(ASTRO) chapter 3 homework

Scientific models are used to __________. make specific predictions that can be tested through observations or experiments

A "model" that does not make such predictions cannot be tested and hence is not scientific.

Part C: When would a new Venus be highest in the sky? at noon

A new Venus occurs when Venus is directly between the Sun and Earth, which means a new Venus will be highest in the sky at the same time that the Sun is highest in the sky, which is around noon (local time).

Which of the following statements about an ellipse is not true? The focus of an ellipse is always located precisely at the center of the ellipse.

An ellipse has two foci (not one), and neither one is located at the center of the ellipse unless the ellipse happens to be a perfect circle.

A vocabulary in context exercise in which students match words to definitions describing elliptical planetary orbits, applying ideas from Kepler's Laws of Planetary Motion.

Earth is located at one focus of the Moon's orbit According to Kepler's second law, Jupiter will be traveling most slowly around the Sun when at aphelion Earth orbits in the shape of a/an ellipse around the Sun The mathematical form of Kepler's third law measures the period in years and the semimajor axis in astronomical units (AU). According to Kepler's second law, Pluto will be traveling fastest around the Sun when at perihelion. The extent to which Mars' orbit differs from a perfect circle is called its eccentricity.

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 __________. the rise and set of all objects depends only on Earth's rotation

Earth rotates from west to east, so objects in the sky must appear to go across our sky from east to west.

Galileo's contribution to astronomy included: making observations and conducting experiments that dispelled scientific objections to the Sun-centered model.

Galileo's telescopic observations provided strong support to the Sun-centered model, and his physics experiments helped overcome physical objections to the idea of a moving Earth.

Part E: In Ptolemy's Earth-centered model for the solar system, Venus always stays close to the Sun in the sky and, because it always stays between Earth and the Sun, its phases range only between new and crescent. The following statements are all true and were all observed by Galileo. Which one provides evidence that Venus orbits the Sun and not Earth? we sometimes see gibbous (nearly but not quite full) Venus.

In the Ptolemaic system, we should never see more than a crescent for Venus. Because we do in fact see more, the Ptolemaic model must be wrong. The full range of phases that we see for Venus is consistent only with the idea that Venus orbits the Sun. Galileo was the first to observe the phases of Venus — and hence to find this evidence in support of the Sun-centered system — because he was the first to observe Venus through a telescope. Without a telescope, we cannot tell that Venus goes through phases.

Part E: Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid?

It will end up on an orbit that is farther from the Sun. Total energy must be conserved, so if one asteroid loses energy and moves to a closer orbit, the other must gain energy and move to a more distant orbit.

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.)

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.

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? The sun is located slightly off=center from the middle of each planet's orbit & Earth is slightly closer to the Sun on one side of its orbit

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 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.

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.

What was the Ptolemaic model? an Earth-centered model of planetary motion published by Ptolemy

The Ptolemaic model was published in about a.d. 150 and held sway for nearly the next 1500 years.

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? Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.

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.

Which of the following statements is not one of Newton's laws of motion?

What goes up must come down. Submit This is not one of Newton's laws, and it's not even true. Objects with escape velocity can go up without coming back down.

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.)

[Earth-centered only]: a planet beyond Saturn rises in west and sets in east [Sun-centered only]: Mercury goes through a full cycle of phases, positions of nearby stars shift slightly back and forth each year [Both models]: stars circle daily around north or south celestial pole, moon rises in east and sets in west, a distant galaxy rises in east and sets in west each day [Neither model]: we sometimes see a crescent Jupiter

Listed following are distinguishing characteristics and examples of reflecting and refracting telescopes. Match these to the appropriate category.

[Reflecting telescopes]: Most commonly used by professional astronomers today, The Hubble Space Telescope, world's largest telescope [Refracting telescopes]: The world's largest is 1-meter in diameter, Galileo's telescopes, very large telescopes become "top-heavy", incoming light passes through glass

When Einstein's theory of gravity (general relativity) gained acceptance, it demonstrated that Newton's theory had been

incomplete Newton's theory works quite well in most cases, but there are some cases (such as very strong gravity) in which it breaks down.

In science, a broad idea that has been repeatedly verified so as to give scientists great confidence that it represents reality is called a __________.

theory Notice that this scientific definition of theory differs from the way the term is often used in everyday life.

Part D: Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result?

A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. The dramatic shrinkage of the Sun would mean the loss of a huge amount of gravitational potential energy. Because energy is always conserved, this "lost" gravitational potential energy must reappear in other forms, such as heat (thermal energy) and light (radiative energy). Meanwhile, conservation of angular momentum would ensure that the collapsed Sun would spin much faster.

Part D: We never see a crescent Jupiter from Earth because Jupiter __________. is farther than Earth from the Sun

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.

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?

Because air resistance has a greater effect on the larger ball. 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.

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.

Both balls fall to the ground in the same amount of time. 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 D: When would you expect to see Venus high in the sky at midnight? never

For Venus to be high in the sky at midnight, it would have to be on the opposite side of our sky from the Sun. But that never occurs because Venus is closer than Earth to 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 p2=a3p2=a3. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's third law? Venus orbits the Sun faster than Earth orbits the Sun & Inner planets orbit the Sun at higher speed than outer planets.

