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Full text of "Test Booklet 2 - Motion in the Heavens: Project Physics"

The Project Physics Course 



Tests 



2 



Motion in the Heavens 



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in 2010 with funding from 

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http://www.archive.org/details/testbool<let2moti00fjam 



The Project Physics Course 



Tests 



UNIT 



2 



Motion in the Heavens 



A Component of the 
Project Physics Course 




Distributed by 

Holt, Rinehart and Winston, Inc. 

New York-Toronto 



This publication is one of the many instructional materials 
developed for the Project Physics Course. These materials 
include Texts, Handbooks, Teacher Resource Books, 
Readers, Programmed Instruction Booklets, Film Loops, 
Transparencies, 16mm films and laboratory equipment. 
Development of the course has profited from the help of 
many colleagues listed in the text units. 



Directors of Harvard Project Physics 

Gerald Holton, Department of Physics, Harvard 

University 
F. James Rutherford, Chairman of the Department 

of Science Education, New York University, New York 
Fletcher G. Watson, Harvard Graduate School of 

Education 



Picture Credit 

Cover photo: (The "whirlpool" galaxy in Canes Venatici) 

Courtesy of Mt. Wilson and Mt. Palomar Observatories. 



Copyright © 1970, Project Physics 

All Rights Reserved 

ISBN 0-03-084816-4 

4567 039 9876543 

Project Physics is a registered trademark 



TESTA 



Directions 

This test consists of fifteen multiple-choice questions and seven problem-and-essay questions, di- 
vided into two groups. Answer ALL multiple-choice questions by marking the letter corresponding 
to the one best answer. Answer THREE of the problem-and-essay questions from Group One and 
ONE from Group Two. Spend about 15 minutes on the multiple-choice questions, 5 minutes on each 
of the problem-and-essay questions from Group One and 10 minutes on the problem-and-essay ques- 
tion from Group Two. 

The numerical values of some physicjil constants and equations that may be useful in the test are 
given on the last page of this booklet. 



MULTIPLE-CHOICE QUESTIONS 

1. To ancient observers, the principal difference between the planets and the stars was that the 
planets appeared 

A. brighter. 

B. more like the earth. 

C. to wander among the other stars, 

D. closer to the earth. 

E. to travel around the sun. 

2. Which of the following statements must be part of any heliocentric theory? 

A. The planets revolve around the sun, 

B. The sun is a sphere. 

C. The earth is a sphere. 

D. The planets revolve around the earth, 

E. The earth turns on its axis. 



If Fj is the magnitude of the force exerted on 
the sun by the earth and F2 is the magnitude 
of the force exerted on the earth by the sun, 
then 

A. Fj is much greater than F2 . 

B. Fi is slightly greater than Fj . 

C. Fj is equal to F2. 

D. Fj is slightly less than Fj . 

E. F, is much less than Fj • 




Zlo 



4. Which one of the following men is famous for the decision to abandon Plato's association of 
heavenly bodies with "uniform motion in perfect circles"? 

A. Aristotle 

B. Copernicus 

C. Kepler 

D. Galileo 

E. Tycho Brahe 

5. Galileo gathered a great deal of evidence which was at odds with the medieval view of the uni- 
verse. ALL EXCEPT ONE of the following are examples of this evidence. Which is the excep- 
tion ? 

A. the discovery of a new star in 1604 

B. the rough appearance of the moon's surface 

C. the motion of four luminous objects around Jupiter 

D. the moon-like phases of planet Venus 

E. the wanderings of the planets among the stars 

6. Two sacks of marbles are hung one meter apart. Which of the following would approximately 
double the gravitational force that one sack of marbles exerts on the other sack? 

A. Double the number of marbles in one sack. 

B. Double the number of marbles in both sacks. 

C. Move them closer, to one-half the separation. 

D. Move them further apart, to twice the separation. 

E. Move them further apart, to four times the separation. 

7. ALL EXCEPT ONE of the following statements are acceptable. Which is the exception ? 

A. The earth is moving fastest when closest to the sun. 

B. The path of the earth lies in a plane which passes through the sun. 

C. A line drawn from the sun to the earth sweeps over the same area from March 21 to March 
23 as it does from December 21 to December 23. 

