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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 1/70 MA #2 Due: 11:59pm on Sunday, October 8, 2023 You will receive no credit for items you complete after the assignment is due. Grading Policy Prelecture Overview: The Science of Astronomy First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A The shadow cast by a simple stick or obelisk allowed ancient people to ANSWER: Correct A stick or obelisk acts as a simple sundial, which allows you to estimate the local time because the position of the shadow changes as the Sun moves across the sky during the day. Part B Why wasn't the Sun-centered model of Copernicus immediately adopted after he proposed it? ANSWER: Correct Even though it featured more elegant explanations for phenomena like retrograde motion, it was no more accurate than the older model, so there was no compelling reason to think it was a better description of nature. Part C An original observation of Galileo’s that helped to overturn the ancient Earth-centered model was ANSWER: tell the time of day show that the solar system is really Sun-centered record accurate measurements of the motions of the stars observe retrograde motion of the planets Aristarchus had already formulated a Sun-centered model some 1500 years earlier. it featured the Earth at the center, which had already been ruled out by observations observations made with telescopes ruled it out it was not noticeably more accurate than the old Ptolemaic model

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 2/70 Correct Galileo's observations of the phases of Venus directly contradicted the predictions of the Earth-centered model, but agreed with what we expect in a Sun-centered model. Part D Which of the following are the three key hallmarks of science? Select exactly three statements. ANSWER: Correct Key Concept: Kepler's Laws in Action Learning Goal: To understand how Kepler's laws apply to the orbits of the planets in our solar system. When the video below first begins, you will see only the orbits of the outer planets; the animation will then switch to a screen showing the orbits of the inner planets. (Note that the video is not perfect; for example, it shows Neptune and Pluto occasionally colliding, which never happens in the real solar system.) Now, click on the image below to launch the video: Kepler's Laws in Action. Once you have watched the entire video, answer the graded follow-up questions on the right. You can watch the video again at any point. Part A The video states that the planetary orbits are shown to scale. Which statement correctly describes the way the planet sizes are shown compared to their orbits? that planets move in elliptical orbits the phases of Venus retrograde motion of planets in our sky stellar parallax Modern science seeks explanations for observed phenomena that rely solely on natural causes. Science progresses through careful application of what is called the scientific method . Models must make testable predictions that will force us to revise or abandon the model if they do not agree with observations. Science progresses through the creation and testing of models of nature that explain the observations as simply as possible. Scientific models must be structured so that they can be proved true by a single good observation or experiment. Scientific models are miniature representations of reality.

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 3/70 Hint 1. How large is Earth compared to its orbit? The radius of Earth's orbit is approximately __________ times as large as the radius of Earth itself. ANSWER: ANSWER: Correct On the scale used to show the orbits in the video, all the planets would be microscopic in size. The planetary motion shown in the video demonstrates all the major features of Kepler's laws. Some of the features are more difficult to see than others. The remaining questions will help you understand how we see Kepler's laws in the real motion of the planets. Part B Kepler's first law states that the orbit of each planet is an ellipse with the Sun at one focus. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's first law? Check all that apply. Hint 1. Properties of ellipses An ellipse can be drawn by stretching a string around two pins and pulling a pencil around, as shown in the diagram. Notice that the two foci (singular: focus ) of the ellipse are the locations of the two pins. The long axis of the ellipse is called the major axis ; half this length is the semimajor axis . The short axis is the minor axis . Hint 2. How does the shape of an ellipse vary? 2.3 230 23,000 The planets are all much too large compared to their orbits. Jupiter is shown correctly to scale with its orbit, but all the other planets are too large. The planet sizes are correctly shown on the same scale as the orbits. The planets should all be about twice as large as shown.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 4/70 The shape of a particular ellipse depends on its eccentricity , which describes __________. ANSWER: ANSWER: Correct None of the planets has a perfectly circular orbit, which means that all planets (including Earth) are closer to the Sun on one side of their orbit than on the other. The Sun's off-center position arises because it is located at a focus of each planet's elliptical orbit, rather than at the center of the ellipse. Part C Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's second law? Check all that apply. Hint 1. What is the key implication of Kepler's second law? This diagram illustrates Kepler's second law, which states that as a planet orbits the Sun, it sweeps out equal areas in equal times. This law means that a planet must __________. ANSWER: how much longer the major axis is than the minor axis the distance from the center of the ellipse to any point on the ellipse the length of the semimajor axis Earth is slightly closer to the Sun on one side of its orbit than on the other side. Venus orbits the Sun faster than Earth orbits the Sun. All the planets orbit the Sun in nearly the same plane. Pluto moves faster when it is closer to the Sun than when it is farther from the Sun. The Sun is located slightly off-center from the middle of each planet's orbit. Inner planets orbit the Sun at higher speed than outer planets. maintain the same orbital speed at all times move slower when it is closer to the Sun and faster when it is farther from the Sun move faster when it is closer to the Sun and slower when it is farther from the Sun

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 5/70 ANSWER: Correct The same ideas holds for any object orbiting the Sun: An object must move faster when it is closer to the Sun and slower when it is farther from the Sun. Part D Kepler's third law states that a planet's orbital period, p , is related to its average (semimajor axis) orbital distance, a , according to the mathematical relationship . Which of the following statements describe a characteristic of the solar system that is explained by Kepler's third law? Check all that apply. Hint 1. What is the key implication of Kepler's third law? Kepler's third law, expressed mathematically as , tells us that __________. ANSWER: ANSWER: Correct From the relationship , it follows that planets closer to the Sun must orbit at higher average speeds than planets farther from the Sun. For example, Venus must orbit the Sun faster than Earth because Venus is closer to the Sun. Prelecture Narrated Figure: Kepler's First Law Earth is slightly closer to the Sun on one side of its orbit than on the other side. The Sun is located slightly off-center from the middle of each planet's orbit. Venus orbits the Sun faster than Earth orbits the Sun. Pluto moves faster when it is closer to the Sun than when it is farther from the Sun. All the planets orbit the Sun in nearly the same plane. Inner planets orbit the Sun at higher speed than outer planets. a planet that is closer to the Sun orbits faster than a planet that is farther from the Sun all planets orbit the Sun in nearly the same plane a planet moves faster in the part of its orbit where it is closer to the Sun and slower in the part of its orbit where it is farther from the Sun All the planets orbit the Sun in nearly the same plane. Pluto moves faster when it is closer to the Sun than when it is farther from the Sun. Inner planets orbit the Sun at higher speed than outer planets. Earth is slightly closer to the Sun on one side of its orbit than on the other side. The Sun is located slightly off-center from the middle of each planet's orbit. Venus orbits the Sun faster than Earth orbits the Sun.

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 6/70 First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Which of the following paths could not be a real orbit for a planet around the Sun? ANSWER:

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 7/70 Correct Kepler’s first law tells us that the orbit of a planet must be an ellipse with the Sun at one focus. Therefore, the path that shows the Sun in the center of the ellipse, rather than at a focus, cannot be the real orbital path of a planet. (Note that the circular path is allowed because a circle is an ellipse in which both foci are at the center.) Part B Which of the following orbits has the largest semimajor axis? ANSWER: Correct The semimajor axis is half of the distance across the ellipse in its longest direction (which means half of the major axis ), which is also the planet’s average distance from the Sun. Therefore, the ellipse that measures the longest across is the one with the largest semimajor axis. Part C Which of the following orbits is the most eccentric? ANSWER:

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 8/70 Correct Eccentricity is a measure of how “stretched out” an ellipse is. A perfect circle has zero eccentricity, and the most stretched out ellipse has the largest eccentricity. Part D Which of the following orbits shows the planet at aphelion? ANSWER:

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 9/70 Correct Aphelion is the point in a planet’s orbit that is farthest from the Sun. Prelecture Narrated Figure: Kepler's Second Law First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Earth is slightly closer to the Sun in January than in July. How does the area swept out by Earth’s orbit around the Sun during the 31 days of January compare to the area swept out during the 31 days of July? ANSWER: The area swept out in July is larger. The area swept out in January is larger. Both areas are the same.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 10/70 Correct Kepler’s second law tells us that a planet always sweeps out equal areas in equal times. Therefore, Earth sweeps out the same area in any 31- day period, no matter what month it is. Part B All of the following statements are true. Which one can be explained by Kepler’s second law? ANSWER: Correct Kepler’s second law tells us that a planet moves faster in its orbit when it is closer to the Sun (near perihelion) than when it is farther (near aphelion). This law applies to all planets and therefore explains the statement about Mars. Ranking Task: Kepler’s Second Law of Planetary Motion Learning Goal: To understand the meaning of Kepler's second law of planetary motion. Part A Parts A through C all refer to the orbit of a single comet around the Sun. Each of the four diagrams below represents the orbit of the same comet, but each one shows the comet passing through a different segment of its orbit around the Sun. During each segment, a line drawn from the Sun to the comet sweeps out a triangular-shaped, shaded area. Assume that all the shaded regions have exactly the same area. Rank the segments of the comet’s orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. What is Kepler’s second law? According to Kepler’s second law, as a planet or other object moves around its orbit, it sweeps out equal __________ in equal __________. ANSWER: ANSWER: Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun. All the planets orbit the Sun in nearly the same plane. Venus orbits the Sun at a faster orbital speed than Earth. The Sun is not in the precise center of Saturn’s orbit. Earth is slightly closer to the Sun in January than in July. distances / areas areas / times distances / times

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 11/70 Correct Although Kepler wrote his laws specifically to describe the orbits of the planets around the Sun, they apply more generally. Kepler's second law tells us that as an object moves around its orbit, it sweeps out equal areas in equal times . Because all the areas shown here are equal, the time it takes the comet to travel each segment must also be the same. Part B Consider again the diagrams from Part A, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet’s orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. How does distance depend on speed? ANSWER: Correct If the time is the same, the distance must be farther for the one that goes faster. Now, remember that from Part A, you already know that the time to cover each segment is the same for all the diagrams shown. Think about what Kepler's second law tells you about orbital speed (you can review this idea in your textbook), and you should be able to complete Part B. ANSWER: Reset Help Suppose two cars both drive for one hour. Which statement is true? They both go the same distance. The one that goes faster travels farther. The one that goes slower travels farther. Shortest Longest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 12/70 Correct Kepler's second law tells us that the comet sweeps out equal areas in equal times. Because the area triangle is shorter and squatter for the segments nearer to the Sun, the distance must be greater for these segments in order for all the areas to be the same. Part C Consider again the diagrams from Parts A and B, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet’s orbit based on the speed with which the comet moves when traveling from Point 1 to Point 2, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. How is Kepler’s second law related to the comet's speed? According to Kepler’s second law, planets and other objects orbiting the Sun move fastest when they are __________. ANSWER: ANSWER: Reset Help traveling toward the Sun traveling away from the Sun nearest to the Sun farthest from the Sun Shortest Longest

