Ch 2 Homework

Observational proof of the heliocentric model Astronomers have made many observations since the days of Galileo and Kepler to confirm that the Sun really is at the center of the solar system, and that the planets revolve around the Sun in elliptical orbits. Which observation(s) could you make today that Galileo and Kepler could not have made to confirm that the heliocentric model is correct? Check all that apply. - Doppler shifts in stellar spectra of nearby stars - Stellar parallax in nearby stars - Orbital periods of Jupiter's moons - Transit of an extrasolar planet

- Doppler shifts in stellar spectra of nearby stars - Stellar parallax in nearby stars - Transit of an extrasolar planet Feedback: Correct When Galileo observed the changing phases of Venus, he showed that at least one planet must be orbiting the Sun. Today, astronomers are confident that all of the planets in our solar system orbit the Sun because of Earth-based observational evidence that supports a heliocentric model. Doppler shifts and stellar parallaxes show that Earth is in motion around the Sun and is thus not stationary. More recent observations of extrasolar planets show astronomers that planets in other planetary systems are orbiting stars.

The geocentric model, in all of its complexity, survived scientific scrutiny for almost 1,400 years. However, in modern astronomy, scientists seek to explain the natural and physical world we live in as simply as possible. The complexity of Ptolemy's model was an indicator that his theory was inherently flawed. Why, then, was the geocentric model the leading theory for such a long time, even though the heliocentric model more simply explained the observed motions and brightness of the planets? Check all that apply. - From Earth, all heavenly bodies appeared to circle around a stationary Earth. - The complexity of the geocentric model was appealing to most ancient astronomers. - Ancient astronomers did not observe stellar parallax, which would have provided evidence in favor of the heliocentric model. - The heliocentric model did not make noticeably better predictions than the geocentric model. - The geocentric model conformed to both the philosophical and religious doctrines of the time.

- From Earth, all heavenly bodies appeared to circle around a stationary Earth. - Ancient astronomers did not observe stellar parallax, which would have provided evidence in favor of the heliocentric model. - The heliocentric model did not make noticeably better predictions than the geocentric model. - The geocentric model conformed to both the philosophical and religious doctrines of the time. Feedback: Correct The geocentric model was the leading model for hundreds of years because it conformed to the common beliefs from observations and religious doctrine of the time. However, the heliocentric model gained widespread acceptance when astronomers obtained new evidence after the time of Copernicus. These astronomers popularized his view and helped pave the way for our current understanding of the solar system.

Galileo's observational contributions Galileo Galilei was the first scientist to perform experiments in order to test his ideas. He was also the first astronomer to systematically observe the skies with a telescope. Galileo made four key observations that challenged the widely accepted philosophical beliefs on which the geocentric model was based, thus providing support for the heliocentric model. From the following list of observations, which are the key observations made by Galileo that challenged widespread philosophical beliefs about the solar system? Check all that apply. - Jupiter has orbiting moons. - Venus is only seen in a crescent phase. - Uranus has a ring system. - Neptune has orbiting moons. - The Moon has a smooth, featureless surface. - The Sun has sunspots and rotates on its axis. - The Moon has mountains, valleys, and craters. - Venus goes through a full set of phases.

- Jupiter has orbiting moons. - The Sun has sunspots and rotates on its axis. - The Moon has mountains, valleys, and craters. - Venus goes through a full set of phases. Feedback: Correct Galileo made four key observations that went against the geocentric model and the common beliefs about the universe at the time. Observing that the Sun and Moon had surface blemishes disproved the idea that celestial objects were perfect. Galileo's observations of Jupiter's orbiting moons showed that there were other centers of motion in the universe. Galileo's most crucial observation was the observation of Venus in different phases, which directly supported the idea that objects orbit the Sun rather than Earth.

Kepler's contributions Johannes Kepler used decades of Tycho Brahe's observational data to formulate an accurate description of planetary motion. Kepler spent almost 30 years of his life trying to develop a simple description of planetary motion based on a heliocentric model that fit Tycho's data. What conclusion did Kepler eventually come to that revolutionized the heliocentric model of the solar system?

