of 70, kneeling before the Inquisition, Galileo read a recantation admitting his errors. Tradition has it that as he rose he whispered, "E pur si muove" ("Still it moves"), referring to Earth. Although he was sentenced to life imprisonment, he was actually ________ at his villa for the next 10 years, perhaps through the intervention of the pope. He died there in 1642, 99 years after the death of Copernicus.

evidence, reality, tested

HOW DO WE KNOW? EVIDENCE AS THE FOUNDATION OF SCIENCE Why is evidence critical in science? From colliding galaxies to the inner workings of atoms, scientists love to speculate and devise hypotheses, but all scientific knowledge is ultimately based on _________ from observations and experiments. Evidence is _____, and scientists constantly check their ideas against reality. When you think of evidence, you probably think of criminal investigations in which detectives collect fingerprints and eyewitness accounts. In court, that evidence is used to try to understand the crime, but there is a key difference in how lawyers and scientists use evidence. A defense attorney can call a witness and intentionally fail to ask a question that would reveal evidence harmful to the defendant. In contrast, the scientist must be objective and not ignore any known evidence. The attorney is presenting only one side of the case, but the scientist is searching for the truth. In a sense, the scientist must deal with the evidence as both the prosecution and the defense. It is a characteristic of scientific knowledge that it is supported by evidence. A scientific statement is more than an opinion or a speculation because it has been _______ objectively against reality. As you read about any science, look for the evidence in the form of observations and experiments. Every hypothesis or conclusion should have supporting evidence. If you can find and understand the evidence, the science will make sense. All scientists, from astronomers to zoologists, demand evidence. You should, too.

propose, explanation, hypothesis, observation, experimentation, theory, description, applicable, evidence, natural law, fundamental principles, confidence,

HOW DO WE KNOW? HYPOTHESIS, THEORY, AND LAW Why is a theory much more than just a guess? Scientists study nature by devising and testing new hypotheses and then developing the successful ideas into theories and laws that describe how nature works. A good example is the connection between sour milk and the spread of disease. A scientist's first step in solving a natural mystery is to ________ a reasonable __________ based on what is known so far. This proposal, called a ________, is an assertion or statement that must be tested through _________ and ___________. From the time of Aristotle, philosophers believed that food spoils as a result of the spontaneous generation of life—for example, mold growing out of drying bread. French chemist Louis Pasteur (1822-1895) hypothesized that microorganisms were not spontaneously generated but were carried through the air. To test his hypothesis he sealed an uncontaminated nutrient broth in glass, completely protecting it from the microorganisms on dust particles in the air. No mold grew, effectively disproving spontaneous generation. Although others had argued against spontaneous generation before Pasteur, it was Pasteur's meticulous testing of his hypothesis by experiment that finally convinced the scientific community. A ________ generalizes the specific results of well-confirmed hypotheses to give a broader _________ of nature, which can be applied to a wide variety of circumstances. For instance, Pasteur's specific hypothesis about mold growing in broth contributed to a broader theory that disease is caused by microorganisms transmitted from sick people to well people. This theory, called the germ theory of disease, is a cornerstone of modern medicine. It is a common misconception that the word theory means a tentative idea, a guess. As you can see, scientists actually use the word theory to mean an idea that is widely _________ and confirmed by abundant __________. Sometimes, when a theory has been refined, tested, and confirmed so often that scientists have great confidence in it, it is called a __________ _______. Natural laws are the most __________ __________of scientific knowledge. Kepler's laws of planetary motion are good examples. Confidence is the key. In general, scientists have more __________ in a theory than in a hypothesis and the most confidence in a natural law. However, there is no precise distinction among hypotheses, theories, and laws, so use of these terms is sometimes a matter of tradition. For instance, some textbooks refer to the Copernican "theory" of heliocentrism, but it had not been well tested when Copernicus proposed it, and it is more rightly called the Copernican hypothesis. At the other extreme, Darwin's "theory" of evolution, containing many hypotheses that have been tested and confirmed over and over for nearly 150 years, might more correctly be called a natural law.