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 13/70 Correct From Parts A and B, you know that the comet takes the same time to cover each of the four segments shown, but that it travels greater distances in the segments that are closer to the Sun. Therefore, its speed must also be faster when it is closer to the Sun. In other words, the fact that that the comet sweeps out equal areas in equal times implies that its orbital speed is faster when it is nearer to the Sun and slower when it is farther away. Part D We'll now leave the comet behind, and instead consider the orbit of an asteroid in Parts D through F. Each of the four diagrams below represents the orbit of the same asteroid, but each one shows it in a different position along its orbit of the Sun. Imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. Rank the positions based on the area that would be swept out by a line drawn between the Sun and the asteroid during the one-week period, from largest to smallest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. What is Kepler’s second law? According to Kepler’s second law, as a planet or other object moves around its orbit, it sweeps out equal __________ in equal __________. ANSWER: ANSWER: Reset Help distances / areas areas / times distances / times Slowest Fastest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 14/70 Correct Kepler's second law tells us that the asteroid will sweep out equal areas in equal time intervals. Therefore, the area swept out in any one week period must always be the same, regardless of the asteroid's location in its orbit around the Sun. Part E Consider again the diagrams from Part D, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions from left to right based on the distance the asteroid will travel during a one-week period when passing through each location, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. How do the areas of swept-out triangles relate to distance? Consider two triangles that represent the swept-out area in some time period as an object orbits the Sun. If one triangle is short and squat (where the object is close to the Sun) and the other is long and thin (where the object is far from the Sun), then the object must have moved __________. ANSWER: ANSWER: Reset Help the same distance in both cases farther in the case where the triangle is short and squat farther in the case where the triangle is long and thin Smallest Largest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 15/70 Correct Notice the similarity between what you have found here and what you found for the comet in Part B. Kepler's second law tells us any object will sweep out equal areas in equal times as it orbits the Sun, which means the area triangles are shorter and squatter when the object is nearer to the Sun, so that the object covers a greater distance during any particular time period when it is closer to the Sun than when it is farther away. Part F Consider again the diagrams from Parts D and E, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions (A–D) from left to right based on how fast the asteroid is moving at each position, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. Hint 1. How does Kepler’s second law describe the asteroid's speed? According to Kepler’s second law, planets or other objects orbiting the Sun move fastest when they are __________. ANSWER: ANSWER: Reset Help traveling toward the Sun traveling away from the Sun nearest to the Sun farthest from the Sun Shortest Longest

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 16/70 Correct Just as you found for the comet in Parts A through C, the asteroid must be traveling at a higher speed during parts of its orbit in which it is closer to the Sun than during parts of its orbit in which it is farther away. You should now see the essence of Kepler's second law: Although the precise mathematical statement tells us that an object sweeps out equal areas in equal times, the key meaning lies in the idea that an object's orbital speed is faster when nearer to the Sun and slower when farther away. This idea explains why, for example, Earth moves faster in its orbit when it is near perihelion (its closest point to the Sun) in January than it does near aphelion (its farthest point from the Sun) in July. Prelecture Narrated Figure: Kepler's Third Law, Part 2 First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A All of the following statements are true. Which one can be explained by Kepler’s third law? ANSWER: Reset Help Slowest Fastest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 17/70 Correct Kepler’s third law can be stated as the precise mathematical relationship ; (where p is the planet’s orbital period in years and a is its average orbital distance in ). The essence of the law, however, is that it means planets closer to the Sun orbit at faster average speeds than planets farther from the Sun. Therefore, Venus orbits at a faster orbital speed than Earth, because Venus is closer to the Sun. Ranking Task: Kepler’s Third Law of Planetary Motion Part A The following diagrams all show the same star, but each shows a different planet orbiting the star. The diagrams are all scaled the same. (For example, you can think of the tick marks along the line that passes through the Sun and connects the nearest and farthest points in the orbit as representing distance in astronomical units (AU).) Rank the planets from left to right based on their average orbital distance from the star, from longest to shortest. (Distances are to scale, but planet and star sizes are not.) Hint 1. What is the average distance for an elliptical orbit? Consider a planet with an elliptical orbit around the Sun. Its average distance from the Sun is __________. ANSWER: ANSWER: Venus orbits the Sun at a faster orbital speed than Earth. Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun. Earth is slightly closer to the Sun in January than in July. The Sun is not in the precise center of Saturn’s orbit. All the planets orbit the Sun in nearly the same plane. half the distance along a line from the nearest to the farthest points in its orbit the distance across the orbit at the place where the ellipse is narrowest the distance from the Sun to the farthest point in its orbit the distance from the Sun to the nearest point in its orbit

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 18/70 Correct Note that the line that passes through the star and connects the nearest and farthest points of the planet's orbit is called the major axis , and half this line is the semimajor axis — which we consider the planet’s average distance from the star. Part B The following diagrams are the same as those from Part A. This time, rank the planets from left to right based on the amount of time it takes each to complete one orbit, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.) Hint 1. What is Kepler’s third law? Kepler’s third law states that for any planet orbiting the Sun, the orbital period squared ( ) is equal to the average orbital distance cubed ( ), or . This implies that __________. ANSWER: Hint 2. What do we call the time it takes to complete an orbit? The time a planet takes to complete one orbit is called its __________. ANSWER: Reset Help a planet with a large average distance from the Sun has a longer orbital period than a planet with a smaller average distance from the Sun a planet with a large average distance from the Sun has a shorter orbital period than a planet with a smaller average distance from the Sun a planet travels faster when it is in the part of its orbit closer to the Sun than it does in the part that is farther from the Sun semimajor axis orbital period perihelion Shortest Longest

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 19/70 ANSWER: Correct Recall that the time it takes a planet to complete an orbit is called its orbital period . The pattern found in this Part illutrates one of the ideas that are part of Kepler’s third law: Planets with larger average orbital distances have longer orbital periods. Part C The following diagrams are the same as those from Parts A and B. This time, rank the planets from left to right based on their average orbital speed , from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.) Hint 1. What does Kepler’s third law tell us about orbital speed? Kepler’s third law states that for any planet orbiting the Sun, the orbital period squared ( ) is equal to the average orbital distance cubed ( ), or . This implies that __________. ANSWER: ANSWER: Reset Help a planet with a large average distance from the Sun travels at a faster average speed than a planet with a smaller average distance from the Sun a planet with a large average distance from the Sun travels at a slower average speed than a planet with a smaller average distance from the Sun a planet travels faster when it is in the part of its orbit closer to the Sun than it does in the part that is farther from the Sun Shortest Longest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 20/70 Correct This pattern illustrates another of the ideas that are part of Kepler’s third law: Planets with larger average orbital distances have slower average speeds. Part D Each of the following diagrams shows a planet orbiting a star. Each diagram is labeled with the planet’s mass (in Earth masses) and its average orbital distance (in AU). Assume that all four stars are identical. Use Kepler's third law to rank the planets from left to right based on their orbital periods , from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.) Hint 1. Does orbital period depend on mass? Suppose Earth doubled in mass. How would Earth’s orbital period around the Sun change? ANSWER: Hint 2. What is Kepler’s third law? Kepler’s third law states that for any planet orbiting the Sun, the orbital period squared ( ) is equal to the average orbital distance cubed ( ), or . This implies that __________. ANSWER: Reset Help The orbital period would decrease, but by less than half. The orbital period would remain exactly one year. The orbital period would increase, but by less than double. The orbital period would fall in half to six months. The orbital period would double to two years. Slowest Fastest

11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 21/70 ANSWER: Correct Kepler’s third law tells us that the orbital period of the planet depends on its average distance from its star, but not on the planet’s mass. As Newton later showed with his version of Kepler's third law, this is actually an approximation that works well whenever the planet's mass is small compared to the mass of the star. Process of Science: Identifying Falsifiable Statements Learning Goal: To understand what we mean by a "falsifiable" claim. Introduction. A scientific model must make predictions that can be tested by observations or experiments. One way you can decide whether a claim can be tested is to first decide whether it is falsifiable , meaning that it could potentially be proven false. As a simple example, the statement "All sharks are gray" is falsifiable because it could be proven false by the discovery of a white shark. Part A Let's start with an example from history. Listed below are a series of claims regarding United States President John F. Kennedy (1917-1963). Classify each statement according to whether or not it is falsifiable. Hint 1. Examples of claims that are not falsifiable Keep in mind that a falsifiable statement is not necessarily false or true; rather, it is a statement that could potentially be proven false by some observation or experiment, whether or not that observation or experiment has already been made. Here are some examples of claims that are not falsifiable by scientific processes: • Claims about ethics, morality, or aesthetics, which are based on belief systems rather than on observations or experiments. a planet with a large average distance from the Sun has a shorter orbital period than a planet with a smaller average distance from the Sun a planet travels faster when it is in the part of its orbit closer to the Sun than it does in the part that is farther from the Sun a planet with a large average distance from the Sun has a longer orbital period than a planet with a smaller average distance from the Sun Reset Help Shortest Longest

