ASTR 1010 – Homework Assignment 13

Chapter 11 – Spring 2009

Question 1 - #1. The basic idea is that as the distance from the Sun increases, the number of planetesimals available for planet formation went down. Thus, Jupiter and Saturn could get bigger faster and then spend more time drawing in hydrogen and helium from the Solar nebula. The accretion of hydrogen and helium stopped at the same time for all the outer planets, so the ones that started earlier (Jupiter and Saturn) ended up bigger.

Question 2 - #3. The outer part of Jupiter is gaseous (mostly hydrogen and helium), but as one descends into the planet, the pressure increases and the hydrogen liquefies (along with the other compounds). As one continues downwards, the pressure forces the liquid hydrogen into a metallic form (which can conduct electricity and gives rise to the planet’s magnetic field). This layer is the largest (see Figure 11.4). At the center likes the core, a mix of hydrogen compounds, rock and metal, but at pressures much larger than anything we have inside the Earth.

Question 3 - #4. Jupiter’s internal heat is produced by a slight overall contraction of the whole planet. This means that a bit of the planet’s gravitational potential energy gets converted into kinetic energy and, thus, thermal energy (recall that the speed of particles is related to their temperature by the thermal velocity formula on p. 315). For Saturn, the contraction idea doesn’t work because it’s pretty much done with that, so here the idea is that helium “droplets” form in the atmosphere and effectively move closer to the center of the planet (think of some weird slow-motion rain…). This is motion of matter towards the center of a massive object, so it is once again the conversion of gravitational potential energy into kinetic and, hence, thermal energy. Uranus does not really generate heat and Neptune’s source of internal energy is still unknown.

Question 4. - #5. Jupiter’s atmospheric structure is similar to Earth’s (though on a larger scale and with totally different components). See Figure 11.6. The atmospheres of the other jovian planets are similar and are shown in figure 11.7. The cloud layers occur in the troposphere and, on Jupiter, are fairly tightly packed together, giving rise to its colorful atmospheric features (see answer below). For the other planets, the atmospheres are colder (because they are farther from the Sun), so the cloud layers are at different altitudes (lower down as we look at the top of the atmosphere) than on Jupiter.

Question 5. - #6. Different compounds condense into droplets at different levels in the jovian atmosphere. These compounds have different colors (see Figure 11.6). The proximity of these levels to the surface allows us to see them and gives rise to the colorful structures in the atmosphere that we see. The same basic thing occurs on Saturn except that this planet has weaker gravity than Jupiter, thus, the colorful layers are spaced further apart and we only see down to the topmost one. The other two are far enough below it that, by this point, the atmosphere is really too opaque to see them. On Uranus and Neptune, we see a blue color in the atmosphere because of the absorption of red light by methane.

Question 6. - #7. Jupiter has planetwide circulation cells like those on Earth. The fast rotation of the planet lets these cells form alternating bands of rising and falling air and this produces the famous stripes on the planet. The Great Red Spot is a long-lived storm on the planet that resembles an enormous hurricane. Saturn and Neptune’s atmospheric circulation resembles that of Jupiter. Uranus is different because its 98 degree tilt (making it effectively rotate on its side) produces long-lived (more than 2 decades in length) seasonal effects.

Question 7. - #10. The four Galilean moons resemble a mini Solar System: the inner ones are small and denser compared to the outer ones. The outer ones, like the jovian planets at their formation, accreted more ice and thus became larger and lower in density. The two inner satellites, Io and Europa are tidally heated by Jupiter (think of this as a “gravitational flexing”). This forces the interior of Io to be molten and erupt continuously to the surface, and this keeps the region of Europa under the ice crust liquid. Io is in an orbital resonance with Europa and Ganymede (see Figure 11.19b) and this forces Io’s orbit to be more elliptical than expected. In turn, this ellipticity makes it easier for Io to be tidally flexed by Jupiter.

Question 8. - 11. Titan’s atmosphere is mostly nitrogen, like that of Earth, and the pressure is 50-60% greater than that of Earth. The composition is basically 90% nitrogen and 10% methane, argon, ethane, and other hydrogen compounds. The methane and ethane in its atmosphere contribute to a greenhouse effect. The Cassini mission’s radar imaging showed signs of wet surfaces (likely due to liquid methane) and valleys, deserts, plains, etc.

Question 9. - #13. Triton, Neptune’s large moon, is one of the 7 large moons of the Solar System. It has a thin atmosphere composed primarily of nitrogen and methane. The most interesting characteristics of the satellite are that it goes around Neptune backwards (compared to how Neptune is spinning) and its orbit has a high inclination (it’s not in Neptune’s equatorial plane). These two facts indicate almost certainly that this moon was captured gravitationally as it passed near Neptune.

Question 10. - #16. The rings of the jovian planets have to be replenished of particles continuously because the particles that comprise the rings eventually get ground down to dust which, in turn, spirals into the planet. Thus, majestic ring systems like those of Saturn cannot last forever.

Question 11. - #50. Mass of Io is 8.9 x 10²² kg. If you lose 1 x 10³ kg of sulfur dioxide to Jupiter’s magnetosphere every second, then in 1 year you would lose 3.2 x 10¹⁰ kg of mass. In 4.5 x 10⁹ years, you would lose a total of 1.4 x 10²⁰ kg. This is 0.0016 of the total mass or 0.16% (not a lot). However, since sulfur dioxide makes up only 1% of Io, that would be 8.9 x 10²⁰ kg of sulfur dioxide. In that case, in 4.5 billion years you would lose 16% of the total. At that rate it would take you almost 30 billion years to lose all of this gas.

Question 12. - #55. The radius of Titan is 2575 km and its mass is 1.35 x 10²³ kg . If the exosphere is 1400 km above the surface, this makes the escape velocity 2.1 km/s. For hydrogen, the thermal velocity at 200 K is 1.8 km/s. So, hydrogen is likely to leave Titan relatively rapidly.