Download Astronomy 101 Exam 2 Form A Name: SUID: Lab section number:

Astronomy 101 Exam 2 Form A
Name:
SUID:
Lab section number:
(In the format “M0**”. See back page.)
• Circle your answers on this page in addition to putting them on the Scantron form.
• Please choose the best answer to each question.
• You may use only pencils and pens for this exam; no calculators, notes, or cellphones are
allowed.
• Students who do not speak English well may use a translation dictionary.
• If you have a question, raise your hand, and a proctor will assist you.
• Do not attempt to communicate with anyone other than teaching staff during the exam.
• This exam has 30 multiple-choice questions, worth 3 points each, and 3 short-answer questions,
worth a total of 30 points.
• The exam is scored out of 120, so a perfect score is 130/120.
Good luck!
Lab Schedule
Reference
Kepler’s three laws of orbital motion state:
• Planets orbit in ellipses with the Sun at one focus
• The line connecting a planet to the Sun sweeps out equal areas in equal times
• The time T required for a planet to orbit the Sun is related to the orbit’s semimajor axis A by
T 2 ∝ A3 .
These laws are equally valid for other gravitationally-bound orbits.
Newton’s first two laws of motion state:
• An object with no net force acting on it travels in a straight line at a constant velocity.
• If a force acts on an object, this creates an acceleration on it, with that acceleration given by
F = ma or equivalently a = F/m.
Newton’s law of universal gravitation states:
• The force of gravity between two objects is given by
Fg =
Gm1 m2
r2
where m1 and m2 are their masses and r is the distance between their centers.
1. Here is a drawing of a planet’s orbit around a star. Assume that the three shaded areas labeled A,
B, and C all have the same area.
In which region is the planet moving fastest?
(A) The planet is moving at the same speed in all three regions
(B) Region B
(C) Region A
(D) Region C
(E) The planet is moving fastest in both regions B and C, but slower in region A
2. Which advance provided Kepler with the information he needed to conclude that the planets’ orbits
are ellipses, not circles?
(A) Galileo’s observations of the phases of Venus through his telescope
(B) Newton’s formulation of the law of universal gravitation Fgrav =
Gm1 m2
r2
(C) Tycho Brahe’s observation of a supernova in the constellation Cassiopeia
(D) Galileo’s observation of the moons of Jupiter through his telescope
(E) Tycho Brahe’s extremely accurate measurements of the locations of the planets in the sky
3. Here is a drawing of a planet’s orbit around a star. Assume that the three shaded areas labeled A,
B, and C all have the same area.
In which region will the planet be speeding up the entire time?
(A) Region A
(B) Region B
(C) Region C
(D) None of them
4. An object is moving in a circular path at a constant speed. Which of the following numbers of forces
could not be acting on it?
(A) Zero
(B) Three
(C) One
(D) Two
5. Suppose an asteroid orbits in a highly eccentric orbit, shaped as shown.
Earth’s orbit is nearly circular with a diameter of 2 AU. It has an orbital period of 1 year. Saturn’s
orbit is nearly circular with a diameter of around 20 AU; it has an orbital period of around 30 years.
Will this asteroid’s orbital period be closest to:
(A) 30 years
(B) 1 year
(C) 0.5 year
(D) 15 years
6. Which of the following objects experiences a greater fractional change in speed during the course of
one orbit around the Sun?
(A) Venus
(B) Earth
(C) Halley’s comet
(D) Mars
(E) Jupiter
7. Earth’s orbit has a semimajor axis of 1 AU. Suppose another planet’s orbit, also orbiting the Sun,
has a semimajor axis of 2 AU. Which of the following is true about this planet?
(A) Its orbital period is between one year and two years
(B) Its orbital period is less than one year
(C) Its orbital period is greater than two years
(D) Its orbital period is exactly one year
(E) Its orbital period is exactly two years
8. Over the course of one year, the speed of the orbit of Earth around the Sun...
(A) Does not change at all
(B) Changes by a small amount (less than ten percent)
(C) Changes by a large amount (greater than ten percent)
9. Which object does Kepler’s laws of orbital motion apply to?
(A) Mars
(B) The Moon
(C) Io, one of the Galilean moons around Jupiter
(D) Halley’s comet
(E) All of the above
10. Which of the following is true about the model of the solar system proposed by Copernicus in the
1500’s?
(A) It explained the retrograde motion of the planets without need for epicycles
(B) Its predictions of the motions of the planets in the sky were not as accurate as the Ptolemaic
model
(C) The planets travel in circular orbits
(D) The planets, including Earth, all orbit the Sun
(E) All of the above
11. A person is whirling a rock tied to a string horizontally above their head. The rock is rotating
counterclockwise as viewed from above. If the string snaps suddenly when the rock is in the position
shown, which path reflects the direction the rock will travel after it breaks?
