Answers to Homework #3 (Astr 212 -- Fall 2003)

Jupiter & Saturn -- Due Mon Dec 1


1) Both Jupiter and Saturn

(A) have liquid metallic hydrogen in their interiors, (B) have rings, (C) emit more energy than they absorb from the sun, (D) have belt and zone circulation, (E) all of the above.

Correct: (E). The huge pressure in both planets squeezes hydrogen atoms into a liquid in which electrons are free to move around (like in a metal; see p. 505 and 522). Both have rings (p.511 and 523-526). On p. 505 we learn that Jupiter emits about 1.7 times more energy than it receives from the sun, and on p.522 we find Saturn emits 1.8 times more than it recieves -- both are because the planets are contracting, albeit very slowly. Belt-zone circulation is the scientific name for the weather pattern that produces the light and dark bands visible in the atmospheres of Jupiter and Saturn.

 

2) Which of the following methods have been used to study Jupiter?

(A) Ground-based telescopes, (B) Robotic spacecraft which flew past, (C) A robotic probe which entered Jupiter's atmosphere, (D) Spacecraft carrying a human crew, (E) Answers A, B, and C.

Correct: (E). Of course A must be true, since we can see and study Jupiter with the BGSU telescopes. Robotic spacecraft that have flown past (not orbited) Jupiter include NASA's Pioneer 10 and Pioneer 11, and Voyager 1 and Voyager 2 (p. 505). Another robotic craft called Galileo orbited Jupiter for 8 years and dropped a probe into Jupiter's atmosphere (p 507). No humans have ever visited Jupiter directly (too far away for our present technology -- more on that in the last week of classes).

 

3) Which of the following characteristics correctly describe the gaseous atmospheres of Jupiter and Saturn?

(A) Composed mainly of hydrogen gas, (B) Most of the light gases have leaked away into space, (C) Composed mainly of ammonia, methane, and water, (D) Bands of clouds move below a transparent layer several hundred kilometers thick, (E) Answers A and D.

Correct: (E). Both planets are composed of hydrogen (about 3/4), helium (about 1/4) and traces of the compounds listed in C (see Table 23-1 on p.504). Both have bands -- the belt-zone circulation mentioned in Question 1 -- embedded in a clear atmosphere of H and He (p. 507). The high masses of these planets produce a strong gravity, leading to very high escape velocities. Not even the light gases like H2 can escape from Jupiter and Saturn (see Figure 22-15 on p. 488).

 

4) Which of the following properties explain the strong magnetic field of Jupiter?

(A) The electrical conductivity of the liquid metallic hydrogen interior, (B) The rapid rotation of the planet, (C) Belt and zone circulation in the cloud layers, (D) Convection in the interior as heat moves from the core to the surface, (E) Answers A, B, and D.

Correct: (E). As with all the planets we have studied (and the sun), the dynamo effect can produce a magnetic field only if all three of the critical components are present: (1) a fluid that conducts electricity (allows electrons to flow freely), (2) convection in that fluid, and (3) rotation of the entire planet. The rotation and convection move the electron-rich fluid in a swirling pattern that gives rise to a magnetic field, just like the "jumping ring" experiment in class weeks ago where the electric current in the loops of wire produced a magnetic field.

 

5) Jupiter has ______ moons.

(A) no, (B) captured all of its, (C) at least sixteen, (D) four, (E) answers B and D.

Correct: (C). Jupiter has four big moons (Io, Europa, Ganymede and Callisto: the "Galilean moons") that probably formed with the planet, and many small moons, most of which are probably captured asteroids.

 

6) Jupiter's moon Europa has few craters because

(A) it is protected from asteroid impacts by Jupiter's gravity, (B) it does not have a solid surface, (C) its active surface erased them, (D) its surface is not strong enough to support craters, (E) the meteoroids all burned up in its thick atmosphere.