- Kepler determined that the planetary orbits are elliptical. Feedback: Correct One of the most crucial conclusions that Kepler reached using Tycho's data was that the planets do not move in circular orbits, but rather in elliptical orbits. Kepler also concluded that the planets do not move with uniform motion. Applying these ideas to the Copernican model, the revised heliocentric model could then accurately predict planetary positions over long periods of time.

The Moon's mass is 7.4×10^22 kg and its radius is 1700 km. A: What is the speed of a spacecraft moving in a circular orbit just above the lunar surface? Express your answer using two significant figures. B: What is the escape speed from the Moon? Express your answer using two significant figures.

A: v = 1700 m/s B: v = 2400 m/s

On which of these assumptions do Ptolemy and Copernicus agree?

All orbits must be perfect circles.

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.

Fastest - Same as Above Slowest Feedback: 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.

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.)

Fastest -Arrange from smallest distance to largest, smaller orbits are faster Slowest Feedback: 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.

Two competing models attempt to explain the motions and changing brightness of the planets: Ptolemy's geocentric model and Copernicus' heliocentric model. Sort the characteristics according to whether they are part of the geocentric model, the heliocentric model, or both solar system models. Drag the appropriate items to their respective bins.

Geocentric - This model is Earth-centered. - Retrograde motion is explained by epicycles. Heliocentric - This model is Sun-centered. - Retrograde motion is explained by the orbital speeds of planets. Both geocentric and heliocentric - The brightness of a planet increases when the planet is closest to Earth. - Planets move in circular orbits and with uniform motion. - Epicycles and deferents help explain planetary motion. Feedback: Correct Ptolemy's geocentric model was based on the idea that Earth is the center of the universe, while Copernicus's heliocentric model was developed around the idea that the Sun is at the center. While these two models were based on opposing ideas, they shared a common belief in uniform circular motion and the use of epicycles. However, Copernicus's heliocentric model does not use epicycles to explain retrograde motion like Ptolemy's geocentric model. In order to explain retrograde motion, Copernicus uses the different orbital speeds of the planets as an explanation to the seemingly backward motion of the planets in the sky.

Copernicus's heliocentric model and Ptolemy's geocentric model were each developed to provide a description of the solar system. Both models had advantages that made each an acceptable explanation for motions in the solar system during their time. Sort each statement according to whether it is an advantage of the heliocentric model, the geocentric model, or both. Drag the appropriate items to their respective bins.

Heliocentric - Explained planetary motions and brightness changes most simply Geocentric - Rooted in widely accepted religious beliefs regarding Earth's place in the universe Both geocentric and heliocentric - Predicted planetary positions accurately over relatively short time periods - Planetary orbits and motions based on Greek ideologies of perfect form and motion Feedback: Correct The geocentric model was compelling because it adhered to religious beliefs about Earth's centrality in the universe. The heliocentric model was compelling because it provided a simpler explanation for observed motions in the solar system. Because both models adhered to the belief in perfect form and motion, they made inaccurate predictions of planetary motions over long periods of time. Since neither model made better predictions than the other, both remained viable.

Which of the following is NOT true about the solar system model of Copernicus? It used an earlier Greek idea that placed the Sun at the center of the solar system. Its central organizing principle and primary attraction to Copernicus were that it was simpler to comprehend than the Ptolemaic model. It was not widely accepted and was not even published until the year that he died. It could explain apparent retrograde motion by showing that fast-moving inner planets "passed" slower outer planets as they went around the Sun. It used elliptical orbits for the motions of the planets.

It used elliptical orbits for the motions of the planets. Feedback: Correct Correct, this is false. Although Copernicus placed the Sun at the center of the solar system with the planets orbiting it instead of Earth, he assumed that planets moved in perfect circular orbits. He retained the ideas of epicycles and deferents to allow for small adjustments to the rates at which the planets orbited the Sun. These ideas were abandoned only after Kepler introduced the idea of elliptical orbits much later.

