21st Century Astronomy

Laura Kay, Stacy Palen, Brad Smith

Chapter 3

Motion of Astronomical Bodies - all with Video Answers

Educators

Chapter Questions

Problem 1

Most ancient Greek astronomers were skeptical about the idea that Earth revolved around the Sun because
a. of their religious beliefs.
b. it feels as though Earth is stationary.
c. Earth is so important.
d. the heavens were thought to be perfect.

Donald Albin

Donald Albin

Numerade Educator

Problem 2

When Earth catches up to a slower-moving outer planet and passes it in its orbit in the same way that a faster runner overtakes a slower runner in an outside lane, the planet
a. exhibits retrograde motion.
b. slows down because it feels Earth's gravitational pull.
c. decreases in brightness as it passes through Earth's shadow.
d. moves into a more elliptical orbit.

Donald Albin

Numerade Educator

Problem 3

Copernicus's model of the Solar System was superior to Ptolemy's because
a. it had a mathematical basis that could be used to predict the positions of planets.
b. it was more accurate.
c. it did not require epicycles.
d. it was simpler.

Donald Albin

Numerade Educator

Problem 4

A planet with an eccentricity of 0.5 has
a. nearly equal semimajor and semiminor axes.
b. a longer semiminor axis than semimajor axis.
c. a longer semimajor axis than semiminor axis.
d. the Sun at the center of its orbit.

Donald Albin

Numerade Educator

Problem 5

Suppose a planet is discovered orbiting a star in a highly elliptical orbit. While the planet is close to the star it moves _______, but while it is far away it moves _______.
a. faster; slower
b. slower; faster
c. retrograde; prograde
d. prograde; retrograde

Eve Rafferty

Numerade Educator

Problem 6

For Earth, $P^{2} / A^{3}=1.0$ (in appropriate units). Suppose a new dwarf planet is discovered that is 14 times as far from the Sun as Earth is. For this planet,
a. $P^{2} / A^{3}=1.0$
b. $P^{2} / A^{3}>1.0$
c. $P^{2} / A^{3}<1.0$
d. you can't know the value of $P^{2} / A^{3}$ without more information.

Donald Albin

Numerade Educator

Problem 7

Place the following in order from largest to smallest semimajor axis.
a. a planet with a period of 84 Earth days
b. a planet with a period of 1 Earth year
c. a planet with a period of 2 Earth years
d. a planet with a period of 0.5 Earth year

Donald Albin

Numerade Educator

Problem 8

Suppose you watch a car sliding on ice down a hill. As it slides, it slowly drifts to your right across the road, speeding up in that direction until it bumps into the curb. In this situation, which of the following is more likely, and why?
a. The car was already traveling diagonally across the street before it hit the patch of ice.
b. The road surface is rounded (or "crowned"), causing the car to be pushed across the street.

Donald Albin

Numerade Educator

Problem 9

Imagine you are walking along a forest path. Which of the following is not an action-reaction pair in this situation?
a. the gravitational force between you and Earth; the gravitational force between Earth and you.
b. your shoe pushing back on Earth; Earth pushing forward on your shoe
c. your foot pushing back on the inside of your shoe; your shoe pushing forward on your foot
d. you pushing down on Earth; Earth pushing you forward 1

Donald Albin

Numerade Educator

Problem 10

An unbalanced force must be acting when an object
a. accelerates.
b. changes direction but not speed.
c. changes speed but not direction.
d. changes speed and direction.
e. all of the above

Donald Albin

Numerade Educator

Problem 11

T/F: Copernicus's determinations of the distances between the planets and the Sun were quite accurate.

Donald Albin

Numerade Educator

Problem 12

T/F: Retrograde motion is the counterclockwise motion of Solar System objects, as seen from Earth.

Donald Albin

Numerade Educator

Problem 13

T/F: Kepler obtained accurate data on the positions of the planets in the sky over time, which Galileo used to prove that planets revolve around the Sun.

Donald Albin

Numerade Educator

Problem 14

$\mathbf{T} / \mathbf{F}:$ Planets with circular orbits travel at the same speed at all points in their orbits; planets with elliptical orbits change their speeds at different points in their orbits.

Donald Albin

Numerade Educator

Problem 15

$\mathbf{T} / \mathbf{F}:$ If an object moves at constant speed, a net force is acting on it.

