21st Century Astronomy

Laura Kay, Stacy Palen, George Blumenthal

Chapter 7

The Birth and Evolution of Planetary Systems - all with Video Answers

Educators

Chapter Questions

Problem 1

Place the following events in the order that corresponds to the formation of a planetary system.
a. Gravity collapses a cloud of interstellar gas.
b. A rotating disk forms.
c. Small bodies collide to form larger bodies.
d. A stellar wind "turns on" and sweeps away gas and dust.
e. Primary atmospheres form.
f. Primary atmospheres are lost.
g. Secondary atmospheres form.
h. Dust grains stick together by static electricity.

Sarah Mccrumb

Sarah Mccrumb

Numerade Educator

Problem 2

If the radius of an object's orbit is halved, and angular momentum is conserved, what must happen to the object's speed?
a. It must be halved.
c. It must be doubled.
b. It must stay the same.
d. It must be squared.

Sarah Mccrumb

Numerade Educator

Problem 3

Unlike the giant planets, the terrestrial planets formed when
a. the inner Solar System was richer in heavy elements than the outer Solar System.
b. the inner Solar System was hotter than the outer Solar
System.
c. the outer Solar System took up more volume than the inner Solar System, so there was more material to form planets.
d. the inner Solar System was moving faster than the outer Solar System.

Sarah Mccrumb

Numerade Educator

Problem 4

The terrestrial planets and the giant planets have different compositions because
a. the giant planets are much larger.
b. the terrestrial planets formed closer to the Sun.
c. the giant planets are made mostly of solids.
d. the terrestrial planets have few moons.

Sarah Mccrumb

Numerade Educator

Problem 5

The spectroscopic radial velocity method preferentially detects
a. large planets close to the central star
b. small planets close to the central star.
c. large planets far from the central star.
d. small planets far from the central star.
e. the method detects all of these equally well

Sarah Mccrumb

Numerade Educator

Problem 6

The concept of disk instability was developed to solve the problem that
a. Jupiter-like planets migrate after formation.
b. there was not enough gas in the Solar System to form Jupiter.
c. the early solar nebula likely dispersed too soon to form Jupiter.
d. Jupiter consists mostly of volatiles.

Sarah Mccrumb

Numerade Educator

Problem 7

Because angular momentum is conserved, an ice-skater who throws her arms out will
a. rotate more slowly.
b. rotate more quickly.
c. rotate at the same rate.
d. stop rotating entirely,

Sarah Mccrumb

Numerade Educator

Problem 8

Clumps grow into planetesimals by
a. gravitationally pulling in other clumps.
b. colliding with other clumps.
c. attracting other clumps with opposite charge.
d. conserving angular momentum.

Sarah Mccrumb

Numerade Educator

Problem 9

The transit method preferentially detects
a. large planets close to the central star.
b. small planets close to the central star.
c. large planets far from the central star.
d. small planets far from the central star.
e. the method detects all of these equally well

Sarah Mccrumb

Numerade Educator

Problem 10

If the radius of a spherical object is halved, what must happen to the period so that the spin angular momentum is conserved?
a. It must be divided by 4.
d. It must double.
b. It must be halved.
e. It must be multiplied by 4
c. It must stay the same.

Sarah Mccrumb

Numerade Educator

Problem 11

The amount of angular momentum in an object does not depend on
a. its radius.
b. its mass.
c. its rotation speed.
d. its temperature.

Sarah Mccrumb

Numerade Educator

Problem 12

The planets in the inner part of the Solar System are made primarily of refractory materials; the planets in the outer Solar System are made primarily of volatiles. The difference occurred because
a. refractory materials are heavier than volatiles, so they sank farther into the nebula.
b. there were no volatiles in the inner part of the accretion disk.
c. the volatiles on the inner planets were lost soon after the planet formed.
d. the outer Solar System has gained more volatiles from space since formation.

Sarah Mccrumb

Numerade Educator

Problem 13

If scientists want to find out about the composition of the early Solar System, the best objects to study are
a. the terrestrial planets.
b. the giant planets.
c. the Sun.
d. asteroids and comets.

Sarah Mccrumb

Numerade Educator

Problem 14

The direction of revolution in the plane of the Solar System was determined by
a. the plane of the galaxy in which the Solar System sits.
b. the direction of the gravitational force within the original cloud.
c. the direction of rotation of the original cloud.
d. the amount of material in the original cloud.