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.

Largest - All the Same Smallest Feedback: 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.

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.

Longest - 1 & 2 both West of Sun - 1 & 2 both South of Sun - 1 & 2 both Northeast of Sun - 1 & 2 both East of Sun Shortest Feedback: 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.

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.

Longest - 1 & 2 both West of Sun - 1 & 2 both South of Sun - 1 & 2 both Northeast of Sun - 1 & 2 both East of Sun Shortest Feedback: 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.

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.)

Longest - 1 Earth Mass 2 AU & 3 Earth Masses 2 AU are SAME - 1 Earth Mass 1 AU & 2 Earth Masses 1 AU are SAME Shortest Feedback: 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 whenver the planet's mass is small compared to the mass of the star.

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.

Longest - All the Same! Shortest Feedback: 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.

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.

Longest - Asteroid south of Sun - Asteroid east of Sun - Asteroid west of Sun - Asteroid north of Sun Shortest Feedback: 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.

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.) HelpReset

Longest -Rank from largest circle/ellipse to smallest Shortest Feedback: 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.

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.)

Longest -Same as above Shortest Feedback: 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.

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.

Strongest Force - Arrange so that spaceship closest to the Moon is the strongest and it gets weaker the closer it is to the Earth Weakest Force Feedback: 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.

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. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). 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.

Strongest Force - Arrange so that spaceship moves closer to the Moon and therefore farther than Earth Weakest Force Feedback: 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.

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.

Strongest Force - d = 1, M = 2, M = 2 - d = 1, M = 1, M = 2 - d = 1, M = 1, M = 1 - d = 2, M = 1, M = 2 - d = 2, M = 1, M = 1 Weakest Force Feedback: Correct You have correctly taken into account both the masses of the asteroids and the distances between them.

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed. Feedback: Correct When the elevator is moving downward, a downward acceleration would mean an increasing downward speed. Therefore, as your answer correctly states, an upward acceleration would mean a decreasing downward speed.

Upon which point do Copernicus and Kepler disagree?

The orbits of the planets are ellipses, with one focus at the Sun.

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. Feedback: Correct In the Ptolemaic system, we should never see more than a crescent in 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.

An accurate sketch of Jupiter's orbit around the Sun would show

a nearly perfect circle.

When would a new Venus be highest in the sky?

at noon Feedback: Correct 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).

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 Feedback: Correct 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.

Figure 2.21 in the textbook ("Gravity"), showing the motion of a ball near Earth's surface, depicts how gravity

causes the ball to accelerate downward.

A major flaw in Copernicus's model was that it still had

circular orbits.

If the Sun and its mass were suddenly to disappear, Earth would

fly off into space.

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 is on the opposite side of the Sun from Earth, although we cannot see the full Venus because it is close to the Sun in the sky Feedback: Correct A full Venus always occurs when it is on the opposite side of the Sun as viewed from Earth. (However, we cannot see the full Venus, because it is always very close to the Sun in the sky at that time.) 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.

Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.

greater than your normal weight at rest Feedback: Correct Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.

less than your normal weight at rest Feedback: Correct Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward; the situation is rather like that of a ball that is still on its way up after you throw it, even though it is being pulled downward with the acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.

If Earth's orbit around the Sun were twice as large as it is now, the orbit would take

more than two times longer to traverse.

When would you expect to see Venus high in the sky at midnight?

never Feedback: Correct 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.

As shown in Figure 2.12 in the textbook ("Venus Phases"), Galileo's observations of Venus demonstrated that Venus must be

orbiting the Sun.

The place in a planet's orbit that is closest to the Sun is called:

perihelion.

Planets near opposition

rise in the east.

How long would a radar signal take to complete a round-trip between Earth and Mars when the two planets are 1.2 AU apart? Express your answer using two significant figures.

t = 1200 seconds

If you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale Feedback: Correct You probably recognize that neither your mass nor the gravitational force exerted on you change when you are in an elevator. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to your normal weight and a force due to the elevator's acceleration.