Donald Albin

Numerade Educator

Problem 16

A_______model of the Solar System puts Earth at the model of the Solar System puts Earth at the center, while a ______ model of the Solar System puts the Sun at the center.
a. geocentric; heliocentric
b. heliocentric; geocentric
c. heliocentric; Copernican
d. geocentric; Ptolemaic

Donald Albin

Numerade Educator

Problem 17

Kepler's first law replaced Copernicus's perfect circles with ellipses, thus shattering the idea that
a. Tycho's data were accurate.
b. the Sun is at a focus.
c. the heavens were perfect, with perfectly round objects and perfectly round orbits.
d. Earth goes around the Sun.

Donald Albin

Numerade Educator

Problem 18

Kepler's second law says that
a. planetary orbits are ellipses with the Sun at one focus.
b. the square of a planet's orbital period equals the cube of its semimajor axis.
c. for every action there is an equal and opposite reaction.
d. unbalanced forces cause changes in motion.
e. planets move fastest when they are closest to the Sun.

Donald Albin

Numerade Educator

Problem 19

Suppose you read in the newspaper that a new planet has been found. Its average speed in orbit is $33 \mathrm{km} / \mathrm{s}$. When it is closest to its star it moves at $31 \mathrm{km} / \mathrm{s}$, and when it is farthest from its star it moves at $35 \mathrm{km} / \mathrm{s}$. This story is in error because
a. the average speed is far too fast.
b. Kepler's third law says the planet has to sweep out equal areas in equal times, so the speed of the planet cannot change.
c. planets stay at a constant distance from their stars; they don't move closer or farther away.
d. Kepler's second law says the planet must move fastest when it's closest, not when it is farthest away.
e. using these numbers, the square of the orbital period will not be equal to the cube of the semimajor axis.

Donald Albin

Numerade Educator

Problem 20

Galileo observed that Jupiter has moons. From this information, you may conclude that
a. Jupiter is the center of the Solar System.
b. Jupiter orbits the Sun.
c. Jupiter orbits Earth.
d. some things do not orbit Earth.

Eve Rafferty

Numerade Educator

Problem 21

Galileo observed that Venus had phases that correlated with its size in his telescope. From this information, you may conclude that Venus
a. is the center of the Solar System.
b. orbits the Sun.
c. orbits Earth.
d. orbits the Moon.

Eve Rafferty

Numerade Educator

Problem 22

A planet with a large orbit _____ than a planet with a smaller orbit.
a. is colder
b. moves faster
c. has a longer period
d. all of the above

Donald Albin

Numerade Educator

Problem 23

Planets with high eccentricity may be unlikely candidates for life because
a. the speed varies too much.
b. the period varies too much.
c. the temperature varies too much.
d. the orbit varies too much.

Eve Rafferty

Numerade Educator

Problem 24

Imagine you are pulling a small child on a sled by means of a rope. Which of the following are action-reaction pairs in this situation?
a. You pull forward on the rope; the rope pulls backward on you.
b. The sled pushes down on the ground; the ground pushes up on the sled.
c. The sled pushes forward on the child; the child pushes backward on the sled.
d. The rope pulls forward on the sled; the sled pulls backward on the rope.

Donald Albin

Numerade Educator

Problem 25

Suppose you read about a new car that can go from 0 to $100 \mathrm{km} / \mathrm{h}$ in only 2.0 seconds. What is this car's acceleration?
a. about $50 \mathrm{km} / \mathrm{h}$
b. about $14 \mathrm{m} / \mathrm{s}^{2}$
c. about $50 \mathrm{km} / \mathrm{s}^{2}$
d. about $200 \mathrm{km}$
e. about $0.056 \mathrm{km} / \mathrm{h}^{2}$

Donald Albin

Numerade Educator

Problem 26

Copernicus and Kepler engaged in what is called empirical science. What do we mean by empirical?

Eve Rafferty

Numerade Educator

Problem 27

Study Figure 3.6. During normal motion, does Mars move toward the east or west? Which direction does it travel when moving retrograde? For how many days did Mars move retrograde?

Donald Albin

Numerade Educator

Problem 28

Each ellipse has two foci. The orbits of the planets have the Sun at one focus. What is at the other focus?

Donald Albin

Numerade Educator

Problem 29

Ellipses contain two axes: major and minor. Half the major axis is called the semimajor axis. What is especially important about the semimajor axis of a planetary orbit?

Donald Albin

Numerade Educator

Problem 30

What is the eccentricity of a circular orbit?

Donald Albin

Numerade Educator

Problem 31

The speed of a planet in its orbit varies in its journey around the Sun.
a. At what point in its orbit is the planet moving the fastest?
b. At what point is it moving the slowest?