D. The sun is at the exact center of the earth's path. 

8. Assume that the earth suddenly shrank to one-half its original diameter, but that its mass re- 
mained unchanged. Under these circumstances, the weight of a person standing on its surface 
would be 



A. four times as great. 

B. twice as great. 

C. the same. 

D. one-half as great. 

E. one-fourth as great. 



9. A friend tells you the earth is fixed in space and that the sun revolves about it. Which one of 
the following facts contradicts his hypothesis? 

A. Each day the sun rises in the east and sets in the west. 

B. During the night the stars appear to move. 

C. The sun makes one complete trip among the stars in one year. 

D. Eclipses of the sun sometimes occur. 

E. none of the above 

10. Which one of the following was an important factor that worked against the acceptance of 
Copernicus' heliocentric solar system hypothesis in the sixteenth century? 

A. When Venus was observed through a telescope, phases were seen. 

B. Stellar parallax had never been observed. 

C. The calendar failed to keep pace with the seasons. 

D. Galileo observed four satellites moving around Jupiter. 

E. Venus had never been observed more than 48° from the sun. 

11. ALL EXCEPT ONE of the following were among Tycho Brahe's contributions to astronomy. 
Which one is the exception? 

A. He established an astronomical observatory. 

B. He proposed an inverse square law of attraction for the solar system. 

C. He developed a theory of the solar system. 

D. He determined the limits of accuracy of his instruments. 

E. He made very accurate observations of the positions of the heavenly bodies. 

12. Assume that the following measurements were made on three planets revolving about a star. 
(Planets listed in order of discovery) 

Planet Orbital Period Mass 



Alpha 14 earth years 10 earth masses 

Beta 188 earth years 17 earth masses 

Gamma 50 earth years 1/2 earth mass 

On the basis of Kepler's laws of planetary motion, these planets could be arranged in order of their 
increasing distance from the star. If the planets were listed in sequence, starting with the planet near- 
est the star, they would be arranged 

A. Alpha, Beta, Gamma. 

B. Beta, Gamma, Alpha. 

C. Gamma, Alpha, Beta. 

D. Beta, Alpha, Gamma. 

E. Alpha, Gamma, Beta. 



13. The following men made significant contributions to our present understanding of planetary 
motion: 

1. Copernicus 

2. Newton 

3. Kepler 

If the names of these men were arranged in the order of their contributions starting with the earliest 
first, they would be 

A. 1, 2, 3 

B. 2, 3, 1 

C. 3, 1, 2 

D. 1,3,2 

E. 2, 1, 3 

14. Time-exposure photographs of stars show arcs of circles. An astronomer who believed the Ptole- 
maic theory of planetary motion would explain that these arcs result from 

A. the rotation of the earth on its axis. 

B. stellar parallax. 

C. retrograde motion. 

D. the inclination of the earth's axis. 

E. the rotation of the starry sphere. 

15. Which one of the following is evidence that supports the universality of Newton's law of gravita- 
tion? 

A. Pairs of stars have been observed that move around each other in accordance with Kepler's 
laws. 

B. A few stars have moved from the positions given for them in Ptolemy's catalogue of stars. 

C. Stellar parallax has been observed for several thousand stars. 

D. A calendar reform was needed in the sixteenth century to keep months and seasons in 
agreement. 



PROBLEM-AND-ESSAY QUESTIONS 
Group One 

Answer THREE of the following five questions, 

1. Indicate briefly the major contributions to astronomy of 

a) Ptolemy 

b) Copernicus 



2. With the aid of a diagram, briefly describe the experiment used by H. Cavendish to determine 
the value of G, the constant of universal gravitation in the equation 



Fgrav - G 



m J m2 



3, The orbit of Mercury about the sun has a radius about 1/3 that of the orbit of the earth about 
the sun, while the period of Mercury is about 3 months. With the aid of a diagram of a helio- 
centric (sun-centered) system explain the retrograde motion of Mercury as seen from the earth. 



According to the theory of relativity, nature may be validly observed and described from all 
frames of reference. Why then have astronomers, in describing the motions of planets, pre- 
ferred a heliocentric rather than a geocentric frame of reference? 



5. Describe the daily and annual motion of the sun from a geocentric point of view. 

Group Two 
Answer ONE of the following two questions. 