geocentric, heliocentric, paradigm, perceptions, deficiencies, evidence

HOW DO WE KNOW? SCIENTIFIC REVOLUTIONS How do scientific revolutions occur? You might think from what you know of the scientific method that science grinds forward steadily as new hypotheses are tested against evidence and accepted or rejected. In fact, science sometimes leaps forward in scientific revolutions. The Copernican Revolution is often cited as the perfect example; in a few decades, astronomers rejected the 2000-year-old ____________ model and adopted the ______________ model. Why does that happen? It's all because scientists are human. The American philosopher of science Thomas Kuhn has referred to a commonly accepted set of scientific ideas and assumptions as a scientific ______________. The pre-Copernican thinkers shared a geocentric paradigm that included uniform circular motion, geocentrism, and the perfection of the heavens. Although they were intelligent, they were prisoners of that paradigm. A scientific paradigm is powerful because it shapes your _____________. It determines what you judge to be important questions and what you judge to be significant evidence. Consequently, the ancient philosophers could not recognize how their geocentric paradigms limited what they understood. You will see here how the work of Copernicus, Galileo, and Kepler overthrew the geocentric paradigm. Scientific revolutions occur when the ________________ of the old paradigm build up until finally a scientist has the insight to think "outside the box." Pointing out the failings of the old ideas and proposing a new paradigm with supporting _____________ is like poking a hole in a dam; suddenly the pressure is released, and the old paradigm is swept away. Scientific revolutions are exciting because they give you a dramatic new understanding of nature, but they are also times of conflict as new insights sweep away old ideas.

far, unchanging, measuring, Kepler

In 1572, astronomers were startled to see a new star (now called Tycho's supernova) appear in the sky. Aristotle had argued that the heavens were perfect and therefore unchanging, so astronomers concluded that the new star had to be nearer than the Moon. Tycho could not detect the new star's parallax (look back to Concept Art 3A), meaning it had to be ______ beyond the Moon; it was a change in the supposedly ______________ starry sphere. When Tycho wrote a book about his discovery, the king of Denmark honored him with a generous income and the gift of an island, Hveen, where Tycho built a fabulous observatory. Tycho lived before the invention of the telescopes, so his observatory was equipped with wonderful instruments for _____________ the positions of the Sun, the Moon, and the planets using the unaided eye and peering along sights. For 20 years, Tycho and his assistants carefully tracked the motions of the planets. After the death of the Danish king, Tycho moved to Prague where he became the Imperial Mathematician to the Holy Roman Emperor Rudolph II. Tycho hired a few assistants including a German school teacher named Johannes _________. Just before Tycho died in 1601, he asked Rudolph II to make Kepler Imperial Mathematician.

ellipses, sun, areas, time, proportional, ellipses, circular, Mercury

Kepler's Laws of Planetary Motion: 1)The orbits of the planets are ____________ with the ______ at one focus. 2) A line from a planet to the Sun sweeps over equal _______ in equal intervals of _______. 3) A planet's orbital period squared is _____________ to its average distance from the Sun cubed: P^2y(years)=a^3AU P (orbital period)= time planet takes to travel around the Sun once P to the 2nd power (y= tears) A (semi-major axis of a planet's orbit)= average distance from the Sun= the Semi-Major axis A to the third power (AU= astronomical units) Kepler's first law states that the orbits of the planets around the Sun are ______ with the Sun at one focus. Thanks to the precision of Tycho's observations and the sophistication of Kepler's mathematics, Kepler was able to recognize the elliptical shape of the orbits even though they are nearly _______. Of the planets known to Kepler, __________ has the most elliptical orbit, which you can measure in Figure 3-7, but even it deviates only slightly from a circle. (The orbits of the planets are nearly circular. You can measure the horizontal and vertical diameters of this orbit to detect its elliptical shape.)

closer, rapidly, farther, same

Kepler's second law states that a line from the planet to the Sun sweeps over equal areas in equal intervals of time. This means that when the planet is _______ to the Sun and the line connecting it to the Sun is shorter, the planet moves more _______ to sweep over the same area that is swept over when the planet is farther from the Sun. Thus the planet in Figure 3-6c would move from point A′ to point B′ in one month, sweeping over the area shown. But when the planet is ________ from the Sun, one month's motion would be shorter, from A to B although the total area swept out is the _______.