Sarah Mccrumb

Numerade Educator

Problem 15

A planet in the "habitable zone"
a. is close to the central star.
b. is far from the central star.
c. is the same distance from its star as Earth is from the Sun.
d. is at a distance where liquid water can exist on the surface.

Sarah Mccrumb

Numerade Educator

Problem 16

What is the source of the material that now makes up the Sun and the rest of the Solar System?

Sarah Mccrumb

Numerade Educator

Problem 17

Describe the different ways by which stellar astronomers and planetary scientists each came to the same conclusion about how planetary systems form.

Sarah Mccrumb

Numerade Educator

Problem 18

What is a protoplanetary disk? What are two reasons that the inner part of the disk is hotter than the outer part?

Sarah Mccrumb

Numerade Educator

Problem 19

Physicists describe certain properties, such as angular momentum and energy, as being conserved. What does this mean? Do conservation laws imply that an individual object can never lose or gain angular momentum or energy? Explain your reasoning.

Sarah Mccrumb

Numerade Educator

Problem 20

The Process of Science Figure in this chapter makes the point that different areas of science must agree with one another. Suppose that a handful of new exoplanets are discovered that appear not to have formed from the collapse of a stellar nebula (for example, the planetary orbits might be in random orientations). What will scientists do with this new information?

Sarah Mccrumb

Numerade Educator

Problem 21

How does the law of conservation of angular momentum control a figure-skater's rate of spin?

Sarah Mccrumb

Numerade Educator

Problem 22

What is an accretion disk?

Sarah Mccrumb

Numerade Educator

Problem 23

Describe the process by which tiny grains of dust grow to become massive planets.

Sarah Mccrumb

Numerade Educator

Problem 24

Look under your bed, the refrigerator, or any similar place for dust bunnies. Once you find them, blow one toward another. Watch carefully and describe what happens as they meet. What happens if you repeat this action with additional dust bunnies? Will these dust bunnies ever have enough gravity to begin pulling themselves together? If they were in space instead of on the floor, might that happen? What force prevents their mutual gravity from drawing them together into a “bunny-tesimal" under your bed?

Sarah Mccrumb

Numerade Educator

Problem 25

Why do we find rocky material everywhere in the Solar System but large amounts of volatile material only in the outer regions?

Sarah Mccrumb

Numerade Educator

Problem 26

Why were the four giant planets able to collect massive gaseous atmospheres, whereas the terrestrial planets could not? Explain the source of the secondary atmospheres surrounding the terrestrial planets.

Sarah Mccrumb

Numerade Educator

Problem 27

Describe four methods that astronomers use to search for
extrasolar planets. What are the limitations of each method; that is, what circumstances are necessary to detect a planet by each method?

Sarah Mccrumb

Numerade Educator

Problem 28

Why is it so difficult for astronomers to obtain an image of an extrasolar planet?

Sarah Mccrumb

Numerade Educator

Problem 29

Many of the first exoplanets that astronomers found orbiting other stars are giant planets with Jupiter-like masses and with orbits located very close to their parent stars. Explain why these characteristics are a selection effect of the discovery method.

Sarah Mccrumb

Numerade Educator

Problem 30

How does Kepler find Earth-like planets, and what do astronomers mean by "Earth-like"?

Sarah Mccrumb

Numerade Educator

Problem 31

Study Figure $7.17 .$ What is the maximum radial velocity of HD $70642 b$ in meters per second? Convert this number to miles per hour (mph). How does this compare to the speed at which Earth orbits the Sun $(67,000 \mathrm{mph}) ?$

Sarah Mccrumb

Numerade Educator

Problem 32

Use Appendix 4 to answer the following:
a. What is the total mass of all the planets in the Solar System, expressed in Earth masses ( $\left.M_{\text {Earth }}\right) ?$
b. What fraction of this total planetary mass is Jupiter?
c. What fraction does Earth represent?