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 22/70 • Claims that involve miracles or supernatural beings, which by definition are assumed to be beyond the realm of natural investigation. • Conspiracy theories in which no amount of evidence will convince believers that the conspiracy didn't occur. • Claims about the motives, dreams, or thoughts of people who are dead and who didn't record their thoughts. Note that claims like those above may or may not be true, but they are not falsifiable because they cannot be tested by observations or experiments. Hint 2. Can a true statement be falsifiable? Suppose your friend Will has a blue car. In that case, the statement "Will's car is blue" is __________. ANSWER: ANSWER: Correct Note that both of the falsifiable claims in this example happen to be true. The claim about Kennedy being the 35th President is falsifiable because it can be checked against historical records. The claim that Kennedy died from a bullet in his brain is falsifiable because it could have been shown false by the medical examiner. The remaining claims are not falsifiable: Statements that call on any type of supernatural being are by definition out of the realm of science. Similarly, a claim of something being "undetectable" could not be falsified, and a claim about what Kennedy would have done if he had lived is a conjecture that cannot be disproven. Part B Let's now consider possible scientific claims. Recall that a scientific claim is falsifiable if it could in principle be shown to be false by observations or experiments, even if those observations or experiments have not yet been performed. Classify each claim according to whether or not it is falsifiable. Hint 1. Examples of claims that are not falsifiable. Keep in mind that a falsifiable statement is not necessarily false or true; rather, it is a statement that could potentially be proven false by some observation or experiment, whether or not that observation or experiment has already been made. Here are some examples of claims that are not falsifiable by scientific processes: • Claims about ethics, morality, or aesthetics, which are based on belief systems rather than on observations or experiments. • Claims that involve miracles or supernatural beings, which by definition are assumed to be beyond the realm of natural investigation. true and not falsifiable true and falsifiable false and falsifiable Reset Help Kennedy was the 35th president of the United States. Kennedy died from a bullet in his brain. Kennedy's death was the will of God. The murder of John F. Kennedy was an act of evil. If he'd lived, Kennedy would have ended the Vietnam War. Kennedy's murder was orchestrated by an undetectable shadow government of the United States. Falsifiable (could be proven false) Not falsifiable (could not be proven false)

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 23/70 • Conspiracy theories in which no amount of evidence will convince believers that the conspiracy didn't occur. • Claims about the motives, dreams, or thoughts of people who are dead and who didn't record their thoughts. Note that claims like those above may or may not be true, but they are not falsifiable because they cannot be tested by observations or experiments. Hint 2. Can a true scientific statement be falsifiable? The statement "Jupiter is the largest planet in our solar system " is __________. ANSWER: ANSWER: Correct Note that falsifiability alone does not make something science. However, scientific models must make predictions that can be tested, and in general we can only test claims or predictions that are falsifiable. Process of Science Task: Earth-Centered vs. Sun-Centered Models Learning Goal: To understand how evidence allows us to distinguish between alternate possible models of the solar system. Imagine that you did not know whether Earth is the center of the solar system (as the Greeks assumed) or just one planet going around the Sun. In this activity, you will consider a set of observations, some real and some not real, that could help you distinguish between the Greek Earth-centered model and our modern Sun-centered model. Note that, in the Greek Earth-centered model, the planets Mercury and Venus lie between Earth and the Sun, while all other planets orbit Earth beyond the orbit of the Sun. Part A true and falsifiable false and falsifiable true and not falsifiable Reset Help The chemical content of the universe is mostly hydrogen and helium. Earth is at the center of the solar system. The Sun is at the center of the solar system. The observable universe contains approximately 100 billion galaxies. The laws of nature are magnificent and beautiful. The universe was created by God. We are all playthings in a computer program created by advanced aliens. Falsifiable (could be proven false) Not falsifiable (could not be proven false)

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 24/70 Consider the following observations. Classify each observation based on whether it is a real observation (a true statement of something we can actually see from Earth) or one that is not real (a statement of something that does not really occur as seen from Earth). Hint 1. What are circumpolar stars? Circumpolar stars are stars that __________. ANSWER: Hint 2. Can we show galaxies on the celestial sphere? The celestial sphere is the imaginary sphere of the heavens that appears to circle around us each day. A model of the celestial sphere usually shows all the constellations and bright stars, as well as reference points such as the north and south celestial poles and the celestial equator. Can we also show distant galaxies on the celestial sphere? ANSWER: Hint 3. How does Saturn move through our sky? Which of the following best describes Saturn’s daily motion through the sky? ANSWER: Hint 4. Why do we sometimes see a crescent moon? Where is the Moon located when we see it as a crescent? ANSWER: Hint 5. What is stellar parallax? Stellar parallax is __________. ANSWER: are located directly over Earth’s North or South Pole rise in the north and set in the south remain above the horizon at all times Yes, because like stars, galaxies have fixed positions among the constellations. No, because galaxies are too far away. No, because galaxies move too rapidly relative to the stars. Saturn usually rises in the east and sets in the west, but sometimes it goes the opposite way and rises in the west and sets in the east Saturn always rises in the east and sets in the west. On any given night, Saturn stays in the same place in the sky all night long. between Earth and the Sun on the opposite side of the Sun from Earth in the part of its orbit in which it is farther than Earth from the Sun

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 25/70 ANSWER: Correct Before you continue to Part B, think about why each of the preceding observations are real or not real. Part B Consider again the set of observations from Part A. This time, classify each observation according to whether it is consistent with only the Earth-centered model, only the Sun-centered model, both models, or neither model. (Note that an observation is “consistent” with a model if that model offers a simple explanation for the observation.) Hint 1. How does the Sun-centered model explain the daily motion of planets through our sky? According to our modern, Sun-centered model, planets rise in the east and set in the west each day because __________. ANSWER: Hint 2. How does the Earth-centered model explain the daily motion of planets through our sky? According to the Earth-centered model, the known planets rise in the east and set in the west each day because __________. ANSWER: an annual shift in a star’s precise position caused by the fact that we view the stars from different points in Earth’s orbit at different times of year a term we use to describe the motions of stars that we can detect visually only if we watch the patterns of constellations change over many centuries. the daily rising and setting of the stars as Earth rotates on its axis Reset Help the planets are much closer to us than any star besides the Sun Earth rotates from west to east each day the planets orbit the Sun from east to west positions of nearby stars shift slightly back and forth each year Moon rises in east, sets in west Mercury goes through a full cycle of phases stars circle daily around north or south celestial pole a distant galaxy rises in east, sets in west each day a planet beyond Saturn rises in west, sets in east we sometimes see a crescent Jupiter Real (true statements) Not real (false statements)

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 26/70 Hint 3. What is stellar parallax? Stellar parallax is __________. ANSWER: Hint 4. How did Galileo prove that Venus orbits the Sun? All three of the following statements are true. Which one of them did Galileo use to prove that Venus orbits the Sun rather than Earth? ANSWER: Hint 5. Why do we sometimes see a crescent moon? Where is the Moon located when we see it as a crescent? ANSWER: ANSWER: Earth rotates from west to east each day the planets have retrograde motion each of these planets circles Earth each day from east to west an annual shift in a star’s precise position caused by the fact that we view the stars from different points in Earth’s orbit at different times of year a term we use to describe the motions of stars that we can detect visually only if we watch the patterns of constellations change over many centuries the daily rising and setting of the stars as Earth rotates on its axis Through his telescope, Galileo noticed that Venus goes through all the phases, including gibbous and full. Through his telescope, Galileo noticed that Venus does not look like a perfectly circular (full) disk. Through his telescope, Galileo noticed that Venus often appears to be in crescent phase. on the opposite side of the Sun from Earth in the part of its orbit in which it is farther than Earth from the Sun between Earth and the Sun

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 27/70 Correct Now continue to the follow-up questions to check that you understand why the observations fall into these categories. Part C Consider the hypothetical observation “a planet beyond Saturn rises in west, sets in east.” This observation is not consistent with a Sun-centered model, because in this model __________. Hint 1. How does the Sun-centered model explain the daily motion of planets through our sky? According to our modern, Sun-centered model, planets rise in the east and set in the west each day because __________. ANSWER: ANSWER: Correct Earth rotates from west to east, so objects in the sky must appear to go across our sky from east to west. Part D We never see a crescent Jupiter from Earth because Jupiter __________. Reset Help the planets are much closer to us than any star besides the Sun the planets orbit the Sun from east to west Earth rotates from west to east each day all objects in space must orbit the Sun in the same direction planets beyond Saturn must orbit the Sun more slowly than closer-in planets there are no planets beyond Saturn the rise and set of all objects depends only on Earth’s rotation a planet beyond Saturn rises in west, sets in east Mercury goes through a full cycle of phases positions of nearby stars shift slightly back and forth each year Moon rises in east, sets in west stars circle daily around north or south celestial pole a distant galaxy rises in east, sets in west each day we sometimes see a crescent Jupiter Earth-centered only Sun-centered only Both models Neither model

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 28/70 Hint 1. Why do we sometimes see a crescent moon? Where is the Moon located when we see it as a crescent? ANSWER: ANSWER: Correct An object must come between Earth and the Sun for us to see it in a crescent phase, which is why we see crescents only for Mercury, Venus, and the Moon. Process of Science — Extraordinary Claims: Earth Orbits the Sun Learning Goal: To examine the evidence that led to the recognition that Earth is a planet and not the center of the universe. Introduction. Read the Extraordinary Claims text around which this tutorial is focused. You may also wish to review sections of your textbook relevant to the claim. Part A Listed below are a series of statements about events that first happened in one of the four time periods identified in the sorting bins. Place each statement in the correct bin corresponding to when it first occurred in human history. Hint 1. Timeline for Copernicus, Tycho, Kepler, Galileo, Newton Copernicus published his book with his Sun-centered model in 1543. Tycho made most of his observations between about 1570and 1600 Kepler published his first two laws in 1609 and third law in 1619 Galileo began his telescope observations in 1609 Newton published the universal law of gravitation in 1687 ANSWER: in the part of its orbit in which it is farther than Earth from the Sun between Earth and the Sun on the opposite side of the Sun from Earth orbits the Sun in the same direction as Earth shines with its own light is farther than Earth from the Sun does not go around Earth

