Questions
Review Questions
Could astronomers in antiquity have seen Uranus? If so, why was it not recognized as a planet?Why do you suppose that the discovery of Neptune is rated as one of the great triumphs of science, whereas the discoveries of Uranus and Pluto are not?
Why is it so difficult to see features in the atmosphere of Uranus?
(a) Draw a figure like Figure 14-3, and indicate on it where Uranus was in 1986 and 2004. Explain your reasoning. (Hint: See Figure 14-1 and Figure 14-2.) (b) In approximately what year will the Sun next be highest in the sky as seen from Uranus’s south pole? Explain your reasoning.
Why do you suppose the tilt of Uranus’s rotation axis was deduced from the orbits of its satellites and not by observing the rotation of the planet itself?
Describe the seasons on Uranus. In what ways are the Uranian seasons different from those on Earth?
Explain the statement “Methane is to Uranus’s atmosphere as water is to Earth’s atmosphere.”A number of storms in the Uranian atmosphere can be seen in Figure 14-2, but none are visible in Figure 14-1. How can you account for the difference?
Why are Uranus and Neptune distinctly blue-green in color, while Jupiter and Saturn are not?
How does the energy source for Uranus’s atmospheric motions differ from those from Jupiter, Saturn, and Neptune?
Why are fewer white clouds seen on Uranus and Neptune than on Jupiter and Saturn?
Why do Uranus and Neptune have higher densities than Jupiter and Saturn?
Discuss the main reason why Uranus and Neptune are substantially smaller than Jupiter and Saturn.
How do the orientations of Uranus’s and Neptune’s magnetic axes differ from those of other planets?
Briefly describe why it is thought that Uranus was struck by at least one large planetlike object several billion years ago.
Compare the rings that surround Jupiter, Saturn, Uranus, and Neptune. Briefly discuss their similarities and differences.
The 1977 occultation that led to the discovery of Uranus’s rings was visible from the Indian Ocean. Explain why it could not be seen from other parts of Earth’s night side.
As Voyager 2 flew past Uranus, it produced images only of the southern hemispheres of the planet’s satellites. Why do you suppose this was?
Why do astronomers think that the energy needed to resurface parts of Miranda came from tidal heating rather than the satellite’s own internal heat?
Briefly describe the evidence supporting the idea that Triton was captured by Neptune.
If you were floating in a balloon in Neptune’s upper atmosphere, in what part of the sky would you see Triton rise? Explain your reasoning.
Why is it reasonable to suppose that Neptune will someday be surrounded by a broad system of rings, perhaps similar to those that surround Saturn?
How can astronomers distinguish a faint solar system object like Pluto from background stars within the same field of view?
What is the evidence that the five moons of Pluto might have a common origin?
How does the presence of Pluto’s moons suggest that there must be other worlds beyond Neptune?
Why are there a large number of objects with the same semimajor axis as Pluto?
Are there any trans-Neptunian objects that are not members of the Kuiper belt? Are there any members of the Kuiper belt that are not trans-Neptunian objects? Explain your answers.
Advanced Questions
Questions preceded by an asterisk (*) involve topics discussed in Box 1-1.
Problem-solving tips and tools
See Box 1-1 for the small-angle formula. Recall that the volume of a sphere of radius r is 4πr3/3. Section 4-7 discusses the gravitational force between two objects and Newton’s form of Kepler’s third law. You will find discussions of the original form of Kepler’s third law in Section 4-4, tidal forces in Section 4-8, Wien’s law for blackbody radiation in Section 5-4, and the transparency of Earth’s atmosphere to various wavelengths of light in Section 6-7.
For which configuration of the Sun, Uranus, and Neptune is the gravitational force of Neptune on Uranus at a maximum? For this configuration, calculate the gravitational force exerted by the Sun on Uranus and by Neptune on Uranus. Then calculate the fraction by which the sunward gravitational pull on Uranus is reduced by Neptune at that configuration. Based on your calculations, do you expect that Neptune has a relatively large or relatively small effect on Uranus’s orbit?
At certain points in its orbit, a stellar occultation by Uranus would not reveal the existence of the rings. What points are those? How often does this circumstance arise? Explain using a diagram.
According to one model for the internal structure of Uranus, the rocky core and the surrounding shell of water-ices and methane-ices together make up 80% of the planet’s mass. This interior region extends from the center of Uranus to about 70% of the planet’s radius. (a) Find the average density of this interior region. (b) How does your answer to (a) compare with the average density of Uranus as a whole? Is this what you would expect? Why?
Uranus’s epsilon (ε) ring has a radius of 51,150 km. (a) How long does it take a particle in the ε ring to make one complete orbit of Uranus? (b) If you were riding on one of the particles in the ε ring and watching a cloud near Uranus’s equator, would the cloud appear to move eastward or westward as Uranus rotates? Explain your answer.