6. According to Newton, the moon is continually falling toward the earth. In what sense is the 
word "falling" used here? Explain your answer by linking the motion of the moon with the 
motion of a freely falling object near the surface of the earth. 



7. Given Newton's assumption for the gravitational force due to the sun on a planet: F «: l/R^ ^ 
and given that the distance of fall of a planet is determined by d = Vi at^ , derive Kepler's third 
law in the form 



(Tp)^ (Rp)- 



TEST B 



Directions 

This test consists of fifteen multiple-choice questions and seven problem-and-essay questions di- 
vided into two groups. Answer ALL multiple-choice questions by marking the letter corresponding 
to the one best answer. Answer THREE of the problem-and-essay questions from Group One and 
ONE from Group Two. Spend about 15 minutes on the multiple-choice questions, 5 minutes on 
each of the problem-and-essay questions from Group One, and 10 minutes on the problem-and-essay 
question from Group Two. 

The numerical values of some physical constants and equations that may be useful in this test are 
given on the last page of this booklet. 



MULTIPLE-CHOICE QUESTIONS 



1. In its orbit, the earth travels 

A. fastest when it is nearest the sun. 

B. fastest at night. 

C. fastest around the time of the new moon, 

D. with constant speed. 

E. zero speed, since the earth is stationary. 



Select answers to questions 2 and 3 from the following list. 

A. Ptolemy 

B. Kepler 

C. Copernicus 

D. Tycho Brahe 

E. Galileo 



2. He tried to relate planetary distances to the five regular geometric solids. 



3. He developed a model of the solar system in which the planets revolved around the sun but the 
earth remained motionless. 



4. ALL EXCEPT ONE of the following are characteristics of geocentric models of the solar sys- 
tem. Which one is the exception? 

A. The earth is at or near the center of the solar system. 

B. The stars are at the greatest distance from the earth. 

C. The sun moves daily around the earth. 

D. The moon's motion is tied to the motion of the sun. 

E. The stars move daily around the earth. 

5. Kepler's three lavsrs of planetary motion were 

A. almost self-evident from Tycho Brahe's data of Mars' orbit. 

B. little used in Newton's development of a general law of universal gravitation. 

C. developed only after Kepler took imaginative steps from the available data. 

D. widely discussed early in the seventeenth century. 

E. used by Copernicus in deriving his heliocentric hypothesis. 

6. Tycho Brahe's most important contribution to science was 

A. the accurate observation of the positions of the stars and planets. 

B. the discovery of a new star that changed its brightness. 

C. the discovery of elliptical orbits. 

D. his theory of planetary motions. 

7. Galileo accumulated a great deal of evidence which was inconsistent with the medieval view of 
the universe. ALL EXCEPT ONE of the following are examples of this evidence. Which is the 
exception? 

A. the discovery of a new star in 1604 

B. the rough appearance of the moon's surface 

C. the motion of four luminous objects around Jupiter 

D. the moon-like phases of planet Venus 

E. the wanderings of the planets among the stars 

8. A satellite with a television camera is placed in an orbit 24,000 miles above the earth so that it 
remains exactly above the same point on earth at all times, with its camera pointed toward the 
earth. As seen from the sun the orbit of the satellite is 

A. an ellipse with the sun at one focus. 

B. an epicycle with its center on the orbit of the sun. 

C. an epicycle with its center on the orbit of the earth. 

D. a circle with the sun at the center. 

E. a parabola constantly accelerated toward the earth. 



9. Assume the earth suddenly became one-half its original diameter, but that its mass was un- 
changed. Under this assumption, the strength of the earth's gravitational pull on the moon 
would be 

A. four times as great. 

B. twice as great. 

C. the same. 

D. one-half as great. 

E. one- fourth as great. 



10. What is the acceleration due to gravity of a meteor at 2 earth radii from the center of the earth? 
Assume the acceleration due to gravity at one earth radius from the center of the earth to be 
^ ^ meters 



lU 


second^ ' 


A. 


2.5 m/sec^ 


B. 


5 m/sec^ 


C. 


7.07 m/sec^ 


D. 


10 m/sec^ 


E. 