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 29/70 Correct You should recognize the correct answer as follows: The Earth-centered (geocentric) model was favored in ancient Greece, even though Aristarchus proposed that Earth might orbit the Sun. One reason was that the Greeks knew that a Sun-centered model should produce stellar parallax, but they were unable to observe this parallax. Ptolemy’s Earth-centered model could predict planetary positions within a few degrees of arc. Copernicus published a detailed, Sun-centered model with circular orbits in 1543. During the next few decades, Tycho made naked eye observations of planetary positions accurate to within 1 minute of arc. Galileo began his telescopic observations, including his observations of the phases of Venus, in 1609. That same year, Kepler published his first two laws of planetary motion (which state that planets have elliptical orbits) and his laws could be used to predict planetary positions in agreement with Tycho’s observations (as well as subsequent observations). Newton published the universal law of gravitation in 1687, which explains how gravity determines planetary orbits. Stellar parallax was not observed until much later (1838). Part B In which of the four time periods did the Sun-centered model gain widespread acceptance, meaning that nearly everyone who looked at the evidence concluded that it was correct? ANSWER: Correct Notice that this widespread acceptance of the Sun-centered model came before Newton explained why the model works or observations of parallax provided direct proof that Earth orbits the Sun. Part C Which of the following were key pieces of evidence that led to widespread acceptance of the Sun-centered model “extraordinary claim” during the period from about 1609 to 1630? Reset Help Ancient Greece (through Ptolemy, ~150 A.D.) Early Copernican Revolution (about 1543 – 1600) Later Copernican Revolution (about 1609-1630) Newton and beyond (after about 1687) Suggestion that Earth might orbit the Sun Recognition that Sun-centered model should lead to stellar parallax Ability to predict planetary positions within a few degrees of arc Copernicus proposes Sun-centered model Planetary observations accurate within 1 minute of arc Ability to predict planetary positions within 1 minute of arc Observation of phases of Venus Sun-centered model with elliptical orbits Mathematical description of how gravity determines planetary orbits Observations of stellar parallax

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 30/70 Select all that apply. ANSWER: Correct Apparent retrograde motion had a more natural explanation in the Sun-centered model than in Ptolemy’s Earth-centered model, but that had already been known since the time of ancient Greece. So the key evidence that causes the change from general acceptance of the Earth- centered model to the Sun-centered model came from Kepler and Galileo. Kepler’s laws offered a precise mathematical model of planetary motion that gave a virtual perfect match to planetary observations, and Galileo’s telescopic observations revealed phenomena (such as the phases of Venus) that could not be explained by an Earth-centered system. Observations of stellar parallax and planets around other stars both represent even further evidence for the Sun-centered model, but that model was already well-accepted long before this additional evidence was discovered. Part D In Carl Sagan’s statement “Extraordinary claims require extraordinary evidence,” what does he mean by “extraordinary evidence”? ANSWER: Correct In this context, Sagan is clearly talking about evidence that is extremely strong. Key Concept: Terminology of Motion Learning Goal: To understand the meaning of these key terms of motion: acceleration, momentum change, and net force. First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Observations of stellar parallax. The discovery of planets around other stars. The fact that the Copernican model explained apparent retrograde motion of the planets. The fact that Kepler’s laws allowed virtually perfect prediction of planetary positions. Galileo’s telescopic observations. Evidence that is of a highly unusual type compared to standard scientific evidence. Evidence that was very difficult to obtain. Evidence that no one could possibly dispute, even if they believe the Earth is flat. Evidence that is extremely strong.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 31/70 Drag each statement into the correct bin based on whether it describes motion that involves acceleration or motion at constant velocity. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth’s rotation or orbit. Hint 1. What is constant velocity? Constant velocity means that an object's __________. ANSWER: Hint 2. What is acceleration? An object is accelerating whenever its __________. ANSWER: ANSWER: Correct Acceleration refers to any change in velocity. Because velocity includes both speed and direction, acceleration is occurring whenever there is any change in speed, direction, or both. Constant velocity means that both speed and direction are unchanging. Part B speed and direction are unchanging speed is constant direction is unchanging speed is changing speed is increasing velocity is changing Reset Help a car is speeding up after being stopped a ball is in freefall after being dropped from a high window a car is slowing down for a stop sign a planet is orbiting the Sun in an elliptical orbit a car is holding a steady speed around a curve a planet is orbiting the Sun in a circular orbit an elevator is going upward at constant speed a car is driving 100 km/hr on a straight road a spaceship is coasting without engine power in deep space Acceleration Constant Velocity

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 32/70 Drag each statement into the correct bin based on whether it describes motion in which the object's momentum is changing. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth’s rotation or orbit. Hint 1. What is momentum? Momentum is defined as __________. ANSWER: ANSWER: Correct Momentum is defined as mass times velocity, so if an object's velocity is changing (that is, if it is accelerating), then its momentum must also be changing. Part C Drag each statement into the correct bin based on whether the motion requires the action of a net force. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth’s rotation or orbit. Hint 1. What does a force do? As stated by Newton's second law of motion, a (net) force always causes ___________. ANSWER: speed times direction mass times speed mass times velocity Reset Help a car is slowing down for a stop sign a ball is in freefall after being dropped from a high window a car is holding a steady speed around a curve a car is speeding up after being stopped a planet is orbiting the Sun in a circular orbit a planet is orbiting the Sun in an elliptical orbit a car is driving 100 km/hr on a straight road a spaceship is coasting without engine power in deep space an elevator is going upward at constant speed Change in Momentum Constant Momentum

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 33/70 ANSWER: Correct The only way to change an object's momentum is to apply a net force to it, so if an object's momentum is changing, then a net force must be acting upon it. For example, in the case of the planets orbiting the Sun, the net force is from gravity. In the case of the accelerating cars, the net force is from the engine. Part D Which of the following statements correctly state general principles of motion? (Assume that the moving object's mass is not changing.) Select all that apply . ANSWER: Correct As long as an object's mass is not changing, a net force will cause an object to undergo some type of acceleration. Because acceleration is a change in velocity, and momentum is mass times velocity, the accelerating object is also undergoing a change in momentum. a change in momentum an object to speed up an object to be squished Reset Help Motion in a circle at constant speed means zero acceleration. Accelerated motion includes any motion involving a change in speed, change in direction, or both. An object that is accelerating is also being acted upon by a (nonzero) net force. An object that is accelerating is also undergoing a change in momentum. A momentum change can occur even when the net force is zero. a ball is in freefall after being dropped from a high window a car is holding a steady speed around a curve a planet is orbiting the Sun in an elliptical orbit a planet is orbiting the Sun in a circular orbit a car is slowing down for a stop sign a car is speeding up after being stopped an elevator is going upward at constant speed a car is driving 100 km/hr on a straight road a spaceship is coasting without engine power in deep space Net Force (nonzero) No Net Force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 34/70 Prelecture Video: Vocabulary of Newton's and Kepler's Laws First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Match the correct laws to their statements. Drag the words in the left-hand column to the appropriate blanks in the right-hand column. ANSWER: Correct Part B Match the correct laws to the examples in which they apply. Use each law only once. Drag the words in the left-hand column to the appropriate blanks in the right-hand column. ANSWER: Reset Help Kepler's first law of planetary motion : the orbit of each planet about the Sun is an ellipse with the Sun at one focus. Newton's third law of motion : for any force, there is an equal and opposite reaction force. Newton's first law of motion : an object moves at constant velocity if there is no net force acting upon it. Kepler's second law of planetary motion : a planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times. Kepler's third law of planetary motion : more distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p 2 = a 3 . Newton's second law of motion : force = mass x acceleration