Sarah Mccrumb

Numerade Educator

Problem 33

Compare Earth's orbital angular momentum with its spin angular momentum using the following values: $m=5.97 \times 10^{24} \mathrm{kg}$ $v=29.8$ kilometers per second $(\mathrm{km} / \mathrm{s}), r=1 \mathrm{AU}, R=6,378 \mathrm{km}$
and $P=1$ day. Assume Earth to be a uniform body. What fraction does each component (orbital and spin) contribute to Earth's total angular momentum? Refer to Working It Out 7.1

Sarah Mccrumb

Numerade Educator

Problem 34

Venus has a radius 0.949 times that of Earth and a mass
0.815 times that of Earth. Its rotation period is 243 days. What is the ratio of Venus's spin angular momentum to that of Earth? Assume that Venus and Earth are uniform spheres.

Sarah Mccrumb

Numerade Educator

Problem 35

Jupiter has a mass equal to 318 times Earth's mass, an orbital radius of $5.2 \mathrm{AU}$, and an orbital velocity of $13.1 \mathrm{km} / \mathrm{s}$. Earth's orbital velocity is $29.8 \mathrm{km} / \mathrm{s}$. What is the ratio of Jupiter's orbital angular momentum to that of Earth?

Sarah Mccrumb

Numerade Educator

Problem 36

In the text, we give an example of an interstellar cloud having a diameter of $10^{13} \mathrm{km}$ and a rotation period of $10^{6}$ years collapsing to a sphere the size of the $\operatorname{Sun}\left(1.4 \times 10^{6} \mathrm{km}$ in diameter) \right. We point out that if all the cloud's angular momentum went into that sphere, the sphere would have a rotation period of only 0.6 second. Do the calculation to confirm this result.

Sarah Mccrumb

Numerade Educator

Problem 37

The asteroid Vesta has a diameter of $530 \mathrm{km}$ and a mass of $2.7 \times 10^{20} \mathrm{kg}$
a. Calculate the density (mass/volume) of Vesta.
b. The density of water is $1,000 \mathrm{kg} / \mathrm{m}^{3},$ and that of rock is about $2,500 \mathrm{kg} / \mathrm{m}^{3} .$ What does this difference tell you about the composition of this primitive body?

Sarah Mccrumb

Numerade Educator

Problem 38

Study Figure 7.20
a. Recalling Kepler's Laws, put the three planets in order, from fastest to slowest.
b. Compare the duration of the transits. Why does the outermost planet have the longest duration?

Sarah Mccrumb

Numerade Educator

Problem 39

The best current technology can measure radial velocities of about $0.3 \mathrm{m} / \mathrm{s}$. Suppose you are observing a spectral line with a wavelength of 575 nanometers (nm). How large a shift in wavelength would a radial velocity of $0.3 \mathrm{m} / \mathrm{s}$ produce?

Sarah Mccrumb

Numerade Educator

Problem 40

Earth tugs the Sun around as it orbits, but it has a much smaller effect (only $0.09 \mathrm{m} / \mathrm{s}$ ) than that of any known extrasolar planet. How large a shift in wavelength does this effect cause in the Sun's spectrum at $500 \mathrm{nm}$ ?

Sarah Mccrumb

Numerade Educator

Problem 41

If an alien astronomer observed a plot of the light curve as Jupiter passed in front of the Sun, by how much would the Sun's brightness drop during the transit?

Sarah Mccrumb

Numerade Educator

Problem 42

A planet has been found to orbit a $1-M_{\text {sun }}$ in 200 days.
a. What is the orbital radius of this extrasolar planet?
b. Compare its orbit with that of the planets around our own Sun. What environmental conditions must this planet
experience?

Sarah Mccrumb

Numerade Educator

Problem 43

One of the planets orbiting the star Kepler-11 with an orbital radius of radius 1.1 solar radii, or $R_{\text {sun }}$ has a radius of 4.5 Earth radii $\left(R_{\text {Earth }}\right) .$ By how much does the brightness of Kepler-11 decrease when this planet transits the star?

Sarah Mccrumb

Numerade Educator

Problem 44

Kepler detected a planet with a diameter of 1.7 Earth $\left(D_{\text {Earth }}\right)$
a. How much larger is the volume of this planet than Earth's?
b. Assume that the density of the planet is the same as Earth's. How much more massive is this planet than Earth?