20 m/sec^ 



11. Which one of the following is evidence that supports the universality of Newton's law of gravi- 
tation? 

A. A few stars have moved from the positions given for them in Ptolemy's catalogue of stars. 

B. Stellar parallax has been observed for several thousand stars. 

C. Eclipses of the sun do not occur at every new moon. 

D. A calendar reform was needed in the sixteenth century to keep months and seasons in 
agreement. 

E. Pairs of stars have been observed that move around each other in accordance with Kepler's 
laws. 



12. If a theory predicts a result which is contrary to common sense, we should 

A. reject the theory since we must rely on common sense. 

B. devise an experiment to test the predicted result. 

C. disregard common sense because it is of no value in a scientific study. 

D. revise the theory to produce a compromise between the theory and common sense. 




'2 



13. If Fj is the magnitude of the force exerted 
on the sun by the earth and Fj is the magni- 
tude of the force exerted on the earth by 
the sun, then 

A. Fi is much greater than F2 . 

B. Fi is slightly greater than F2 . / \ Fi Fi 

C. Fi is equal to F2 . ( ) — ^ -•-O 

D. Fi is slightly less than F2 . 

E. Fi is much less than F2 . 

14. In describing the motion of a thrown rock, Newtonian physics introduced a premise which was 
not part of Aristotelian physics. Which of the following is the Newtonian premise? 

A. A force is needed to change the state of the rock from rest to motion. 

B. The rock has no properties that affect its motion. 

C. The undisturbed motion of the rock is uniform motion along a straight line. 

D. The natural state of the rock is rest. 

15. Galileo's discovery of Jupiter's moons provided supporting evidence for 

A. Aristotle's solution to Plato's problem. 

B. the Copernican theory of planetary motion. 

C. the existence of epicycles. 

D. the geocentric hypothesis of Ptolemy. 

E. the accuracy of Tycho Brahe's observations. 



PROBLEM-AND-ESSAY QUESTIONS 
Group One 

Answer THREE of the following five questions. Allow about 5 minutes for each. 

1 . Describe the annual motion of the sun against the background of the stars as observed from the 
earth. 

2. Describe the role played by stellar parallax in the arguments for and against a heliocentric theory 
of the universe. 

3. Describe the relationship between Newton's law of gravitation Fgrav = G — 5^2 — and Galileo's 
observation that the gravitational acceleration at the surface of the earth is the same for all fall- 
ing bodies. 



4. The scientific theories of Galileo and Copernicus were severely critized by some of their con- 
temporaries. Were they criticized on scientific grounds? Explain your answer. 

5. If two planets A and B have the same mass but the radiiis of A is twice that of B, 

a) which planet has the greater gravitational pull at its surface? 

b) what is the ratio of the surface gravitational pulls of the two planets? 



Group Two 
Answer ONE of the two questions in this group. Allow about 10 minutes. 



6. The text indicates that Galileo, Kepler and Newton each made contributions that helped change 
man's scientific outlook from an Aristotelian to a modem point of view. Pick two of these men 
and describe briefly their contributions in producing this changed outlook. 



7. Two criteria for an adequate theory are: 

1. that it be based upon simple assumptions. 

2. that it be in agreement with experimental observations. 

Consider the sun-centered system of planetary motion published by Copernicus in 1543. 

a) Did it satisfy these criteria? 

b) Did it satisfy them better than the older Ptolemaic (earth -centered) system? Explain your 
answer. 



10 



TEST C 



Directions 

Answer ALL 40 multiple-choice questions by marking the letter corresponding to the one best 
answer. 

The numerical values of some physical constants and equations that may be useful in this test are 
given on the inside of the back cover. 

1 . Which of the following statements must be part of any heliocentric theory? 

A. The planets revolve around the sun. 

B. The sun is a sphere. 

C. The earth is a sphere. 

D. The planets revolve aroimd the earth. 

E. The earth turns on its axis. 

2. Time exposure photographs of stars show an arc of a circle for each star. An astronomer who 
believed the Ptolemaic theory of planetary motion would explain that these arcs result from 

A. the rotation of the earth on its axis, 

B. stellar parallax. 

C. retrograde motion. 

D. the inclination of the earth's axis. 

E. the rotation of the starry sphere. 

3. Which of the following was an important factor that worked against the acceptance of Coper- 
nicus' hehocentric solar system hypothesis in the sixteenth century? 