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 35/70 Correct Key Concept: Understanding Tides Learning Goal: To understand the cause and basic properties of tides on Earth. Click the image below to launch the video: Understanding Tides. Once you have watched the entire video, answer the follow-up questions on the right. You can watch the video again at any point. Note: Before you begin, you should identify the positions in the Moon's orbit shown in the video that correspond to new moon, full moon, and first- and third- quarter moon (if necessary, review the section of your textbook on phases of the Moon). You will need to recognize these positions to follow the video explanation. Part A As shown in the video, Earth has two tidal bulges at all times. Approximately where are these bulges located? Hint 1. Identifying the locations of the tidal bulges Reset Help Kepler's first law of planetary motion explains why Earth's distance from the Sun varies over the course of each year. Newton's first law of motion explains why a spaceship with no forces acting on it will continue moving even if it has no fuel. Kepler's second law of planetary motion explains why Earth's orbital speed varies over the course of each year. Kepler's third law of planetary motion explains why Earth orbits the Sun at a faster average speed than Mars. Newton's third law of motion tells us that, when you are standing, the ground is pushing up on you with a force that precisely balances the downward force of your weight. Newton's second law of motion explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 36/70 Notice the labels identifying the locations of the tidal bulges, and observe how their positions change as the Moon orbits Earth. Hint 2. How are the bulges in the video related to high and low tide? In the video, high tide on Earth is represented by __________. ANSWER: ANSWER: Correct The tidal bulges face toward and away from the Moon, because they are caused primarily by the gravitational attraction between Earth and the Moon. Friction explains why the bulges are slightly ahead of the Earth-Moon line, rather than directly on the Earth-Moon line. We'll ignore that detail for now. Part B Most people are familiar with the rise and fall of ocean tides. Do tides also affect land? Hint 1. Do tides affect Earth's atmosphere? Do tides affect Earth's atmosphere? ANSWER: ANSWER: Correct Tides affect the entire Earth, but they are much more noticeable for the oceans because water flows so much more easily than land. Still, the land rises and falls about 1 centimeter with the tides. the two places where the light blue region is thinnest the two places where the light blue region is thickest the regions at which the double yellow arrow points Both are on lines perpendicular to the Earth-Moon line. One is over the Atlantic Ocean, and one is over the Pacific Ocean. One faces the Moon and one faces opposite the Moon. One faces the Moon and one faces the Sun. Yes, because atmospheric gas has mass. No, because tides only affect liquids like ocean water. No, because tides only affect water, not other molecules. Yes, though land rises and falls by a much smaller amount than the oceans. No, tides can only affect liquids and gases, not solids. No, tides only affect the oceans. Yes, land rises and falls with tides equally as high (and low) as the oceans.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 37/70 Part C Any particular location on Earth experiences __________. Hint 1. How to determine days and months in the video You can easily tell the amount of time passing in the video. A day is one full rotation of Earth, while a month is approximately one orbit of the Moon around Earth. You should now be able to answer Part C by carefully watching the video and observing how often a particular location on Earth has high and low tides. ANSWER: Correct The video shows that any location on Earth passes through both tidal bulges and both tidal minima (the places where the tides are smallest) each day, which means two high tides and two low tides. Again, recall that this is true for both land and oceans, though tides are more noticeable in the oceans because water flows so much more readily than land. Part D One tidal bulge faces toward the Moon because that is where the gravitational attraction between Earth and the Moon is strongest. Which of the following best explains why there is also a second tidal bulge? Hint 1. How gravity leads to the tidal force The figure below shows how the gravitational attraction to the Moon varies across Earth. This variation in gravitational force is the source of the tidal force: One side of Earth is pulled more strongly toward the Moon than the other, causing Earth to stretch along the Earth-Moon line. ANSWER: two high tides and two low tides each day one high tide and one low tide each day two sets of high and low tides in the ocean, but only one set on land one high tide and one low tide each month two high tides and two low tides each month The second tidal bulge is a rebound effect, created when water on the side facing the Moon falls back down and thereby pushes up the water on the opposite side of Earth. The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line. The second tidal bulge is created by the centrifugal force caused by Earth's rapid rotation. The second tidal bulge is created by the Sun's gravity.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 38/70 Correct Tides are created by gravity, and the tidal force is caused by the fact that gravity weakens with distance. Therefore, the parts of Earth that are closer to the Moon feel a stronger gravitational attraction to the Moon, and the parts of Earth that are farther away feel a weaker gravitational attraction to the Moon. This varying gravitational attraction essentially stretches Earth along the Earth-Moon line, creating tidal bulges on both sides. Part E As you watch the video, notice that the size of the tidal bulges varies with the Moon's phase, which depends on its orbital position relative to the Sun. Which of the following statement(s) accurately describe(s) this variation? Select all that apply. Hint 1. How to identify Moon phases in the video? Recall that the phase of the Moon depends on its position in its orbit relative to the Sun (notice the "To Sun" arrow in the video): Full moon occurs when the Moon is on the opposite side of Earth from the Sun. New moon occurs when the Moon and Sun are on the same side of Earth. First- and third-quarter moons occur halfway between the new and full positions; that is, when the Moon lies 90 away from the Earth-Sun line (which is along the direction "To Sun"). Now, watch the video and observe how the sizes of the tidal bulges and the tidal minima (the places where the tides are smallest) change as the Moon's phase changes. ANSWER: Correct As the video shows, the tidal bulges are largest and the tidal minima are smallest at full moon and new moon. Those are the times when the tidal forces of the Sun and Moon align (and therefore add to one another). Therefore, high tides are higher and low tides are lower at these times, which are called spring tides . (In contrast, we have neap tides at first- and third-quarter moons, when high tides are not as high and low tides are not as low.) Part F You have found that tides on Earth are determined primarily by the position of the Moon, with the Sun playing only a secondary role. Why does the Moon play a greater role in causing tides than the Sun? Hint 1. Is gravity stronger between Earth and the Sun or Earth and the Moon? The gravitational attraction between Earth and the Sun is __________ the gravitational attraction between Earth and the Moon. ANSWER: High tides are highest at both full moon and new moon. High tides are highest at first- and third-quarter moon. Low tides are highest at both full moon and new moon. High tides are highest at full moon and lowest at new moon. Low tides are highest at full moon and lowest at new moon. Low tides are lowest at both full moon and new moon. weaker than stronger than the same as

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 39/70 ANSWER: Correct The Sun exerts a stronger gravitational force on Earth, which is why Earth orbits the Sun. However, tides are caused by the variation in the gravitational attraction across Earth. Even though the gravitational attraction between Earth and the Moon is smaller than the attraction between Earth and the Sun, the Moon's much closer distance makes this attraction vary more across Earth. That is why tides are due primarily to the Moon, with only a secondary effect from the Sun. Process of Science: Testing the Law of Gravity Learning Goal: To understand how different variables affect the design of experiments used to test the universal law of gravitation. Introduction . More than 400 years ago, Galileo claimed that all objects on Earth should fall with the same acceleration of gravity if we neglect air resistance. A few decades later, Newton showed this claim to be a consequence predicted by his theory of gravity. For the following questions, assume that you have been asked to test Newton's theory with experiments that involve dropping balls and timing their falls. Part A Each diagram shows a single experimental trial in which you will drop a ball from some height. In each case, the ball's size, mass, and height are labeled. Note that two diagrams show a basketball, one diagram shows a bowling ball of the same size but larger mass, and one diagram shows a much smaller marble with the same mass as the basketball. You have a timer that allows you to measure how long it takes the ball to fall to the ground. Which pair of trials will allow you to test the prediction that an object's mass does not affect its rate of fall? Check exactly two of the following diagrams. Hint 1. Does size affect the rate of fall? Take a sheet of paper and drop it from shoulder height. Then pick it up, crumple it into a ball, and drop it again from the same height. What happens? ANSWER: Hint 2. How does height affect the time of fall? Suppose you drop the same ball from two different heights. Which ball will take longer to hit the ground? ANSWER: ANSWER: because the gravitational attraction between Earth and the Moon varies more across Earth than does the gravitational attraction between Earth and the Sun because the Moon orbits Earth faster than Earth orbits the Sun because the gravitational force between Earth and the Moon is stronger than the gravitational force between Earth and the Sun The paper falls to the ground in the same amount of time in both cases. The flat paper falls to the ground faster. The crumpled paper falls to the ground faster. The ball dropped from lower down. The ball dropped from higher up. Both balls will take the same amount of time to reach the ground.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 40/70 Correct The simplest way to test the effects of mass is to compare the results of two trials that are identical except for the mass of the balls. In the language of experimental design, we say that the mass is the "variable of interest" for this experiment, and we therefore hold the other variables (size and height) constant so that they cannot affect the results. Part B Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton's theory of gravity? Neglect effects of air resistance. Hint 1. The acceleration of gravity on Earth The acceleration of gravity on Earth is about 10 (or, more precisely, 9.8 ). This means that, without air resistance, after one second a falling object would be traveling downward at about 10 , after two seconds it would be traveling downward at about 20 , and so on. The mass of the object does not matter; without air resistance, all objects fall at the same rate. ANSWER: The more massive ball takes longer to reach the ground. The less massive ball takes longer to reach the ground. Both balls fall to the ground in the same amount of time. The two balls take different amounts of time to reach the ground.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 41/70 Correct Newton's theory of gravity predicts that, in the absence of air resistance, all objects on Earth should fall with the same acceleration of gravity, regardless of mass. This means that balls dropped from the same height should take the same amount of time to reach the ground. Part C Consider again the experimental trials from Part A. This time, you wish to test how the size of an object affects the rate of its fall. Which pair of trials should you compare? Check exactly two of the following diagrams. Hint 1. Does size affect the rate of fall? Take a sheet of paper and drop it from shoulder height. Then pick it up, crumple it into a ball, and drop it again from the same height. What happens? ANSWER: ANSWER: Correct The variable of interest is now size , so appropriate trials to compare are those in which size differs but other variables are constant. The paper falls to the ground in the same amount of time in both cases. The flat paper falls to the ground faster. The crumpled paper falls to the ground faster.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 42/70 Part D If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why? Hint 1. Does size affect the rate of fall on the Moon? Suppose you were outside on the Moon (wearing a spacesuit) and you dropped a small, heavy rock and a flat sheet of paper from the same height. What would happen? ANSWER: ANSWER: Correct The larger size and lower density of the basketball means it will encounter more air resistance than the marble, so it will take slightly longer to reach the ground. Newton's theory of gravity has been tested extensively, and while it passed many tests, it did not pass all of them. For example, its prediction for how Mercury's orbit changes with time disagrees slightly with observations. Einstein's general theory of relativity improves on Newton's theory: In most cases the two theories of gravity predict the same results, but in the situations where they differ, Einstein's theory works better than Newton's. Part E Einstein's theory, like Newton's, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein's theory? ANSWER: Correct Dropping the balls on the Moon removes any potential effects due to air resistance, so a result in which mass affects the rate of fall would directly contradict the prediction of Einstein's (as well as Newton's) theory. Ranking Task: The Universal Law of Gravitation Part A The rock would fall to the Moon's surface faster and hit the ground first. The flat paper would fall to the Moon's surface faster and hit the ground first. The rock and paper would fall at the same rate and hit the ground at the same time. Because gravity has a greater effect on the smaller ball. Because gravity has a greater effect on the larger ball. Because air resistance has a greater effect on the smaller ball. Because air resistance has a greater effect on the larger ball. Scientists dropping balls from the Leaning Tower of Pisa find that balls of different size but the same mass fall at slightly different rates. Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates. Scientists dropping balls from the Leaning Tower of Pisa find that balls of different mass but the same size fall at slightly different rates.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 43/70 Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. (Assume the spaceship has the same mass throughout the trip; that is, it is not burning any fuel.) Hint 1. What does the strength of gravity depend on? For the situations shown, the two objects we are concerned with are Earth and the spaceship, which both have constant masses. Therefore, the strength of gravity between them: __________. ANSWER: ANSWER: Correct Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth. Part B The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest. Hint 1. What does the strength of gravity depend on? For the situations shown, the two objects we are concerned with are the Moon and the spaceship, which both have constant masses. Therefore, the strength of gravity between them __________. ANSWER: increases in direct proportion to their distance apart decreases with the square of their distance apart decreases in direct proportion to their distance apart increases with the square of their distance apart Reset Help Weakest force Strongest force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 44/70 ANSWER: Correct Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as the spaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity. Part C The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances ( d ) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d =2 is twice as large as a distance of d =1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest. Hint 1. How do we calculate the gravitational force between two objects? To calculate the gravitational force between two objects we __________, and then multiply by the gravitational constant . ANSWER: decreases in direct proportion to their distance apart decreases with the square of their distance apart increases in direct proportion to their distance apart increases with the square of their distance apart Reset Help square the two masses, divide by their distance multiply the two masses together, divide by their distance add the two masses together, divide by their distance squared multiply the two masses, divide by their distance squared add the two masses together, divide by their distance Weakest force Strongest force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 45/70 ANSWER: Correct You have correctly taken into account both the masses of the asteroids and the distances between them. Ranking Task: Pairs of Gravitationally Interacting Objects Part A The following five diagrams show pairs of astronomical objects that are all separated by the same distance . Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left. Hint 1. What does the strength of gravity depend on? The force of gravity follows an inverse square law, meaning that the strength of the force declines with the square of the distance between two masses. But if the distances between pairs of objects are all the same, as in Part A, then the strength of gravity depends only on __________. ANSWER: Hint 2. Comparative masses for the objects shown Here are some comparisons for the masses of the objects on the right: • The Sun’s mass is about 330,000 times the mass of the Earth. • Earth’s mass is about 80 times the mass of the Moon. • The Moon’s mass is about a million times that of a typical small asteroid. Reset Help the product of the two object masses ( ) the sum of the two object masses ( ) the size of the larger mass in the pair the size of the smaller mass in the pair Weakest force Strongest force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 46/70 • A typical small asteroid has a mass at least a million trillion trillion trillion times that of a hydrogen atom. With this information and an understanding of the factors that determine the strength of gravity, you should be able to complete Part A. ANSWER: Correct Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the same asteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right. Part B The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right. Hint 1. How can Newton’s third law help you solve this problem? ANSWER: ANSWER: Reset Help According to Newton’s third law __________. the gravitational force exerted by the asteroids on the left will be equal for each pair of objects because all the asteroids have the same mass the strength of the force that the object on the left exerts on the object on the right has to be exactly the same (but in an opposite direction) as the force the object on the right exerts on the object on the left to find the force on the object on the right, you just have to divide the asteroid mass by the mass of the object on the right Weakest force Strongest force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 47/70 Correct Newton’s third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be equal in magnitude, but opposite in direction to the gravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A. Part C The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest. Hint 1. How can Newton’s second law help you solve this problem? According to Newton’s second law, the greater the force exerted on an object, the greater the object’s _____. ANSWER: ANSWER: Reset Help distance mass acceleration velocity Weakest force Strongest force