Suppose you were standing on Pluto. Describe the motions of Charon relative to the Sun, the stars, and your own horizon. Would you ever be able to see a total eclipse of the Sun? (Hint: You will need to calculate the angles subtended by Charon and by the Sun as seen by an observer on Pluto.) In what circumstances would you never see Charon?
It is thought that Pluto’s tenuous atmosphere may become even thinner as the planet moves toward aphelion (which it will reach in 2113), then regain its present density as it again moves toward perihelion. Why should this be?
The brightness of sunlight is inversely proportional to the square of the distance from the Sun. For example, at a distance of 4 AU from the Sun, sunlight is only (¼)2 =
= 0.0625 as bright as at 1 AU. Compared with the brightness of sunlight on Earth, what is its brightness (a) on Pluto at perihelion (29.649 AU from the Sun) and (b) on Pluto at aphelion (49.425 AU from the Sun)? (c) How much brighter is it on Pluto at perihelion compared with aphelion? (Even this brightness is quite low. Noon on Pluto is about as dim as it is on Earth a half hour after sunset on a moonless night.)*If Earth-based telescopes can resolve angles down to 0.25 arcsec, how large could a trans-Neptunian object be at Pluto’s average distance from the Sun and still not present a resolvable disk?
*Calculate the maximum angular separation between Pluto and Charon as seen from Earth. Assume that Pluto is at perihelion (29.649 AU from the Sun) and that Pluto is at opposition as seen from Earth.
Presumably Pluto and Charon raise tidal bulges on each other. Explain why the average distance between Pluto and Charon is probably constant, rather than increasing like the Earth-Moon distance or decreasing like the Neptune-Triton distance. Include a diagram like Figure 10-20 as part of your answer.
(a) Find the semimajor axis of the orbit of an object whose period is 3/2 of the orbital period of Neptune. How does your result compare to the semimajor axis of Pluto’s orbit? (b) A number of Kuiper belt objects called plutinos have been discovered with the same orbital period and hence the same semimajor axis as Pluto. Explain how these objects can avoid colliding with Pluto.
Find the semimajor axis of the orbit of an object whose period is twice the orbital period of Neptune. How does your result compare to the outer limit of the Kuiper belt?
Suppose you wanted to search for trans-Neptunian objects. Why might it be advantageous to do your observations at infrared rather than visible wavelengths? (Hint: At visible wavelengths, the light we see from planets is reflected sunlight. At what wavelengths would you expect distant planets to emit their own light most strongly? Use Wien’s law to calculate the wavelength range best suited for your search.) Could such observations be done at an observatory on Earth’s surface? Explain your answer.
The New Horizons spacecraft swung by Jupiter to get a boost from that planet’s gravity, enabling it to reach Pluto relatively quickly. To see what would happen if this technique were not used, consider a spacecraft trajectory that is an elliptical orbit around the Sun. The perihelion of this orbit is at 1 AU from the Sun (at Earth) and the aphelion is at 30 AU (at Pluto’s position). Calculate how long it would take a spacecraft in this orbit to make the one-way trip from Earth to Pluto. Based on the information in Section 14-10, how much time is saved by making a swing by Jupiter instead?
Discussion Questions
Discuss the evidence presented by the outer planets that suggests that catastrophic impacts of planetlike objects occurred during the early history of our solar system.
Some scientists are discussing the possibility of placing spacecraft in orbit about Uranus and Neptune. What kinds of data should be collected, and what questions would you like to see answered by these missions?
If Triton had been formed along with Neptune rather than having been captured, would you expect it to be in a prograde or retrograde orbit? Would you expect the satellite to show signs of tectonic activity? Explain your answers.
Would you expect the surfaces of Pluto and Charon to be heavily cratered? Explain why or why not.
Imagine that you are in charge of planning the New Horizons flyby of Pluto and Charon. In your opinion, what data should be collected and what kinds of questions should the mission attempt to answer?
In 2006 the International Astronomical Union changed Pluto’s designation from planet to dwarf planet. One criterion that Pluto failed to meet was that a planet must have “cleared the neighborhood” around its orbit. In what sense has Pluto not done so? In what sense have the eight planets (Mercury through Uranus) cleared their neighborhoods? Do you agree with this criterion?
Web/eBook Questions
Miranda. Access and view the video “Uranus’s Moon Miranda” in Chapter 14 of the Universe Web site or eBook. Discuss some of the challenges that would be involved in launching a spacecraft from Earth to land on the surface of Miranda.Charon was discovered by an astronomer at the U.S. Naval Observatory. Why do you suppose the U.S. Navy carries out work in astronomy? Search the World Wide Web for the answer.
Search the World Wide Web for a list of trans-Neptunian objects. What are the largest and smallest objects of this sort that have so far been found, and how large are they? Have any objects larger than Eris been found?