distance, decreases, square, increases, inverse square relation, attracting, objects, time, square, distance

Newton also realized that the _______ between the objects is important. The gravitational force between two bodies depends not only on the masses of the bodies but also on the distance between them. He recognized that the force of gravity ________ as the ________ of the distance between the objects ________. Specifically, if the distance from, say, Earth to the Moon were doubled, the gravitational force between them would decrease by a factor of 2^2, or 4. If the distance were tripled, the force would decrease by a factor of 3^2, or 9. This relationship is known as the ________ _______ _________. Newton guessed that gravity works by an inverse square relation because he had already discovered that light behaves this way (to be discussed in more detail in Chapter 9). To summarize, the force of gravity __________ two _________ to each other equals a constant ________ the product of their masses divided by the ________ of the __________ between the objects. Gravity is universal: Your mass affects the planet Neptune and the galaxy M31, and every other object in the Universe, and their masses affect you—although not much, because they are so far away and your mass is relatively very small.

straight, acted upon, force, change, force, direction, equal, opposite

Newton's Three Laws of Motion 1) A body continues at rest or in uniform motion in a ________ line unless _____ ____ by some _____. (inertia) 2) A body's ______ of motion is proportional to the ______ acting on it, and is in the ________ of the force. 3) When one body exerts a force on a second body, the second body exerts an ______ and __________ force back on the first body.

equant

_____________- In the Ptolemaic model of the Solar System, the point off-center in a deferent from which the center of an epicycle appears to move uniformly.

questioned, inquisition, certain statements, hypotheses

Sidereus Nuncius was popular and made Galileo famous. In 1611, Galileo visited Rome and was treated with great respect. He had friendly discussions with the powerful Cardinal Barberini, but because he was outspoken, forceful, and sometimes tactless he offended other important people who ________ his telescopic discoveries. Some critics said he was wrong, and others said he was lying. Some refused to look through a telescope lest it mislead them, and others looked and claimed to see nothing (hardly surprising given the awkwardness of those first telescopes). When Galileo visited Rome again in 1616, Cardinal Bellarmine interviewed him privately and ordered him to cease public debate about models of the Universe, an order Galileo appears to have mostly followed. The _________ (renamed in the 20th century the Congregation of the Holy Office) banned books relevant to the Copernican hypothesis, although De Revolutionibus itself was only suspended pending revision because it was recognized as useful for its predictions of planet positions. Everyone who owned a copy of the book was required to cross out _____ ________ and add handwritten corrections stating that Earth's motion and the central location of the Sun were only ________ and not facts, a situation that you will recognize as recurring today in connection with textbooks discussing biological evolution.

parallax

_____________- The apparent change in position of an object due to a change in the location of the observer. Astronomical parallax is measured in seconds of arc. An apparent shift in the position of an object when viewed from different locations

retrograde

______________- The apparent backward (westward) motion of planets as seen against the background of stars.

epicycle

______________- The small circle followed by a planet in the Ptolemaic theory. The center of the epicycle follows a larger circle (the deferent) around Earth.

paradigm

________________- A commonly accepted set of scientific ideas and assumptions.

geosynchronous satellite

_________________ _______________- A satellite that orbits eastward around Earth with a period of 24 hours and remains above the same spot on Earth's surface.

tides, smaller, extra high, extra low, neap tide, tidal bulges, friction, moon, same side, orbits, forward, 4 cm