A. When Venus was observed through a telescope, phases were seen. 

B. The calendar failed to keep pace with the seasons. 

C. Galileo observed four satellites moving around Jupiter. 

D. Venus had never been observed more than 48° from the sun. 

E. Stellar parallax had never been observed. 

4. Galileo's discovery of Jupiter's moons provided supporting evidence for 

A. Aristotle's solution to Plato's problem. 

B. the Copemican theory of planetary motion. 

C. the existence of epicycles. 

D. the geocentric hypothesis of Ptolemy. 

E. the accuracy of Tycho Brahe's observations. 



11 



5. To ancient astronomers, planets were different from stars because planets 

A. moved in circles. 

B. were unlike the earth in composition. 

C. moved against the background of stars. 

D. moved around the sun. 

E. were within the sphere of the sun. 

6. Which of the following led to a numerical value of the constant G in the equation 

' grav ^ j^2 

A. calculations of the moon's orbit by Tycho Brahe 

B. a laboratory experiment by Cavendish 

C. observations of Jupiter's moons by Galileo 

D. an experiment with balls rolling down an incline by Galileo 

E. calculations of the orbit of Mars by Kepler 

7. ALL EXCEPT ONE of the following are objections which were raised against the heUocentric 
model of the solar system. Which one is the exception? 

A. It failed to fit the observations. 

B. It displaced man from his unique position in the center of the imiverse. 

C. It was contrary to common sense which demonstrates that the earth is motionless. 

D. It failed to distinguish between base terrestrial matter and heavenly matter. 

E. It conflicted with Aristotelian physics. 

8. ALL EXCEPT ONE of the following were among Tycho Brahe 's contributions to astronomy. 
Which one is the exception? 

A. He established an astronomical observatory. 

B. He proposed an inverse square law of attraction for the solar system. 

C. He developed a theory of the solar system. 

D. He determined the limits of accuracy of his instruments. 

E. He made very accurate observations of the positions of the heavenly bodies. 

9. Which of the following correctly places the earth, Jupiter, Mars, the moon and sim in order of 
increasing mass? 

A. moon, earth. Mars, sun, Jupiter 

B. moon. Mars, earth, Jupiter, sun 

C. Mars, earth, moon, Jupiter, sun 

D. moon, Jupiter, Mars, earth, sun 

E. moon, earth, Jupiter, Mars, sun 



12 



10. Explorer 7 is a U.S. satellite in an elliptical orbit in which its distance from the center of the 
earth varies between 4150 and 5500 miles. Compared to the speed at a distance of 5500 mUes, 
its speed at a distance of 4150 miles is 

A. greater, in the ratio 4150 to 1. 

B. greater, in the ratio 5500 to 4150. 

C. the same. 

D. smaller, in the ratio 4150 to 5500. 

E. smaller, in the ratio 1 to 5500. 

11. ALL EXCEPT ONE of the following were arguments used by followers of Copernicus to defend 
his heliocentric theory. Which one is the exception? 

A. A rotating earth is no more likely to break up than a much larger rotating celestial sphere. 

B. Lenses change what one sees and, therefore, telescopic evidence may be distorted. 

C. It is a simpler, more harmonious system and, therefore, more pleasing to the divine archi- 
tect. 

D. Friction drags the atmosphere along with the rotating earth; therefore clouds and birds are 
not left behind. 

E. The stars are at too great a distance to show a parallax. 

Select answers to questions 12 and 13 from the following list. 

A. Ptolemy 

B. Galileo 

C. Kepler 

D. Tycho Brahe 

E. Newton 

12. He demonstrated that the observed planetary motions were consistent with general principles 
that described all motion everywhere in the universe. 

13. His major contributions to astronomy were his accurate measurements. 

14. Opponents of Copernicus gave many arguments in support of the Ptolemaic system. ALL EX- 
CEPT ONE of the following support the Ptolemaic system. Which one is the exception? 