From the relationship p2=a3p2=a3, 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.

Tycho Brahe's contribution to astronomy included: collecting data that enabled Kepler to discover the laws of planetary motion.

Kepler used Tycho's data to test how well various models could predict planetary positions.

Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler's second law: Earth travels faster in its orbit around the Sun in January than in July.

Kepler's second law states that a planet sweeps out equal areas in equal times as it goes around its orbit, which means it must move faster when it is closer to the Sun.

Part D: 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.

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 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. [falsifiable]: Kennedy died from a bullet in his brain, Kennedy was the 35th president of the United States [not falsifiable]: If he'd lived, Kennedy would have ended the Vietnam War, Kennedy's death was the will of God, the murder of John F. Kennedy was an act of evil, Kennedy's murder was orchestrated

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 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.)

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 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? the planets are all much too large compared to their orbits

On the scale used to show the orbits in the video, all the planets would be microscopic in size.

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?

Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates. 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.

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?

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 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?

The variable of interest is now size, so appropriate trials to compare are those in which size differs but other variables are constant.

Which of the following claims can be tested by scientific means? People born when the Sun appears in the constellation Leo have larger average incomes than other people.

This can be tested by comparing the incomes of people born when the Sun appears in Leo to those of all others.

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.)

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 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.

You have correctly taken into account both the masses of the asteroids and the distances between them.

Part A: 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).

[Real (true statements)]: Mercury goes through a full cycle of phases, Moon rises in east and sets in west, stars circle daily around north or south celestial pole, positions of nearby stars shift slightly back and forth each year, a distant galaxy rises in east and sets in west each day [Not real (false statements)]: a planet beyond Saturns rises in west and sets in east, we sometimes see a crescent Jupiter

Part C: As the cloud shrinks in size, its central temperature __________ as a result of its __________.

[blank 1]: increases [blank 2]: gravitational potential energy As the cloud shrinks in size, its gravitational potential energy decreases. Because energy cannot simply disappear, the "lost" gravitational potential energy must be converted into some other form. Some of it is converted into thermal energy, which raises the temperature of the gas cloud. The rest is mostly converted into radiative energy, which is released into space as light.

According to the universal law of gravitation, if you triple the distance between two objects, then the gravitational force between them __________.

decreases by a factor of 9 Gravity follows an inverse square law, so the force goes down with the square of the distance; in this case, increasing the distance by a factor of 3 causes the force to decrease by a factor of 32 = 9.

If Earth were twice as far as it actually is from the Sun, the force of gravity attracting Earth to the Sun would be

one-quarter as strong. Gravity follows an inverse square law with distance, so doubling the distance weakens gravity by a factor of 2 squared, which is 4.

Part A: In Ptolemy's Earth-centered model for the solar system, Venus's phase is never full as viewed from Earth because it always lies between Earth and the Sun. In reality, as Galileo first recognized, Venus is __________. full whenever it lies directly between Earth and the Sun

A full Venus always occurs when it is on the opposite side of the Sun as viewed from Earth. Galileo used this fact as evidence for the Sun-centered view of the solar system: The fact that Venus goes through all the phases must mean it goes all the way around the Sun. In contrast, in the Ptolemaic model, Venus only varies between new and crescent phases.

Part B: Imagine that Venus is in its full phase today. If we could see it, at what time would the full Venus be highest in the sky? at noon

Because Venus is full when it is on the opposite side of the Sun from Earth, the Sun and Venus both appear to move through the sky together at that time. Venus therefore rises with the Sun, reaches its highest point at noon, and sets with the Sun.

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.

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 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.)

Recall that the time it takes a planet to complete an orbit is called its orbital period. The pattern found in this Part illustrates one of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have longer orbital periods.

Part A: 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.

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 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.

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 A: 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.)

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 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.

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.

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.

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 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. [falsifiable]: the chemical contents 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 [not falsifiable]: we are all playthings in a computer program created by advanced aliens, the laws of nature are magnificent and beautiful, the universe was created by God

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.

Part A: The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward _________________ because _________________.

[blank 1]: gradually becomes stronger [blank 2]: the strength of gravity follows an inverse law with distance The force of gravity between any two particles increases as the particles come closer together. Therefore, as the cloud shrinks and particles move closer together, the force of gravity strengthens. This will tend to accelerate the collapse as long as no other force resists it. This is the case during the early stages of the collapse before the internal gas pressure builds up. (Once the gas pressure builds up, the outward push of the pressure can counteract the inward pull of gravity, which is why the cloud eventually stops contracting.)

Part B: As the cloud shrinks in size, its rate of rotation ____________ because _______________.

[blank 1]: speeds up [blank 2]: its total angular momentum is conserved The law of conservation of angular momentum states that, in the absence of external influences (torques), the angular momentum of an object or a system of objects stays constant. Since the angular momentum of an object depends on both its size and rate of rotation, the cloud's rate of rotation will increase as its size (or radius) decreases in order to conserve angular momentum.

Which of the following is not true about a scientific theory?

a theory is essentially an educated guess. An educated guess is a hypothesis; a scientific theory must be backed by a great deal of evidence.