The Sun also produces __________ on Earth, although they are ___________ than lunar tides. At new and full moons, the lunar and solar tides add together to produce ________ ________ and _______ _______ tides that are called spring tides. At first- and third-quarter moons, the solar tides cancel out part of the lunar tides so that high and low tides are not extreme (see Figure 3-12a). These are called ________ ________. Although the oceans flow easily into ________ _______, the nearly rigid bulk of Earth flexes into tidal bulges and the plains and mountains rise and fall a few centimeters twice a day. ____________ is gradually slowing Earth's rotation, and fossil evidence shows that Earth used to rotate faster. In the same way, Earth's gravity produces tidal bulges in the _________, and, although the Moon used to rotate faster, friction has slowed it down and it now keeps the _________ ________ facing Earth. Tides can also affect _________. The rotation of Earth drags the tidal bulges slightly ahead of the Moon, and the gravitation of the bulges of water pull the Moon _________ in its orbit. This makes the Moon's orbit grow larger by about __ ___ a year, an effect that astronomers can measure by bouncing lasers off reflectors left on the Moon by the Apollo astronauts. Spring tides (are extreme) occur when the Sun and moon add together (Full and new moon) Neap tides (are mild) occur when tides caused by the Sun and the Moon partially cancel (first and third quarter) friction with ocean beds slow earth and drags its tidal bulges slightly ahead. Gravity of tidal bulges pulls moon forward and alters its orbit

semi-major axis, a, half, longest, shape, half, foci, one, elongated, zero, circular, zero, farther, flatter, one, natural laws

The geometry of an ellipse is described by two simple numbers. The _____-_______ ______, __, is ____ of the ________ diameter (Figure 3-6b). The eccentricity, e, of an ellipse is half the distance between the ____ divided by the semi-major axis. The eccentricity of an ellipse tells you its ______: If e is nearly equal to _____, the ellipse is very ____________; if e is close to ______, the ellipse is more ________. To draw a circle with the string and tacks shown in Figure 3-6a, you would move the two thumbtacks together, which shows that a circle is the same as an ellipse with eccentricity equal to ________. As you move the thumbtacks _________ apart, the ellipse becomes ________, and the value of its eccentricity moves closer to ________. Kepler used ellipses to describe the motion of the planets in three fundamental rules that have been tested and confirmed so many times that astronomers now refer to them as "___________ ________." They are commonly called Kepler's laws of planetary motion, summarized in Table 3-1 (See How Do We Know?.).

copernican, earth could not move, jupiter, centers of motion, shortest, longer, sun, phases, crescent, complete set, revolved

The moons of Jupiter supported the _______ over the Ptolemaic model. Critics of Copernicus had said _____ ______ ___ ____ because the Moon would be left behind; but Jupiter moved and kept its satellites. Galileo's discovery suggested that Earth, too, could move and keep its Moon. Also, Aristotle's philosophy included the belief that all heavenly motion was centered on Earth. Galileo showed that Jupiter's moons revolve around _______, so there could be _______ ___ _______ other than Earth. Later, after the Messenger was published, Galileo noticed that Jupiter's inner-most moon had the ________ orbital period and the moons farther from Jupiter had proportionally ______ periods. In this way, Jupiter's moons made up a harmonious system ruled by Jupiter, just as the planets in the Copernican universe were a harmonious system ruled by the ____. This similarity didn't constitute proof, but Galileo saw it as an indication that the Solar System could be Sun centered and not Earth centered. In the years of further exploration with his telescope, Galileo made additional fundamental discoveries (Figure 3-9). When he observed Venus, Galileo saw that it was going through _______ like those of the Moon. In the Ptolemaic model, Venus moves around an epicycle centered on a line between Earth and the Sun. If that were true, it would always be seen as a _______, like the model in Figure 3-10a. But Galileo saw Venus go through a _______ ___ of phases, including full and gibbous, which proved that it did indeed ________ around the Sun (Figure 3-10b). ((a) Galileo is remembered as the great defender of Copernicanism. (b) Two of Galileo's telescopes, on display in a museum in Florence. Although he did not invent telescopes, Galileo will always be associated with them because they were the source of much of the observational evidence he used to try to understand the Universe.) ((a) Galileo is remembered as the great defender of Copernicanism. (b) Two of Galileo's telescopes, on display in a museum in Florence. Although he did not invent telescopes, Galileo will always be associated with them because they were the source of much of the observational evidence he used to try to understand the Universe.)