A. It predicted positions of the bodies of the solar system with fair accuracy. 

B. It explained why the fixed stars showed no stellar parallax. 

C. It was in accordance with the ideas of "natural motion" and "natural place." 

D. It was based on what they sensed: that the earth is motionless and the sim, planets and 
stars are moving. 

E. It explained how comets' orbits could come close to the sun. 



13 



15. ALL EXCEPT ONE of the following statements are true. Which is the exception? 

A. The earth moves fastest when it is nearest to the sun. 

B. The earth's orbit lies in a plane which passes through the sun. 

C. A line drawn from the sun to the earth sweeps over the same area from March 21 to 
March 23 as it does from December 21 to December 23. 

D. The sun is at the exact center of the earth's orbit. 

E. The earth's orbit around the sun is an ellipse. 



16. ALL EXCEPT ONE of the following are correct statements about a satellite in an elliptical 
orbit around the earth. Which is the exception? 

A. One focus of its elliptical orbit is at the center of the earth. 

B. Its orbit lies on a plane which passes through the center of the earth. 

C. A line drawn from the center of the earth to the satellite sweeps over equal areas in equal 
time intervals. 

D. The satellite moves fastest when it is closest to the earth. 

E. There is no net force acting on the satellite. 



17. Which one of the following is evidence that supports the universality of Newton's law of gravi- 
tation? 

A. Pairs of stars have been observed that move around each other in accordance with Kepler's 
laws. 

B. A few stars have moved from the positions given for them in Ptolemy's catalogue of stars. 

C. Stellar parallax has been observed for several thousand stars. 

D. Eclipses of the sun do not occur at every new moon. 

E. A calendar reform was needed in the sixteenth century to keep months and seasons in 
agreement. 



18. If the planets were to be listed in order of increasing mean distance from the sun (i.e., Mercury, 
Venus. . .Pluto), that order would necessarily be the same as listing the planets in order of 
increasing 

A. period of revolution around the sun. 

B. period of rotation around their axes. 

C. eccentricity of orbit around the sun. 

D. size of the planet. 

E. brightness of the planet in the sky. 



14 



19. Kepler's three laws of planetary motion were 

A. almost self-evident from Tycho Brahe's data of Mars' orbit. 

B. little used in Newton's development of a general law of universal gravitation. 

C. developed only after Kepler took imaginative steps from the available data. 

D. widely discussed early in the sixteenth century. 

E. used by Copernicus in deriving his heliocentric hypothesis. 



20. Heliocentric models of the solar system explain retrograde motion of planets by means of 

A. the differences between the rates of motion of the earth and the planets along their orbits. 

B. the daily rotation of the earth. 

C. combination of the sun's motion northward on the ecliptic and the planets' revolution 
around the sun. 

D. changes in the speed of planets as their distance from the sun changes. 

E. corrections to the inaccurate measurements of the ancient astronomers. 

21 . The following men made significant contributions to our present understanding of planetary 
motion : 

1 . Copernicus 

2. Newton 

3. Kepler 

If the names of these men were arranged in the order of their contributions starting with the 
earliest first, they would be 



A. 


1,2,3. 


B. 


2,3,1. 


C. 


3,1,2. 


D. 


1,3,2. 


E. 


2,1,3. 



22. What is the acceleration due to gravity of a meteor at two earth radii from the center of the 
earth? Assume the acceleration due to gravity at one earth radius from the center of the earth 
is 10 meters /second^. 



A. 


2.5 m/sec^ 


B. 


5 m/sec^ 


C. 


7.07 m/sec^ 


D. 


10 m/sec^ 


E. 


20 m/sec^ 



15 



23. Which of the following can be explained by a model of the solar system in which the sun re- 
volves around the earth? 

1. Each day the sun rises in the east and sets in the west. 

2. During the night the stars appear to move about the North Celestial Pole. 

3. Eclipses of the sun sometimes occur. 

A. 1 and 2 only 

B. 2 and 3 only 

C. 1 and 3 only 

D. 1,2 and 3 

E. none of the above 



24. A simple geocentric model with uniform motion about the center of circular orbits explains 
only one of the following observations. Which one is it? 

A. The sun moves slower in the summer th£in in the winter. 

B. The moon shows phases with a period of one month. 

C. The planets vary in speed at different points in their orbits. 

D. The size and duration of Mars' retrograde motion is not the same at successive occurrences. 

E. The planets move with different speeds against the stars at different points of their 
orbits. 



25. Two sacks, each containing 10 oranges of equal mass, are hung four meters apart. Which 
one of the following would double the gravitational force that one sack of oranges exerts on 
the other sack? 