Sarah Mccrumb

Numerade Educator

Problem 45

The planet COROT-11b was discovered using the transit method, and astronomers have followed up with radial velocity measurements, so both its size (radius $1.43 R_{\text {Jup }}$ ) and its $\operatorname{mass}\left(2.33 M_{\text {Jup }}\right)$ are known. The density provides a clue about whether the object is gaseous or rocky.
a. What is the mass of this planet in kilograms?
b. What is the planet's radius in meters?
c. What is the planet's volume?
d. What is the planet's density? How does this density compare to the density of water $\left(1,000 \mathrm{kg} / \mathrm{m}^{3}\right) ?$ Is the planet likely to be rocky or gaseous?

Sarah Mccrumb

Numerade Educator

Problem 46

Go to the "Extrasolar Planets Global Searches" Web page (http://exoplanet.eu/searches.php) of the Extrasolar Planets Encyclopedia. Click on one ongoing project under "Ground" and one ongoing project under "Space." What method is used to detect planets in each case? Has the selected project found any planets, and if so, what type are they? Now click on one of the future projects. When will the one you chose be ready to begin? What will be the method of detection?

Alex Bretton

Numerade Educator

Problem 47

Using the exoplanet catalogs:
a. Go to the "Catalog" Web page (http://exoplanet.eu/catalog) of the Extrasolar Planets Encyclopedia and set to "All Planets detected." Look for a star that has multiple planets. Make a graph showing the distances of the planets from that star, and note the masses and sizes of the planets. Put the Solar System planets on the same axis. How does this extrasolar planet system compare with the Solar System?
b. Go to the "Exoplanets Data Explorer" website (http:// exoplanets.org and click on "Table." This website lists planets that have detailed orbital data published in scientific journals, and it may have a smaller total count than the website in part (a). Pick a planet that was discovered this year or last, as specified in the "First Reference" column. What is the planet's minimum mass? What is its semimajor axis and the period of its orbit? What is the eccentricity of its orbit? Click on the star name in the first column to get more information. Is there a radial velocity curve for this planet? Was it observed in transit, and if so, what is the planet's radius and density? Is it more like Jupiter or more like Earth?

Donald Albin

Numerade Educator

Problem 48

Space missions:
a. Go to the website for the Kepler Mission (http://kepler . nasa.gov). How many confirmed planets has Kepler discovered? Mouse over "confirmed planets": How many planet candidates are there? What kinds of follow-up observations are being done to verify whether the candidates are planets? What is new?
b. Search for the latest version of the "Kepler Orrery," an animation that shows multiplanet systems discovered by Kepler. Do most of these systems look like our own?
c. Go to the website for the European Space Agency (ESA) mission Gaia (http://sci.esa.int/gaia). This mission was launched in $2013 .$ Click on the "Exoplanets" link on the left-hand side. What method(s) will GAIA use to look for planets? What are the science goals? Have some planets been found?

Alex Bretton

Numerade Educator

Problem 49

Citizen science projects:
a. Go to the "PlanetHunters" website at http://planethunters.org. PlanetHunters is part of the Zooniverse, a citizen science project that invites individuals to participate in a major science project using their own computers. To participate in this or any of the other Zooniverse projects mentioned in later chapters, you will need to sign up for an account. Read through the sections under “About," including the FAQ. What are some of the advantages to crowdsourcing Kepler data analysis? Back on the PlanetHunters home page, click on "Tutorial" and watch the "Introduction" and "Tutorial Video." When you're ready to try looking for planets, click on "Classify" and begin. Save a copy of your stars for your homework.
b. Go to the "Disk Detective" website at http://www diskdetective.org/, another Zooniverse project for which you will need to make an account as in part (a). In this project, you will look at observations of young stars to see if there is evidence for a planetary disk. Under "Menu," read "Science" and “About," and then "Classify." Work through an example, and then classify a few images.

Alex Bretton

Numerade Educator

Problem 50

Go to the "Super Planet Crash" Web page (http://www stefanom.org/spc/ or http://apod.nasa.gov/apod/ap150112 .html). Read "Help" to see the rules. First build a system like ours with four Earth-sized planets in the inner 2 AU-is this stable? What happens if you add in super-Earths or "ice giants"? Build up a few completely different planetary systems and see what happens. What types of situations cause instability in the inner 2 AU of these systems?

Jheremiah Simon

Jheremiah Simon

Numerade Educator