move, universe

The most important consequence of the Copernican hypothesis was not what it said about the Sun but what it said about Earth. By placing the Sun at the center, Copernicus made Earth ______ along an orbit like the other planets. By making Earth a planet, Copernicus revolutionized humanity's view of its place in the ____________ and triggered a controversy that would eventually bring the astronomer Galileo Galilei before the Inquisition, a controversy over the nature of scientific and religious truths that continues even today.

closed orbits

____________ _________- An orbit that repeatedly returns to the same starting point.

circular velocity

____________ ___________- The velocity an object needs to stay in orbit around another object. the velocity needed to achieve a circular orbit

hypothesis

____________- A conjecture, subject to further tests, that accounts for a set of facts.

heliocentric universe

_____________ ____________- A model universe with the Sun at the center, such as the Copernican universe.

escape velocity

_____________ ____________- The initial velocity an object needs to escape from the surface of a celestial body. (the velocity needed to escape a body's gravitational pull)

once, P, distance, sun, semi-major axis, a, related, empirical, why, held, around

The time that a planet takes to travel around the Sun _____ is its orbital period, ___, and its average ________ from the _____ equals the _____-_____ _____ of its orbit, ___. Kepler's third law tells us that these two quantities, orbital period and semi-major axis, are ________: Orbital period squared is proportional to the semi-major axis cubed. For example, Jupiter's average distance from the Sun (which equals the semi-major axis of its orbit) is 5.2 AU. The semi-major axis cubed would be about 140.6, so the period must be the square root of 140.6, roughly 11.9 years. P^2y(years)=a^3AU P^2y=5.2^3AU P^2y=140.6AU Py=√140.6 P=11.9 years It is important to notice that Kepler's three laws are _________. That is, they describe a phenomenon without explaining _____ it occurs. Kepler derived them from Tycho's extensive observations without referring to any first principles, fundamental assumptions, or theory. In fact, Kepler never knew what ______ the planets in their orbits or why they continued to move ________ the Sun in the ways he discovered.

uniform circular motion

_____________ _____________ _______________- The classical belief that the perfect heavens could move only by the combination of uniform motion along circular orbits. the movement of an object at a constant speed around a circle with a fixed radius the motion of an object in a circular path at constant speed

geocentric universe

_____________ ______________- A model universe with Earth at the center, such as the Ptolemaic universe.

geocentric universe

_____________ _______________- A model universe with Earth at the center, such as the Ptolemaic universe. the idea that planets revolved in perfect circular orbits around the earth in the universe

ellipse

_____________- A closed curve around two points called the foci, such that the total distance from one focus to the curve and back to the other focus remains constant.

humanity, planets, nature, fundamental laws, motions,

WHAT ARE WE? THINKERS The scientific revolution began when Copernicus made ____________ part of the Universe. Before Copernicus, people thought of Earth as a special place different from any of the objects in the sky, but in trying to explain the motions in the sky, Copernicus made Earth one of the _________. Galileo and those who brought him to trial understood the significance of making Earth a planet. It made Earth and humanity part of _________, part of the Universe. Kepler showed that the planets move according to simple rules. We are not in a special place ruled by mysterious planetary forces. Earth, the Sun, and all of humanity are part of a Universe in which motions can be described by a few _______________ ______. If simple laws describe the _________ of the planets, then the Universe is not ruled by mysterious influences as in astrology or the whims of the gods atop Mount Olympus. And if the Universe can be described by simple rules, then it is open to scientific study. Before Copernicus, people felt they were special because they thought they were at the center of the Universe. Copernicus, Kepler, and Galileo showed that we are not at the center but nevertheless are part of an elegant and complex Universe. Astronomy tells us that we are special because we can study the Universe and eventually understand what we are. It also tells us that we are not only part of nature; we are the part of nature that can think about nature.

pull, center, straight, gravitation, third, pairs, attracts, mutual, universal, matter, gravity, no weight, matter