A. adding 20 oranges of the same mass, 10 to each sack 

B. adding 10 oranges of the same mass, 5 to each sack 

C. adding 10 oranges of the same mass, to one sack only 

D. moving 5 oranges from one sack to another 

E. moving 10 oranges from one sack to another 



26. Two baseballs are supported at a distance of four meters from each other. If they were 
moved, at what distance would the gravitational force between them be approximately one- 
fourth its previous value? 

A. 1 meter 

B. 2 meters 

C. 6 meters 

D. 8 meters 

E. 16 meters 



16 



27. Which one of the following posed no serious difficulties for the Platonic view of heavenly 
perfection? 

A. the new star discovered in 1572 

B. the rough appearance of the moon's surface 

C. the four satellites of Jupiter 

D. sunspots 

E. the observed motion of the stars 



28. Which ONE of the following statements was not an observation used to support the ancient 
idea that there is a fundamental difference between the substance of the heavenly bodies and 
the substance of the earth. 

A. Heavenly bodies moved along a regular path whereas earth bound objects moved in an 
irregular fashion. 

B. The heavens seemed perfect whereas the earth did not. 

C. The material of the heavenly bodies seemed eternal and unchanging whereas earthly mat- 
ter was constantly changing. 

D. Events in the heavens could not generally be predicted whereas those on earth could be. 

E. Heavenly bodies seemed to move without forces whereas a force was required to keep an 
object in motion on the earth. 



29. To Ptolemy ALL EXCEPT ONE of the following statements were part of the solution to Plato's 
problem of accounting for the motions of the planets. Which one is the exception? 

A. Planetary paths must be composed of circles or combinations of circles. 

B. Planets must move relative to the stars. 

C. The sun must stand still. 

D. The stars must move in paths composed of circles. 

E. The moon must be nearest the earth. 



30. A space probe that missed its target went into orbit around the sun at a mean distance 9 times 
as great as the earth's. On the basis of Kepler's third law, the period of the space probe is ap- 
proximately 



A. 3 years. 

B. 9 years. 

C. 27 years. 

D. 54 ye£irs. 

E. 81 years. 



17 



31. If the earth's mass were twice as great as it is, its period of revolution about the sun (assuming 
it stayed in the same orbit) would be 



A. increased by a factor of 4. 

B. increased by a factor of 2. 

C. hardly changed at all. 

D. decre£ised by a factor of 2. 

E. decreased by a factor of 4. 

32. A theory predicts a result which is contrary to common sense. We should 

A. reject the theory since we must rely on common sense. 

B. devise an experiment to test the predicted result. 

C. disregard common sense because it is of no value in a scientific study. 

D. revise the theory to produce a compromise between the theory and common sense. 

E. revise common sense to agree with the new theory. 

33. A space ship travels at a constant speed directly away from the earth. Which of the following 
graphs shows how the force of gravity exerted by the earth on the space ship changes with the 
distance from the earth? 



/ 


§ 
a 


A 


a 




a 


L. 


a 


\ 




\ 


distance 
A 


distance 
B 


distance 
C 


distance 
D 


distance 
E 



34. Scientists usually publish their findings in journals which are then distributed throughout the 
world. One reason they do not try to keep their discoveries secret is that 

A. few discoveries have any economic or military importance. 

B. scientists are not concerned with political or economic affairs. 

C. someone would soon give the secret away anyway. 

D. scientists want to let others Imow what they have done. 

35. Newton's law of universal gravitation was distinctive in the history of physics because it was 
the first 

A. explanation of the cause of gravity. 

B. demonstration that the same equations can be used to describe motion on the earth and 
in the heavens. 

C. accurate mathematical description of the planetary orbits. 

D. demonstration that Kepler's laws and Copernicus' hypotheses were alternate explanations 
of the same observations. 

E. use of algebra to describe physical phenomena. 



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36. If Fi is the magnitude of the force exerted on the 
sun by the earth and Fj is the magnitude of the 
force exerted on the earth by the sun, then 

A. Fj is much greater than Fj. 

B. Fi is shghtly greater than Fj. / \ Fj Fj 

C. Fi is equal to Fj . \ J ~^ -•— O 

D. Fj is slightly less than F2. 

E. Fj is much less than Fj. 

37. Assume that the following measurements were made on three planets revolving about a star. 
(Planets listed in order of discovery.) 