12. Suppose that another planet with twice the mass of the Earth was discovered at the same distance
from the Sun as Earth. Which of the following would be true about this planet?
(A) It would take half a year to travel around the Sun.
(B) It would take exactly one year to travel around the Sun.
(C) It would take less than half a year to travel around the Sun.
(D) It would take more than two years to travel around the Sun.
(E) It would take two years to travel around the Sun.
13. A satellite orbiting Earth in a circular orbit with a radius of about 42,000 km travels around the
Earth every 24 hours.
Another satellite orbits Earth closer to the surface, in a circular orbit with a radius of only 9000 km.
How long will it take the second satellite to travel around the Earth?
(A) More than 24 hours
(B) Less than 24 hours
(C) Exactly 24 hours
(D) It depends on the mass of the satellites
14. Which diagram correctly shows the relative sizes and directions of the gravitational forces that the
Earth and Moon apply to each other? The directions of the forces are shown, and the length of the
arrows indicate their size.
15. Which of the following is not true about the recent discovery of gravitational waves?
(A) Gravitational-wave measurements give us a way to study the heavens that does not involve
collecting lightcoming from the sky.
(B) Work on gravitational-wave astronomy is being done right here at Syracuse University.
(C) The detection of gravitational waves is powerful evidence that Einstein’s theory of general
relativity is accurate.
(D) Last year, astronomers detected gravitational waves coming from the Sun.
(E) The detection of gravitational waves requires the measurement of very tiny movements of
mirrors.
16. Suppose I hold a 2 kilogram rock in one hand and a 1 kilogram rock in the other, both held the same
distance above the ground, and drop them both.
Which one experiences a greater force due to gravity?
(A) The 2 kg rock
(B) The 1 kg rock
(C) Both experience the same force
17. Three asteroids are floating in space as shown. Their masses are given, expressed in arbitrary units,
and the distances separating them are shown, also expressed in arbitrary units.
Which asteroid exerts a stronger gravitational force on the asteroid labeled A?
(A) The force exerted by asteroids B and C is equal.
(B) Asteroid B
(C) Asteroid C
(D) It is not possible to tell from this picture.
18. Here is a table showing the orbital distances, orbital periods, and masses for the six planets known
in Kepler’s time. Jupiter is the most massive of these planets, and Mercury is the least.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Semimajor axis (AU) Orbital period (years) Mass (in units of Earth’s mass)
0.38
0.24
0.06
0.72
0.61
0.81
1.0
1.0
1.0
1.52
1.88
0.11
5.20
11.86
318
9.54
29.46
95.2
An asteroid has a semimajor axis of a = 1.49 AU. Using the data from the table above, the asteroid’s
orbital period would be
(A) 2.14 years
(B) 1.82 years
(C) 0.21 years
(D) 0.97 years
(E) 0.55 years
19. The ancient Greek astronomer Ptolemy constructed a model of the solar system. What feature of
his model allowed it to accurately predict the retrograde motion of the planets?
(A) The planets traveled along “epicycles”, circular paths whose centers moved along larger circular
paths
(B) The Sun was at the center of the model
(C) The celestial spheres carrying the planets sometimes rotated backwards for a while
(D) The planets traveled in elliptical orbits
20. How many of the following orbits obey Kepler’s first law of planetary motion? The grey dot is the
Sun.
(A) Three
(B) Four
(C) Two
(D) One
(E) All five
21. Which of the following is not true regarding Newton’s laws of motion? (Or, if all of them are true,
choose option E.)
(A) Kepler’s laws of orbital motion are a consequence of Newton’s laws of motion
(B) When combined with mathematics, they can explain why the planets move in elliptical orbits
(C) They describe the response of objects to forces that act upon them
(D) They apply in space in the same way that they apply on Earth
(E) All of the above are true.
22. Star A and Star B are separated by a distance of 4 AU and exert a certain gravitational force Fg on
each other.
Which actions will result in the gravitational force Fg becoming four times as big?
(A) Multiplying the mass of Star A by two
(B) Multiplying the mass of both Star A and Star B by four
(C) Bringing the stars twice as close together, so they are only separated by a distance of 2 AU
(D) Bringing the stars four times as close together, so they are only separated by a distance of 1
AU
(E) None of the above
23. A spacecraft is launched from Earth toward the Moon.
Note that the Earth’s mass is about eighty times greater than the Moon’s mass.
When the spacecraft is halfway between the Earth and the Moon, which object exerts the largest
gravitational force on the spacecraft?