When Newton thought carefully about motion, he realized that some force must ____ the Moon toward Earth's ____. If there were no such force altering the Moon's motion, it would continue moving in a _______ line and leave Earth forever. It can circle Earth only if Earth attracts it. Newton's insight was to recognize that the force that holds the Moon in its orbit is the same as the force that makes apples fall from trees. Newtonian ________ is sometimes called universal mutual gravitation. Newton's ____ law points out that forces occur in ____. If one body _______ another, the second body must also attract the first. Thus, gravitation is _______. Furthermore, gravity is _________. That is, all objects with mass attract all other masses in the Universe. The mass of an object is a measure of the amount of _______ in the object, usually expressed in kilograms. Mass is not the same as weight. An object's weight is the force that Earth's ______ exerts on the object. Thus an object in space far from Earth might have ___ _________, but it would contain the same amount of ______ and would thus have the same mass that it has on Earth.

velocity, mass, center, circular velocity

When the captain of a spaceship says to the pilot, "Put us into a circular orbit," the ship's computers must quickly calculate the __________ needed to achieve a circular orbit. That circular velocity depends only on the _______ of the planet and the distance from the __________ of the planet. Once the engines fire and the ship reaches __________ __________, the engines can shut down. The ship is in orbit and will fall around the planet forever, as long as it is above the atmosphere's friction. No further effort is needed to maintain orbit, thanks to the laws Newton discovered (See Circular Velocity in the Math Reference Cards MR).

inaccurate, uniform circular motion, heliocentric, simplicity, symmetry, same

You should notice the difference between the Copernican model and the Copernican hypothesis. The Copernican model is ____________. It includes __________ _____________ ____________and thus does not precisely describe the motions of the planets. But the Copernican hypothesis that the Solar System is ______________ is correct—the planets do circle the Sun, not Earth. Why that hypothesis gradually won acceptance is a question historians still debate. There are probably a number of reasons, including the revolutionary spirit of the times, but the most important factor may be the ___________ of the idea. For one thing, placing the Sun at the center of the Universe produced a _____________ among the motions of the planets that is elegant, pleasing to the eye and mind (Figure 3-3). In the Ptolemaic model, Mercury and Venus had to be treated differently from the rest of the planets: Their epicycles had to remain centered on the Earth-Sun line. In Copernicus's model, all of the planets were treated the __________. They all followed orbits that circled the Sun at the center.

semi-major axis, a

_____-_______ ______, __- Half of the longest diameter of an ellipse.

mass

______- A measure of the amount of matter making up an object.

first principles

_______ _________-Something that seems obviously true and needs no further examination. the self-evident truths, as explained by Aristotle

inverse square relation

________ _________ ________- A rule that the strength of an effect (such as gravity) decreases in proportion as the distance squared increases. the force of gravity decreases as the inverse square of the distance separating the objects

theory

________- A system of assumptions and principles applicable to a wide range of phenomena that has been repeatedly verified.

weight

________- The force that gravity exerts on an object.

natural law

_________ _____- A theory that has been so well confirmed that it is almost universally accepted as correct.

open orbit

_________ _________- An orbit that carries an object away, never to return to its starting point.

empirical

__________- Description of a phenomenon without explaining why it occurs.

spring tides

___________ _________- Ocean tide of large range that occurs at full and new moon. Note that the term "spring" refers to leaping, not to the season of spring.

neap tides

___________ _________- Ocean tide of small range occurring at first- and third-quarter moon.

center of mass

____________ ___ ________- The balance point of a body or system of masses. The point about which a body or system of masses rotates in the absence of external forces.

eccentricity, e

_________________, ___- A number between 1 and 0 that describes the shape of an ellipse; the distance from one focus to the center of the ellipse divided by the semi-major axis. e=c/a c- the distance from one focus to center a- half the longest diameter (center to one side)

apogee

an object in an elliptical orbit has its lowest velocity when it is farthest from Earth (___________) the point in an orbit most distant from the body being orbited; the highest point

perigee

highest velocity when it is closest to Earth (perigee). _____________ must be above Earth's atmosphere, or friction will rob the satellite of energy and it will quickly fall back to Earth. point in an orbit that is closest to the earth

orbital velocity

the velocity with which an object moves in orbit