Planet Orbital Period Mass 




Alpha 14 earth years 10 earth masses 

Beta 188 earth years 17 earth masses 

Gamma 50 earth years 1/2 earth mass 

On the basis of Kepler's laws of planetary motion, these planets could be arranged in order 
of their increasing distance from the star. If the planets were listed in sequence, starting with 
the planet nearest the star, they would be arranged 

A. Alpha, Beta, Gamma. 

B. Beta, Gamma, Alpha. 

C. Gamma, Alpha, Beta. 

D. Beta, Alpha, Gamma. 

E. Alpha, Gamma, Beta. 

38. One of Newton's contributions to astronomy was his description of 

A. the algebraic equations of ellipses and other conic sections. 

B. the forces that produce the elliptical orbits of the planets. 

C. the distances to the planets. 

D. the geometry of the elliptical orbits of the planets. 

E. the theory of light. 

39. Assume the earth suddenly became one-half its original diameter, but that its mass was unchanged. 
Under this assumption, the strength of the earth's gravitational pull on the moon would be 

A. four times as great. 

B. twice as great. 

C. the same. 

D. one-half as great. 

E. one-fourth as great. 



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40. ALL EXCEPT ONE of the following state aspects of Kepler's work. Which one is the 
exceptionl 

A. He emphasized the mathematical regularities of planetary motion. 

B. He recognized the value of precise observations. 

C. He gave a mathematical description of the cause of planetary motion. 

D. He helped to perfect the theory of the solar system in which the planets move around 
the sun. 

E. He recognized that a planet's path was not a circle. 



20 



TEST D 

Directions 

This test consists of 8 questions in two groups. Answer only FOUR of the five questions in Group 
One, and only TWO of the three questions in Group Two. Spend about 5 minutes on each of the 
questions from Group One, and 10 minutes on each of the questions from Group Two. 

The numerical values of some physical constants and equations that may be useful in this test are 
given on the last page of this booklet. 

Group One 
Answer only FOUR of the five questions in this group. 

1 . Indicate briefly the major contributions to astronomy of 

a) Kepler 

b) Newton 

2. Briefly describe what is meant by "Newton's great synthesis." 

3. State and discuss briefly one hypothesis used by both Ptolemy and Copernicus, but completely 
abandoned by Kepler in his theory of planetary motion. 

4. According to Kepler's "harmonic law" the period of revolution of a planet is related to the 
mean radius of its orbit by the equation T^ = ka^. The mean radius of the orbit of Saturn 
around the sun is 9 Astronomical Units. What is its period of revolution in ye£irs? (Show your 
calculations.) 

5. Draw a graph of the earth's gravitational attraction on a 10-kilogram mass versus its distance 
from the center of the earth. Let R equal the earth's radius. Make entries at distances R, 2R, 
3R and 4R. 

Group Two 
Answer only TWO of the three questions in this group. Spend about ten minutes on each question. 

6. a) What is retrograde motion? 

b) Explain retrograde motion (with the aid of a diagram) using either a heUocentric or a 
geocentric model of the solar system. State which model you are using. 



21 



7. In order to develop an equation for the gravitational force F grav between the sun and a planet, 
Newton had to determine the way in which the force of gravitation depends upon the mass of 
the sun Mg and the mass of the planet Mp . Among the possible hypotheses are the following 
proportionalities : 

A. Fgrav « (Ms + Mp) 

B. Fgrav « (MsMp) 

C. Fgrav « (Ms/Mp) 

a) Which of the above is the relationship Newton chose? 

b) Pick one of the other two options and give a reasonable argument for rejecting it. 

8. Two criteria for an adequate theory are: 

a) the theory that it be based upon simple assumptions. 

b) that it be in agreement with experimental observations. 

Did the Ptolemaic (earth-centered) theory of planetary motion of 150 A.D. satisfy these 
criteria? Explain your answer. 



22