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 48/70 Correct According to Newton’s second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on it by the object on the right. That is why the ranking here is the same as the ranking for Part A. Part D Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton’s second law of motion __________. Hint 1. How can Newton’s second law help you solve this problem? Newton’s second law of motion states that force equals mass times acceleration, or F=ma . Suppose you have already calculated the gravitational force, which we will call F g , attracting Earth and the Moon. Then the amount of acceleration of Earth due to this force is __________. ANSWER: ANSWER: Correct Newton’s second law of motion, F=ma , means that for a particular force F , the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa. Reset Help F g divided by the acceleration of the Earth F g divided by the acceleration of the Moon F g divided by the mass of the Earth F g divided by the mass of the Moon the Moon has a larger acceleration than Earth, because it has a smaller mass the Moon and Earth both have equal accelerations, because the forces are equal Earth has a larger acceleration than the Moon, because it has a larger mass Smallest acceleration Largest acceleration

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 49/70 Chapter 3 Concept Quiz Part A - Quiz Question 1 Suppose the planet Uranus were much brighter in the sky, so that it was as easily visible to the naked eye as Jupiter or Saturn. Which one of the following statements would most likely be true in that case? Hint 1. What is named for planets visible to the naked eye? ANSWER: Correct A week has seven days because seven naked-eye objects appear to move among the stars: the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn. If Uranus had been an eighth object visibly moving among the stars, a week likely would have eight days. Part B - Quiz Question 2 How does a 12-month lunar calendar differ from our 12-month solar calendar? Hint 1. Study Section 3.1 of The Essential Cosmic Perspective . ANSWER: Correct This is true because the lunar cycle averages about 29.5 days, so 12 of these cycles makes about 354 days, or 11 days short of our 365-day solar year. Part C - Quiz Question 3 Which of the following best describes a set of conditions under which archaeoastronomers would conclude that an ancient structure was used for astronomical purposes? Hint 1. Study Section 3.1 of The Essential Cosmic Perspective . Its gravity would cause the tides to be much higher than they actually are. The discovery that the Earth is a planet going around the Sun would have come hundreds of years earlier. Its slow motion through the sky would have led it to be named after the Goddess of Procrastination. Its brightness would make it possible to read by starlight at night. A week would have eight days instead of seven. It uses a 23-hour rather than a 24-hour day. Its new year always occurs in February instead of on January 1. It does not have seasons. It has about 11 fewer days.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 50/70 ANSWER: Correct In fact, this answer describes the evidence for astronomical purposes at Machu Piccu, as described in Section 3.1 of The Essential Cosmic Perspective. Part D - Quiz Question 4 How did the Ptolemaic model explain the apparent retrograde motion of the planets? Hint 1. Study Section 3.2 of The Essential Cosmic Perspective . ANSWER: Correct This created a "loop-the-loop" motion that made the planets in the model appear to sometimes go backward as viewed from Earth. Part E - Quiz Question 5 When Copernicus first created his Sun-centered model of the universe, it did not lead to substantially better predictions of planetary positions than the Ptolemaic model. Why not? Hint 1. Study Section 3.3 of The Essential Cosmic Perspective . ANSWER: Correct Because orbits are actually elliptical, his model did not make particularly accurate predictions. Part F - Quiz Question 6 They find that looking out from the center of the building there are two windows that align with the rise and set points of two bright stars. The structure consists of lines in the desert that make patterns visible only from high above. The structure has numerous features indicating alignments with movements of the Sun and cultural heritage claimed that the rulers were descendants of the Sun. The structure has the same dome shape as modern astronomical observatories. The planets sometimes stopped moving and then reversed to move backward along their circular orbits. The planets resided on giant spheres that sometimes turned clockwise and sometimes turned counterclockwise. The planets moved along small circles that moved on larger circles around the Earth. The model showed that apparent retrograde motion occurs as Earth passes by another planet in its orbit of the Sun. Copernicus placed the planets in the wrong order going outward from the Sun. Copernicus placed the Sun at the center but did not realize that the Moon orbits the Earth. Copernicus used perfect circles for the orbits of the planets. Copernicus misjudged the distances between the planets.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 51/70 Earth is farthest from the Sun in July and closest to the Sun in January. During which Northern Hemisphere season is Earth moving fastest in its orbit? Hint 1. Consider Kepler's second law. ANSWER: Correct Kepler's second law tells us that Earth moves fastest when it is nearest to the Sun. Becuase this in January for Earth, it is Northern Hemisphere winter. Part G - Quiz Question 7 According to Kepler's third law ( p 2 = a 3 ), how does a planet's mass affect its orbit around the Sun? Hint 1. Study Kepler's laws in Section 3.3 of The Essential Cosmic Perspective . ANSWER: Correct Kepler's third law makes no allowance for planetary mass, and in fact the planet's mass has virtually no effect on its orbit of the Sun. (The Sun's mass has a major effect, however.) Part H - Quiz Question 8 All the following statements are true. Which one follows directly from Kepler's third law ( p 2 = a 3 )? Hint 1. Study Kepler's laws in Section 3.3 of The Essential Cosmic Perspective . ANSWER: Summer Winter Spring Fall More massive planets orbit the Sun at higher average speed. A planet's mass has no effect on its orbit around the Sun. More massive planets must have more circular orbits. A more massive planet must have a larger semimajor axis. Venus has a thicker atmosphere than Mercury. Venus takes longer to rotate than it does to orbit the Sun. Venus orbits the Sun at a slower average speed than Mercury. Venus is more massive than Mercury.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 52/70 Correct Kepler's third law tells us that orbital speed declines with distance, so Venus must orbit the Sun at a slower speed than Mercury. Part I - Quiz Question 9 Suppose a comet orbits the Sun on a highly eccentric orbit with an average (semimajor axis) distance of 1 AU. How long does it take to complete each orbit, and how do we know? Hint 1. Think about how orbital period is related to orbital distance according to Kepler's laws. ANSWER: Correct Kepler's third law tells us that any object with the same average distance as Earth will orbit in the same time of 1 year. Part J - Quiz Question 10 Galileo challenged the idea that objects in the heavens were perfect by _________. Hint 1. Study Section 3.3 of The Essential Cosmic Perspective . ANSWER: Correct Both the Sun and Moon had been generally assumed to have "perfect" surfaces. Part K - Quiz Question 11 Galileo observed all of the following. Which observation offered direct proof of a planet orbiting the Sun? Hint 1. Study Section 3.3 of The Essential Cosmic Perspective . ANSWER: Each orbit should take about 2 years because the eccentricity is so large. One year, which we know from Kepler's third law. It depends on the eccentricity of the orbit, as described by Kepler's second law. It depends on the eccentricity of the orbit, as described by Kepler's first law. inventing the telescope observing sunspots on the Sun and mountains on the Moon showing that heavy objects fall at the same rate as lighter objects proving Kepler's laws were correct