(A) The Moon
(B) The gravitational forces from the two bodies are equal and opposite here
(C) The Earth
(D) Neither object exerts a gravitational force on the spacecraft at this point
24. The orbit of a comet around the Sun is shown below.
This comet takes one year to move from point 1 to point 2, and 4 years to move from point 3 to
point 4. Which of the following best describes the area swept out by a line connecting the comet to
the Sun? (You may wish to shade in these areas on your exam paper.)
(A) The area swept out between points 1 and 2 is equal to the area swept out between points 3 and
4
(B) The area swept out between points 1 and 2 is four times as large as the area swept out between
points 3 and 4
(C) The area swept out between points 3 and 4 is four times as large as the area swept out between
points 1 and 2
25. Here is a drawing of a planet’s orbit around a star. Assume that the three shaded areas labeled A,
B, and C all have the same area.
In which region will the planet have the largest angular momentum?
(A) Region A
(B) Region B
(C) Region C
(D) The angular momentum is equal in all three regions
26. Suppose I hold a 2 kilogram rock in one hand and a 1 kilogram rock in the other, both held the same
distance above the ground, and drop them both.
Which one experiences a greater acceleration due to gravity?
(A) The 2 kg rock
(B) The 1 kg rock
(C) Both experience the same acceleration
27. Suppose that the Earth were to suddenly shrink in size, but its mass remained the same. According
to the law of the conservation of angular momentum, which of the following would happen?
(A) Its rate of rotation around its axis would increase; the day would get shorter
(B) Its rate of rotation around its axis would decrease; the day would get longer
(C) Neither of the above
28. Kepler’s second law states that the line connecting a planet to its star sweeps out equal areas in
equal times.
Of which principle of physics is this a direct consequence?
(A) The conservation of angular momentum
(B) Newton’s first law of motion
(C) The law of universal gravitation
(D) Newton’s second law of motion
29. Jupiter is the most massive of the planets, but the Sun is a thousand times more massive than
Jupiter. Which of the following is a correct statement about Jupiter’s gravity acting on the Sun?
(A) The force of gravity that Jupiter exerts on the Sun is equal to the force of gravity thatthe Sun
exerts on Jupiter. However, since the Sun is at the center of the Solar System,it does not move
at all.
(B) Jupiter exerts no gravitational force at all on the Sun; thus the Sun does not move.
(C) The force of gravity that Jupiter exerts on the Sun is equal to the force of gravity thatthe Sun
exerts on Jupiter. However, since the Sun has so much more mass, this forcecauses the Sun to
move much less than Jupiter does.
(D) The force of gravity that the Sun exerts on Jupiter is one thousand times greater than the
force of gravity that Jupiter exerts on the Sun. This small force causes the Sun to moveslightly,
much less than Jupiter does.
(E) None of the above are true.
30. Suppose a person on Earth and a person on the Moon both drop identical apples from a height of
one meter. Which of the following is true?
(A) The apple dropped on the Moon will take the same amount of time to hit the ground, but the
force of gravity on it is less
(B) The apples will take the same amount of time to fall, and they will experience the same
gravitational force.
(C) The apple dropped on the Moon will take longer to hit the ground, and the force of gravity on
it will be less
(D) The apple dropped on the Moon will take longer to hit the ground, but the force of gravity on
it will be the same
Short-Answer Questions
Answer the following questions.
(This question is worth 14 points.)
Choose three people from the list of the astronomers we have studied: Ptolemy, Copernicus, Galileo,
Tycho, Kepler, and Newton. Briefly explain their contributions to the quest to figure out the workings
of the solar system, and explain how they relate to each other and to the broader mission to explain
the motions of the Solar System.
(This question is worth 8 points)
In class our study of orbital motion concluded with learning two sets of laws:
1. Kepler’s laws of orbital motion
2. Newton’s laws of motion and of gravity
Which of these sets of laws is more fundamental? That is, is one of them a consequence of the other?
Is there a difference in what Kepler’s laws do for us, and what Newton’s laws do for us?
(This question is worth 8 points.)
Galileo observed the phases of Venus through his telescope, which allowed him to conclude that
Copernicus’ heliocentric model is correct. In this problem, you will determine at what time of day
the planets appear high in the sky.
The planets have phases for the same reason that the Moon does: half of their surfaces are always
sunlit, but we may see some, all, or none of this sunlit half, depending on the locations of Earth, the
Sun, and the planet.
Here is a diagram of the Earth, Sun, and the orbits of Venus and Mars, showing the positions of the
Earth and the Sun.
a) Draw in the position of Venus that corresponds to the full phase.
b) Draw in the position of Mars that corresponds to the full phase.
c) Will an observer on Earth see a full Venus high in the sky during the day, or at night?
d) Will an observer on Earth see a full Mars high in the sky during the day, or at night?
End of Exam