Donald Albin

Numerade Educator

Problem 32

The distance that Neptune has to travel in its orbit around the Sun is approximately 30 times greater than the distance that Earth must travel. Yet it takes nearly 165 years for Neptune to complete one trip around the Sun. Explain why.

Donald Albin

Numerade Educator

Problem 33

Galileo came up with the concept of inertia. What do we mean by inertia? How is it related to mass?

Donald Albin

Numerade Educator

Problem 34

If Kepler had lived on Mars, would he have deduced the same empirical laws for the motion of the planets?

Sheh Lit Chang

University of Washington

Problem 35

What is the difference between speed and acceleration?

Donald Albin

Numerade Educator

Problem 36

You push your book across the desk, and it slides off the edge and falls to the floor. Identify the forces that act on the book during the three parts of this scenario: (a) while you are pushing the book, (b) while the book is sliding, and (c) while the book is falling.

Donald Albin

Numerade Educator

Problem 37

Imagine you throw a ball straight up in the air. At the top of its flight, it stops and then falls again. What is the acceleration of the ball at the top of its flight?

Donald Albin

Numerade Educator

Problem 38

Consider the ball in question 37. Neglecting air resistance, compare the velocity of the ball just after it leaves your hand to the velocity of the ball just before you catch it. (Assume that your hand is at the same height above the ground at both times.)

Donald Albin

Numerade Educator

Problem 39

When involved in an automobile collision, a person not wearing a seat belt will move through the car and often strike the windshield directly. Which of Newton's laws explains why the person continues forward, even though the car stopped?

Eve Rafferty

Numerade Educator

Problem 40

When riding in a car, we can sense changes in speed or direction through the forces that the car applies on us. Do we wear seat belts in cars and airplanes to protect us from speed or from acceleration? Explain your answer.

Eve Rafferty

Numerade Educator

Problem 41

Study the graph in Figure $3.13 .$ Is this graph linear or logarithmic? From the data on the graph, find the approximate semimajor axis and period of Saturn. Show your work.

Donald Albin

Numerade Educator

Problem 42

Study Figure 3.15 , which shows that the apparent size of Venus changes as it goes through phases. Approximately how many times larger is Venus in the sky at the tiniest crescent than at the gibbous phase shown? Therefore, approximately how many times closer is Venus to us at the phase of that tiniest crescent than at the gibbous phase?

Donald Albin

Numerade Educator

Problem 43

Assume a new dwarf planet is discovered. It is located at $18.3 \mathrm{AU} .$ Its synodic period is 370 days.
a. Use Math Tools 3.1 to find the sidereal period.
b. Use Kepler's law to find the sidereal period.
c. Compare your results for (a) and (b).

Donald Albin

Numerade Educator

Problem 44

Suppose a new dwarf planet is discovered orbiting the Sun with a semimajor axis of 50 AU. What would be the orbital period of this new dwarf planet?

Eve Rafferty

Numerade Educator

Problem 45

Suppose you discover a planet around a Sun-like star. From careful observation over several decades, you find that its period is 12 Earth years. Find the semimajor axis.

Donald Albin

Numerade Educator

Problem 46

Suppose you read in a tabloid newspaper that "experts have discovered a new planet with a distance from the Sun of 2 AU and a period of 3 years." Use Kepler's third law to argue that this is impossible.

Donald Albin

Numerade Educator

Problem 47

Show, as Galileo did, that Kepler's third law applies to the four moons of Jupiter that he discovered, by calculating $P^{2}$ divided by $A^{3}$ for each moon. (Data on the moons can be found in Appendix $4 .)$

Donald Albin

Numerade Educator

Problem 48

A sports car accelerates from a stop to $100 \mathrm{km} / \mathrm{h}$ in 4 seconds.
a. What is its acceleration?
b. If it went from $100 \mathrm{km} / \mathrm{h}$ to a stop in 5 seconds, what would be its acceleration?
c. Suppose the car has a mass of 1,200 kg. How strong is the force on the car?
d. What supplies the "push" that accelerates the car?

Donald Albin

Numerade Educator

Problem 49

A train pulls out of a station accelerating at $0.1 \mathrm{m} / \mathrm{s}^{2}$. What is its speed, in kilometers per hour, $21 / 2$ minutes after leaving the station?

Donald Albin

Numerade Educator

Problem 50

A Fermi problem involves making reasonable estimates to arrive at a reasonable answer, even if you do not know something in detail. Estimate the mass of a train, and then estimate the force that accelerates the train described in question 49.