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 53/70 Correct Galileo's observed that Venus goes through all the phases, which cannot be explained unless Venus is orbiting the Sun. (In the Ptolemaic system, Venus's phases vary only from new to crescent and back.) Part L - Quiz Question 12 Which of the following is not consistent with the major hallmarks of science? Hint 1. Hallmarks of science are discussed in Section 3.4 of The Essential Cosmic Perspective . ANSWER: Correct This statement is not consistent with the hallmarks of science because scientific theories can never be proven beyond all doubt. Part M - Quiz Question 13 Which of the following is not part of a good scientific theory? Hint 1. The definition of a scientific theory is discussed in Section 3.4 of The Essential Cosmic Perspective . ANSWER: Correct Scientific theories can never be proven true beyond all doubt; they can only be supported by a wide body of evidence. Part N - Quiz Question 14 Only one of the statements below uses the term theory in its correct, scientific sense. Which one? Patterns of shadow and sunlight near the dividing line between the light and dark portions of the Moon's face Phases of Venus Four moons of Jupiter. The Milky Way is composed of many individual stars. Science consists of proven theories that are understood to be true explanations of reality. Scientific explanations should be based solely on natural causes. A scientific model must make testable predictions. Science progresses through the creation and testing of models that explain observation as simply as possible. A scientific theory must make testable predictions that, if found to be incorrect, could lead to its own modification or demise. A scientific theory cannot be accepted until it has been proven true beyond all doubt. A scientific theory should be based on natural processes and should not invoke the supernatural or divine. A scientific theory must explain a wide variety of phenomena observed in the natural world.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 54/70 Hint 1. The definition of a scientific theory is discussed in Section 3.4 of The Essential Cosmic Perspective . ANSWER: Correct The term theory is used in its correct scientific sense in this statement. Part O - Quiz Question 15 Which of these hypothetical observations (none of them are real) would force us to reconsider our modern, Sun-centered view of the solar system? Hint 1. Think carefully about how different observations could or could not be explained by our Sun-centered model of the solar system. ANSWER: Correct If Earth is rotating from west-to-east, then all celestial objects must move from east to west across our sky. (The only exception is satellites in low- Earth orbit, where they orbit faster than Earth rotates.) So a planet going in the opposite direction across the sky would pose a direct challenge to our view of Earth as a rotating planet. Chapter 4 Concept Quiz Part A - Quiz Question 1 Which of the following represents a case in which you are not accelerating? Hint 1. Study Section 4.1 of The Essential Cosmic Perspective . ANSWER: Einstein's theory of relativity has been tested and verified thousands of times. I have a new theory about the cause of earthquakes, and I plan to start testing it soon. Evolution is only a theory, so there's no reason to think it really happened. I wrote a theory that is 152 pages long. We discover that the universe is actually contracting, not expanding. We discover a small planet beyond Saturn that rises in the west and sets in the east each day. We discover an Earth-sized planet orbiting the Sun beyond the orbit of Pluto. We find that we are unable to measure any parallax for a distant galaxy.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 55/70 Correct This is constant velocity, which means zero acceleration. Part B - Quiz Question 2 Suppose you drop a 10-pound weight and a 5-pound weight on the Moon, both from the same height at the same time. What will happen? Hint 1. Study Section 4.1 of The Essential Cosmic Perspective . ANSWER: Correct The acceleration of gravity on the Moon is smaller than it is on Earth, but it still is the same for all objects. Therefore, both objects will fall at the same rate. (And because there is no air on the Moon, they'll hit at the same time no matter what shape or density they have.) Part C - Quiz Question 3 Why are astronauts weightless in the Space Station? Hint 1. Study Section 4.1 of The Essential Cosmic Perspective . ANSWER: Correct You are weightless whenever you are in freefall, and the Space Station and other objects orbiting Earth are in a constant state of freefall. Part D - Quiz Question 4 A net force acting on an object will always cause a change in the object's _________. Going from 0 to 100 kilometers per hour in 10 seconds Driving in a straight line at 100 kilometers per hour Slamming on the brakes to come to a stop at a stop sign Driving 100 kilometers per hour around a curve Both weights will float freely because everything is weightless on the Moon. Both will hit the ground at the same time. The 10-pound weight will hit the ground before the 5-pound weight. The 5-pound weight will hit the ground before the 10-pound weight. Because the Space Station is moving at constant velocity Because the Space Station is traveling so fast Because there is no gravity in space Because the Space Station is constantly in freefall around the Earth

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 56/70 Hint 1. Study Section 4.1 of The Essential Cosmic Perspective . ANSWER: Correct Force is actually defined as the rate of change in momentum. Part E - Quiz Question 5 Suppose you are in an elevator that is traveling upward at constant speed. How does your weight compare to your normal weight on the ground? Hint 1. Study Section 4.1 of The Essential Cosmic Perspective . ANSWER: Correct As long as the elevator is not accelerating, your weight on a scale in the elevator will be the same whether the elevator is on the ground or rising (or falling) at constant speed. Part F - Quiz Question 6 The planets never travel in a straight line as they orbit the Sun. According to Newton's second law of motion, this must mean that _________. Hint 1. Study Section 4.2 of The Essential Cosmic Perspective . ANSWER: direction speed mass momentum It is greater. It is the same. It is less. You are weightless. a force is acting on the planets The planets will eventually fall into the Sun. The planets have angular momentum. The planets are always accelerating.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 57/70 Correct Because the planets are not traveling in straight lines, the planets are always accelerating, and Newton's second law tells us that a force must be acting to cause the acceleration. Part G - Quiz Question 7 Suppose the Sun were suddenly to shrink in size but that its mass remained the same. According to the law of conservation of angular momentum, what would happen? Hint 1. Study Section 4.3 of The Essential Cosmic Perspective . ANSWER: Correct Angular momentum is the product mass velocity (of rotation) radius. Shrinking the Sun's radius does not affect its mass, so the rotational velocity must increase to keep angular momentum constant. Part H - Quiz Question 8 Suppose you kick a soccer ball straight up to a height of 10 meters. Which of the following is true about the gravitational potential energy of the ball during its flight? Hint 1. Study Section 4.3 of The Essential Cosmic Perspective . ANSWER: Correct Gravitational potential energy is greater at for a larger height because the ball has a greater distance that it can fall (and it accelerates as it falls). Part I - Quiz Question 9 Suppose you heat an oven to 400° F (about 200° C) and boil a pot of water. Which of the following explains why you would be burned by sticking your hand briefly in the pot but not by sticking your hand briefly in the oven? Hint 1. Study Section 4.3 of The Essential Cosmic Perspective . ANSWER: The Sun's angular size in our sky would stay the same. This could never happen because it is impossible for an object to shrink in size without an outside torque. The Sun's rate of rotation would slow. The Sun would rotate faster than it does now. The ball's gravitational potential energy is always the same. The ball's gravitational potential energy is greatest at the instant the ball leaves your foot. The ball's gravitational potential energy is greatest at the instant it returns to hit the ground. The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 58/70 Correct The boiling water has a lower temperature (212° F or 100° C) than the air in the hot oven, but because it is much more dense, heat is transferred to your arm at a higher rate as a result of the more frequent collisions between your arm and the water molecules. Part J - Quiz Question 10 Which of the following scenarios involves energy that we would typically calculate with Einstein's formula E = mc 2 ? Hint 1. Study Section 4.3 of The Essential Cosmic Perspective . ANSWER: Correct Hydrogen fusion in a nuclear bomb converts a small amount of the mass (about 0.7%) of the hydrogen into energy (the rest becomes helium). Any time that mass is converted to energy we can calculate the amount of energy with Einstein's formula. Part K - Quiz Question 11 A rock held above the ground has potential energy . As the rock falls, this potential energy is converted to kinetic energy . Finally, the rock hits the ground and stays there. What has happened to the energy? Hint 1. Study Section 4.3 of The Essential Cosmic Perspective . ANSWER: Correct Energy is always conserved, so the energy of the rock cannot simply disappear. Instead, it dissipates (becomes "spread out") among so many molecules in the air and ground that we no longer notice it. Part L - Quiz Question 12 The molecules in the water are moving faster than the molecules in the oven. The water can transfer heat to your arm more quickly than the air. The oven has a higher temperature than the water. The water has a higher temperature than the oven. A burning piece of wood produces light and heat, therefore giving off radiative and thermal energy. A mass raised to a great height has a lot of gravitational potential energy. A small amount of the hydrogen in of a nuclear bomb becomes energy as fusion converts the hydrogen to helium. An object accelerated to a great speed has a lot of kinetic energy. It is transformed back into gravitational potential energy. The rock keeps the energy inside it in the form of mass-energy. The energy goes into the ground, and as a result, the orbit of the Earth about the Sun is slightly changed. The energy goes to producing sound and to heating the ground, rock, and surrounding air.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 59/70 Suppose that the Sun shrank in size but that its mass remained the same. What would happen to the orbit of the Earth? Hint 1. Remember that the force of gravity determines planetary orbits, and study Section 4.4 of The Essential Cosmic Perspective . ANSWER: Correct The force of gravity between Earth and the Sun, and hence the orbital distance and speed of Earth, depends only on the Sun's mass (and the Earth-Sun distance), not on the Sun's size. Part M - Quiz Question 13 Imagine another solar system, with a star of the same mass as the Sun. Suppose a planet with a mass twice that of Earth (2 M Earth ) orbits at a distance of 1 AU from the star. What is the orbital period of this planet? Hint 1. Study Newton's version of Kepler's third law (although if you think about it, you'll realize that you could actually answer this one with Kepler's law in its original form). ANSWER: Correct The planet's mass is so small compared to the star's mass that it has essentially no effect on the planet's orbit. (We know this from Newton's version of Kepler's third law.) The fact that the planet has the same orbital distance as Earth therefore means it must have the same orbital period as Earth. Part N - Quiz Question 14 Imagine another solar system, with a star more massive than the Sun. Suppose a planet with the same mass as Earth orbits at a distance of 1 AU from the star. How would the planet's year (orbital period) compare to Earth's year? Hint 1. Consider how mass affects the strength of gravity. ANSWER: Earth would change from a bound orbit to an unbound orbit and fly off into interstellar space. The size of Earth's orbit would shrink, and it would take less than one year to orbit the Sun. Earth's orbit would be unaffected. Earth's orbit would expand, and it would take more than 1 year to orbit the Sun. 2 years It cannot be determined from the information given. 6 months 1 year