Correct: (C). Europa has a crust of frozen water that has a few craters, but not as many as Callisto. Since Jupiter's strong gravity tends to attract meteoroids, one would expect more impacts on the inner moons like Europa than the outer moons (see Figure 23-13). Something must erase the craters on Europa. Detailed pictures of Europa's surface shows it to be covered with cracks where liquid water has flowed up from below and frozen (Fig 23-14). Repeated cycles of cracking, flooding and freezing erase the pre-existing craters.

 

7) The densities and compositions of Jupiter's "Galilean" moons change in a particular way when considered in order of closest to farthest distance from Jupiter. The moons farther from Jupiter are

(A) denser and icier, (B) denser and rockier, (C) less dense and icier, (D) less dense and rockier, (E) denser and more rich in hydrogen gas.

Correct: (C). The densities decrease as you go outward, from Io (rocky and iceless, 3.4 grams/cm3) to Callisto (roughly equal amounts of rock and ice, 1.8 grams/cm3). This behavior was important in helping us to develop the theory of how Jupiter and its moons formed: a disk of gas and dust like a miniature solar nebula developed around proto-Jupiter. Near the center, the gas and dust were warmed by proto-Jupiter and water stayed gasesous so did not condense into ice grains. Icy grains could form in the colder regions farther out. Dust collected to form rocky grains at all distances. As the grains accreted into planetesimals and eventually proto-moons, the inner moons were richer in rocky material while the outer moons contained more ices. This is a case where remembering the theory of how Jupiter and its moons formed helps you remember the properties (densities and compositions) of the moons.

 

8) Astronomers interpret the trend in density and composition discussed in Problem 7 to mean what?

(A) Jupiter's strong gravity pulled all the icy material away from its innermost moons, (B) Jupiter's strong gravity focused more asteroids at the outermost moons, (C) As it formed, Jupiter was surrounded by a gas disk which evolved like a mini-solar nebula, (D) Jupiter's strong gravity captured the Galilean moons quickly, (E) As it formed, volcanoes on Jupiter spewed layers of ice onto its innermost moons.

Correct: (C). See the answer to 7.

 

9) The rings of Saturn

(A) are composed of vast numbers of particles, (B) turn as a solid body like a spinning CD, (C) physically touch the planet, (D) may be the remnants of an icy moon that was shattered by tidal forces long ago, (E) answers A and D.

Correct: (E). The rings encircle the planet without touching it. They are not a single, solid object like a CD -- if they were, then the outer edge would take the same amount of time to complete one rotation as the inner edge. However, observations show the inner edge spins faster, consistent with Kepler's third law (p2 = a3). This implies that the rings are composed of many small objects --partcles -- that orbit Saturn. The particles are too small to see individually, but together they reflect sunlight back to Earth. One theory for where the ring particles come from is that an icy moon broke apart under the tidal pull of Saturn (tidal bulge got too big and tore moon apart). Another possibility is that icy comets collide with Saturn's moon and the scattered fragments replenish the rings. Both processes might contribute.

 

10) The "spokes" of Saturn's rings are thought to

(A) support the rings against the pull of Saturn's gravity like spokes on a wagon wheel, (B) be clouds of dust swept along by the rotation of Saturn's magnetic field, (C) be kept in position by "shepherd moons", (D) glow as the planet's magnetic field focuses the solar wind onto the rings, (E) orbit with the same orbital period (p) as Saturn's moon Titan.

Correct: (B). We discounted the "spinning CD/wheel" idea in 9. The spokes, discussed on p. 526, are clouds of electrostatically charged (have positive or negative electrical charges) dust that are trapped in Saturn's strong magnetic field. The field rotates with the planet, and dust in the rings can't cross the field lines, so are carried along. The spokes go around at the same speed as the planet (once every 10 hours 39 min), not at the orbital speeds dictated by Kepler's third law (p2 = a3). The spokes are an interesting example of a case where the electro-magnetic force is more important than gravity in determining the motion of an astronomical object.


Andy Layden, Fall 2003.