MA HW 2 : The Copernican Revolution
12 Part B: Select the correct explanation of why the geocentric model was accepted for so long. Check all that apply.
-There was no sensation of motion as the Earth moved through space. -There was parallax as the Earth moved around the Sun, but it was not measurable until the mid- 1800s.
15 Part A: What is a scientific theory?
A theory is a framework of ideas and assumptions that represents our best possible explanation for something.
2 Part A: The major axis for a particular planet is known. In order to determine the perihelion and the aphelion, what other information about the planet is needed?
The eccentricity of the orbit.
8 Part D: If you are standing on a scale in an elevator, what exactly does the scale measure?
The force you exert on the scale.
9 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 __________.
the Moon has a larger acceleration than Earth, because it has a smaller mass
25 Part 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.
v = 1700 m/s
25 Part B: What is the escape speed from the Moon? Express your answer using two significant figures.
v = 2400 m/s
2 Part B: The major axis for a new comet has been determined to be 100 AUAU. The eccentricity of the orbit was measured to be 0.94. What is the distance of closest approach to the Sun for this comet?
3 AU
3 Part B: 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.
9 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.
Largest Acceleration to Smallest Acceleration: -asteroid to Sun -asteroid to Earth -asteroid to Moon -asteroid to asteroid -asteroid to hydrogen atom
12 Part A: Briefly describe the geocentric model of the universe. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer.
The geocentric model of Aristotle had the SUN, Moon, planets, and stars orbiting a stationary EARTH. A modifiction of Ptolemy had most of the planets moving in small circles called EPICYCLES. The center of these EPICYCLES moved around the EARTH in larger circles called DEFERENTS. Over the centuries, however, other astronomers further altered the model, and dozens of circles were needed to fully describe the motions of the 7 visible "planets."
15 Part B: Can a theory ever be proved to be absolutely true?
Theory can never be proven to be absolutely true.
4 Part C: When would a new Venus be highest in the sky?
at noon
8 Part B: 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.
14 Part A: As shown in Figure 2.12 in the textbook ("Venus Phases"), Galileo's observations of Venus demonstrated that Venus must be
orbiting the Sun. also: see image
11 Part A: Planets near opposition
rise in the east.
21 Part A: What is the maximum possible parallax of Mercury during a solar transit, as seen from either end of a 4000 kmkm baseline on Earth? Express your answer using two significant figures.
11 arc seconds
23 Part C: What is the gravitational acceleration at the altitude of 20000 kmkm ? Express your answer using two significant figures.
a = 0.58 m/s^2
5 Part A: 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's 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 unites (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 is ECCENTRICITY.
3 Part C: 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. -Transit of an extrasolar planet.
1 Part C: 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.
-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.
3 Part A: 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.
-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.
1 Part A: 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: -Epicycles and deferents help explain planetary motion. -Planets move in circular orbits and uniform motion. -The brightness of a planet increases when the planet it closest to Earth.
1 Part B: 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.
7 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.)
Longest: -One Earth Mass 2AU -Three Earth Masses 2AU Middle: -One Earth Mass 1AU -Two Earth Masses 1AU Shortest: none also: see image
9 Part A: The following five diagrams show pairs of astronomical objects that are all separated by the same distance ddd. 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.
Strongest force to Weakest force: -asteroid to Sun -asteroid to Earth -asteroid to Moon -asteroid to asteroid -asteroid to hydrogen atom
9 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.
Strongest force to Weakest force: -asteroid to Sun -asteroid to Earth -asteroid to Moon -asteroid to asteroid -asteroid to hydrogen atom
10 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.
Strongest force to Weakest force: (top, left bottom, right bottom) -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=2 also: see image
8 Part C: 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.
4 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.
23 Part B: What is the gravitational acceleration at the altitude of 2000 kmkm ? Express your answer using two significant figures.
a = 5.7 m/s^2
23 Part A: What is the gravitational acceleration at the altitude of 200 kmkm ? Take Earth's radius to be 6400 kmkm. Express your answer using two significant figures.
a = 9.2 m/s^2
16 Part A: An accurate sketch of Jupiter's orbit around the Sun would show
a nearly perfect circle.
6 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. Rank 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.
all in middle/see image
6 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. Rank 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.
all in middle/see image
4 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
22 Part A: 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.
13 Part A: A major flaw in Copernicus's model was that it still had
circular orbits.
19 Part A: Halley's comet has a perihelion distance of 0.6 AUAU and an orbital period of 76 years. What is the aphelion distance of Halley's comet from the Sun? Express your answer using two significant figures.
da = 35AU
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 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.
8 Part A: 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.
17 Part A: An asteroid with an orbit lying entirely inside Earth's
has an orbital semimajor axis of less than 1 AU
18 Part A: 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.
24 Part A: Figure 2.26(b) in the textbook ("Orbits") shows the orbits of two stars of unequal masses. If one star has twice the mass of the other, then the more massive star
moves more slowly than the less massive star.
4 Part D: When would you expect to see Venus high in the sky at midnight?
never
10 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. 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.
see image
10 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.
see image
6 Part B (Parts A through C all refer to the orbit of a single comet around the Sun.): 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. Rank 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.
see image
6 Part E (We'll now leave the comet behind, and instead consider the orbit of an asteroid in Parts D through F.): 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. Rank 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.
see image
6 Part F (We'll now leave the comet behind, and instead consider the orbit of an asteroid in Parts D through 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. Rank 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.
see image
7 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.)
see image
7 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.)
see image
7 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.)
see image
20 Part A: How long would a radar signal take to complete a round-trip between Earth and Mars when the two planets are 0.5 AUAU apart? Express your answer using two significant figures.
t = 500 seconds