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 60/70 Correct This is true because the greater mass of the star would mean a stronger force of gravity at any given distance, which in turn would mean a higher orbital velocity. Part O - Quiz Question 15 Newton showed that Kepler's laws are _________. Hint 1. Study how Newton extended Kepler's laws in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Correct Kepler discovered his laws by looking for a mathematical way to explain Tycho's observations of the planets. His laws successfully predicted planetary positions, but he did not know why they were true. Newton showed that they are true as a result of the universal law of gravitation. Part P - Quiz Question 16 Each of the following lists two facts. Which pair of facts can be used with Newton's version of Kepler's third law to determine the mass of the Sun? Hint 1. Study Newton's version of Kepler's third law in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Correct A single planet's orbital distance and orbital period are all we need to determine the Sun's mass Newton's version of Kepler's third law. Part Q - Quiz Question 17 When space probe Voyager 2 passed by Saturn, its speed increased (but not as a result of firing its engines). What must have happened? An orbit at a distance of 1 AU would not be possible around a star more massive than the Sun. The planet's year would be longer than Earth's. The planet's year would be shorter than Earth's. The planet's year would be the same as Earth's. the key to proving that Earth orbits our Sun seriously in error actually only three of seven distinct laws of planetary motion natural consequences of the law of universal gravitation Earth rotates in 1 day and orbits the Sun in 1 year. Mercury is 0.387 AU from the Sun and Earth is 1 AU from the Sun. The mass of Earth is 6 10 24 kg and Earth orbits the Sun in 1 year. Earth is 150 million km from the Sun and orbits the Sun in 1 year.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 61/70 Hint 1. Study the section on orbital energy in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Correct Voyager 2 gained orbital energy by taking it from Saturn. Part R - Quiz Question 18 Suppose that a lone asteroid happens to be passing Jupiter on an unbound orbit (well above Jupiter's atmosphere and far from all of Jupiter's moons.) Which of the following statements would be true? Hint 1. Study the section on orbital energy in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Correct This is true because orbits cannot change spontaneously, and there is nothing in this situation to add or subtract to the asteroid's orbital energy. Part S - Quiz Question 19 Which of the following best describes the origin of ocean tides on Earth? Hint 1. Study the section on tides in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Voyager 2 must have dipped through Saturn's atmosphere. Saturn must have captured an asteroid at precisely the moment that Voyager 2 passed by. Saturn's rotation must have sped up slightly. Saturn must have lost a tiny bit of its orbital energy. There is no way to predict what would happen. The asteroid's orbit around Jupiter would not change, and it would go out on the same unbound orbit that it came in on. Jupiter's gravity would capture the asteroid, making it a new moon of Jupiter. Jupiter's gravity would suck in the asteroid, causing it to crash into Jupiter. Tides are caused on the side of the Earth nearest the Moon because the Moon's gravity attracts the water. The Moon's gravity pulls harder on water than on land because water is less dense than rock. Tides are caused by the difference in the force of gravity exerted by the Moon across the sphere of the Earth. Tides are caused by the 23.5-degree tilt of the Earth's rotational axis to the ecliptic plane.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 62/70 Correct This is an accurate statement; be sure you understand it. Part T - Quiz Question 20 At which lunar phase(s) are tides most pronounced (for example, the highest high tides)? Hint 1. Study the section on tides in Chapter 4 of The Essential Cosmic Perspective ; remember that high tides are highest when the Sun and Moon are creating tides along the same line through the Earth. ANSWER: Correct These are the spring tides, when the tidal forces of the Sun and Moon work together. Part U - Quiz Question 21 Which of the following best explains why the Moon's orbital period and rotation period are the same? Hint 1. Review the effects of tidal friction in Chapter 4 of The Essential Cosmic Perspective . ANSWER: Correct For the same basic reason, nearly all moons orbiting large planets show the same face to the planet at all times. Motion and Gravity Tutorial This tutorial will help you understand how the force of gravity determines the motion of stars and planets. Launch the Motion and Gravity tutorial. Answer the ungraded questions in the tutorial and the graded follow-up questions below. Third-quarter moon only Both new and full moons New moon only Both first and third quarters Full moon only The law of conservation of angular momentum ensured that the Moon must have the same amount of rotational angular momentum as it has of orbital angular momentum. The equality of the Moon's orbital and rotation periods is an extraordinary astronomical coincidence. The Moon was once closer to Earth, but the force of gravity got weaker as the Moon moved farther away. The Moon once rotated faster, but tidal friction slowed the rotation period until it matched the orbital period.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 63/70 Part A Suppose a parachutist is falling toward the ground, and the downward force of gravity is exactly equal to the upward force of air resistance. Which statement is true? ANSWER: Correct Part B A kilogram is a measure of an object's ____________. ANSWER: Correct Part C Suppose object A has three times as the mass of object B. Identical forces are exerted on the two objects. Which statement is true? ANSWER: The velocity of the parachutist is increasing with time. The velocity of the parachutist must be zero. The velocity of the parachutist is not changing with time. The velocity of the parachutist is decreasing with time. weight mass gravity force The accelerations of the two objects are equal. The acceleration of object B is three times that of object A. The acceleration of object A is three times that of object B.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 64/70 Correct Part D A bowling ball and a small marble will fall downward to the surface of the Moon at the same rate because ____________. ANSWER: Correct Part E If you stood on a planet with four times the mass of Earth, and twice Earth's radius, how much would you weigh? ANSWER: Correct Part F Imagine Earth's identical twin planet "Farth" is twice as far away from the Sun as Earth is. Compared to the force of gravity the Sun experiences due to Earth, how strong is the force of gravity the Sun experiences due to Farth? ANSWER: Correct Part G Suppose the Sun suddenly shrunk, reducing its radius by a half (but keeping its mass the same). The force of gravity exerted on Earth by the Sun would ____________. ANSWER: the ratio of the force of gravity exerted on an object to the object's mass is the same. the force of gravity on an object in a vacuum is zero. the force of gravity is the same for each object. Four times your weight on Earth. Twice your weight on Earth. The same as on Earth. One-half your weight on Earth. One-fourth your weight on Earth. One-fourth as strong. One-half as strong. The same strength. Twice as strong. Four times as strong.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 65/70 Correct Part H When the Sun dies it will become a white dwarf, which will be roughly the same size as the Earth. Assuming the Sun doesn't lose any mass as it becomes a white dwarf, the force of gravity exerted on Earth due to the Sun will ____________. ANSWER: Correct Orbits and Kepler's Laws Tutorial This tutorial will help you understand the shape, speed, and period of a planet's orbit in terms of Kepler's Laws. Launch the Orbits and Kepler's Laws tutorial. Answer the ungraded questions in the tutorial and the graded follow-up questions below. Part A Why do the planets orbit the Sun (i.e. why don't they crash into the Sun)? ANSWER: double remain the same decrease by a half quadruple not change as the Sun turns into a white dwarf increase as the Sun turns into a white dwarf decrease as the Sun turns into a white dwarf

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 66/70 Correct Part B If an astronomer claims to have discovered an object with a very eccentric orbit, which of the following best describes the orbital trajectory of the object? ANSWER: Correct Part C Suppose two comets, comet A and comet B, were orbiting the Sun, having the same average orbital radii. If comet A had a higher eccentricity than comet B, which comet would, during some portion of its orbit, have the highest orbital speed? ANSWER: Correct Part D Two planets are observed going around a star. Planet Xoron has an orbital period that is twice as long as planet Krypton. Which planet has a shorter average orbital radius? ANSWER: Correct Part E Although the planets experience a force of gravity from the Sun, since they are moving, their trajectories bend around the Sun rather than lead directly into the Sun. All astronomical objects move in circular orbits. There is no gravity in space. It looks like a figure 8. It looks like a very squashed oval. It is circular. None of the above. Comet A. Comet B. Both comets would have the same highest speed. Planet Xoron Planet Krypton Both planets have the same average orbital radius. There’s not enough information to determine.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 67/70 A planet is discovered orbiting the star 51 Peg with a period of four days (0.01 years). 51 Peg has the same mass as the Sun. Mercury's orbital period is 0.24 years, and Venus's is 0.62 years. The average orbital radius of this planet is ANSWER: Correct Part F If Earth's orbit were very eccentric, but the average distance from the Sun were still 1 AU, its orbital period ANSWER: Correct Part G The Moon takes roughly 28 days to complete one orbit around Earth. If the orbital radius of the Moon were twice its actual value, its orbital period would be ANSWER: Correct Part H As a comet orbits around the Sun, its maximum speed is twice its minimum speed. What can we say about its orbit? ANSWER: Correct less than Mercury's. between Mercury's and Venus's. greater than Venus's. would be less than one year would be longer than one year. would still be one year. less than 28 days. roughly 28 days. roughly 56 days. more than 56 days. The orbit cannot be an elipse. The comet is twice as far from the Sun at aphelion as at perihelion. The eccentricity of the orbit must be over 0.95. The orbit is nearly circular.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 68/70 Energy Tutorial This tutorial will help you understand different forms of energy and the principle of energy conservation. Launch the Energy tutorial. Answer the ungraded questions in the tutorial and the graded follow-up questions below. Part A A person has a choice of sliding down three slides, which are shown below. All slides start at the same height above the ground. Ignoring friction, for which slide will the final speed of the person at the bottom be the highest? ANSWER: Correct Part B Slide A Slide B Slide C The final speed will be the same, regardless of which slide is used.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 69/70 A 2-kg ball is moving with a speed of 4 m/s, and a 4-kg ball is moving with a speed of 2 m/s. What can you conclude about the of kinetic energies of the two balls? ANSWER: Correct Part C A ball is dropped from a distance 5 m above the ground, and it hits the ground with a certain speed. If the same ball is dropped from a distance 10 m above the ground, its final speed will be ANSWER: Correct Part D A satellite is orbiting Earth with a distance R = 2 R Earth from Earth's center. If the satellite is moved to a distance R = 4 R Earth (twice as far away), its potential energy would be ____________ what is was before. ANSWER: Correct Part E If an object had a temperature of absolute zero (0 K), its ANSWER: Correct Part F A star forms by a gas cloud collapsing due to gravity. As the size of the cloud decreases, the temperature of the cloud The 2-kg ball has more kinetic energy. The 4-kg ball has more kinetic energy. The two balls have the same kinetic energy. the same. 1.4 times as high. twice as high. greater than but less than twice twice half thermal energy would be zero. gravitational potential energy would be zero. rest-mass energy would be zero.

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11/3/23, 2:46 PM MA #2 https://session.masteringastronomy.com/myct/assignmentPrintView?assignmentID=2409605 70/70 ANSWER: Correct Part G A positron is a particle similar to an electron, but with the opposite charge of an electron. If a positron and an electron collide, sometimes both the electron and positron disappear, and two photons are created. This is an example of ANSWER: Correct Part H Three helium nuclei can fuse together, forming one carbon nucleus. The mass of carbon is less than three times the mass of helium. When helium fuses into carbon, which of the following occurs? ANSWER: Correct Score Summary: Your score on this assignment is 99.9%. You received 39.97 out of a possible total of 40 points. decreases. increases. remains the same. rest-mass energy being converted into kinetic energy. rest-mass energy being converted into radiative energy. kinetic energy being converted into rest-mass energy. potential energy being converted into thermal energy. Some other form of energy is converted into rest-mass energy. Rest-mass energy is converted into some other form of energy. Energy is created out of vacuum.

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