Donald Albin

Numerade Educator

Problem 51

Flybynite Airlines takes 3 hours to fly from Baltimore to Denver at a speed of $800 \mathrm{km} / \mathrm{h}$. To save fuel, management orders the airline's pilots to reduce their speed to $600 \mathrm{km} / \mathrm{h}$ How long will it now take passengers on this route to reach their destination?

Donald Albin

Numerade Educator

Problem 52

You are driving down a straight road at a speed of $90 \mathrm{km} / \mathrm{h},$ and you see another car approaching you at a speed of $110 \mathrm{km} / \mathrm{h}$ along the road.
a. Relative to your own frame of reference, how fast is the other car approaching you?
b. Relative to the other driver's frame of reference, how fast are you approaching the other driver's car?

Donald Albin

Numerade Educator

Problem 53

You are riding along on your bicycle at $20 \mathrm{km} / \mathrm{h}$ and eating an apple. You pass a bystander.
a. How fast is the apple moving in your frame of reference?
b. How fast is the apple moving in the bystander's frame of reference?
c. Whose perspective is more valid?

Donald Albin

Numerade Educator

Problem 54

During the latter half of the 1 9 th century, a few astronomers thought there might be a planet circling the Sun inside Mercury's orbit. They even gave it a name: Vulcan. We now know that Vulcan does not exist. If a planet with an orbit one-fourth the size of Mercury's actually existed, what would be its orbital period relative to that of Mercury?

Donald Albin

Numerade Educator

Problem 55

Suppose you are pushing a small refrigerator of mass $50 \mathrm{kg}$ on wheels. You push with a force of $100 \mathrm{N}$
a. What is the refrigerator's acceleration?
b. Assume the refrigerator starts at rest. How long will the refrigerator accelerate at this rate before it gets away from you (that is, before it is moving faster than you can run-on the order of $10 \mathrm{m} / \mathrm{s}$ )?

Eve Rafferty

Numerade Educator

Problem 56

Go to the Web page "This Week's Sky at a Glance"(http:// skyandtelescope.com/observing/ataglance) on Sky \& Telescope magazine's website. Which planets are visible in your sky this week? Why are Mercury and Venus visible in the morning before sunrise or in the evening just after sunset? Before telescopes, how did people know the planets were different from the stars?

Donald Albin

Numerade Educator

Problem 57

Look up the dates for the next opposition of Mars, Jupiter, or Saturn. One source is the NASA "Sky Events Calendar" at http://eclipse.gsfc.nasa.gov/SKYCAL/SKYCAL.html. Check only the "Planet Events" box in "Section 2: Sky Events"; and in Section $3,$ generate a calendar or table for the year. As noted in Connections 3.1 , opposition means that the planet will be opposite the Sun in the sky, so it will rise at sunset and set at sunrise. It is also during opposition that the planet is closest to Earth and you can observe retrograde motion. If you are coming up on an opposition, take pictures of the planet over the next few weeks. Can you see its position move in retrograde fashion with respect to the background stars?

Donald Albin

Numerade Educator

Problem 58

Refer to the website from question 57 to find the current observational positions of all the planets.
a. Which ones are in or near to conjunction, opposition, or greatest elongation?
b. Which are visible in the morning sky? In the evening sky?
c. Sketch the Solar System with Earth, Sun, and planets as it looks from "above." Check your result using NASA's "Solar System Simulator" (http://space.jpl.nasa.gov): Set it for Solar System as seen from above, and look at the field of view of $2^{\circ}, 5^{\circ},$ and $30^{\circ}$ to see the inner and then the outer planets. Does the simulator agree with your sketch?

Donald Albin

Numerade Educator

Problem 59

Go to the Museo Galileo website (http://brunelleschi.imss .fi.it/telescopiogalileo/index.html), and view the exhibit on Galileo's telescope. What did his telescope look like? What other instruments did he use? From the museum page you can link to short videos (in English) on his science and his trial (http://catalogue.museogalileo.it). Why is Galileo considered the first modern scientist? Why is his middle finger on display in the museum?

Donald Albin

Numerade Educator

Problem 60

Go to the online "Extrasolar Planets Encyclopedia" (http://exoplanet.eu/catalog-all.php), and find a planet with an orbital period similar to that of Earth. What is the semimajor axis of its orbit? If it is very different from 1 AU, then the mass of the star is different from that of the Sun. Click on the star name in the first column to see the star's mass. What is the orbital eccentricity? Now select a star with multiple planets. Verify that Kepler's third law applies by showing that the value of $P^{2} / A^{3}$ is about the same for each of the planets of this star. How eccentric are the orbits of the multiple planets?

Donald Albin

Numerade Educator