ASTR 1010 – Homework Assignment 11

Chapter 9 – Spring 2009

Question 1 - #2. Differentiation is the sinking to a planet’s core of heavy material. This means that the metals are primarily in the core, with the less dense rock above it in the mantle. The lowest density stuff makes up the crust and solidifies fastest because it is where the temperature gradient is steepest (i.e., the difference between the temperature of the crust and interplanetary space is the greatest over a relatively small distance). A steep temperature gradient leads to rapid cooling.

Question 2 - #3. The lithosphere is the relative rigid outer layer of a planet; generally encompassing the crust and the uppermost portion of the mantle. It isn’t listed as one of the three layers because the upper part of the mantle has the same average density and so both the lithosphere and the upper part of the mantle form the layer known s the crust. The lithospheric thickness varies from thick to thin as the size of the planet increases (see Figure 9.2).

Question 3 - #4. Planet interiors get hot by accretion, differentiation, and radioactive decay. Large planets retain heat more than cold planets because heat is held by the volume of the planet while cooling occurs via the surface. Thus the ratio of heating to cooling is proportional to r³/r² = r. So the larger the planet, the larger r, and the larger the rate of heating to cooling. Thus, large planets retain more heat than smaller planets that have a smaller heating to cooling rate.

Question 4. - #5. Earth has a global magnetic field because part of its core is molten and the planet rotates fairly rapidly. The resulting convecting motion of charged particles sets up a magnetic field. The Moon and Mars cooled off rapidly and have no molten core. Venus rotates too slowly, and Mercury is an enigma: Even though the planet cooled rapidly, its core must still be partially molten and convecting.

Question 5. - #6. The four major geologic processes are: 1) Impact cratering, volcanism, tectonics, and erosion. They are defined on page 264. Examples are shown in Figures 9.7 to 9.14.

Question 6. - #7. Outgassing is the process of releasing gases from a planetary interior, usually through volcanic processes. This is the mechanism by which Earth, Venus, and Mars produced their secondary atmospheres…or so the book says. As I mentioned in class, there is currently a controversy about how much of the secondary atmosphere was brought to these planets by impacting icy planetesimals.

Question 7. - #8. After the era of heavy bombardment, the cratering rate was (and is) pretty much constant. Thus, the number of craters per unit area can be used to approximately date the surfaces. The Moon’s surface hasn’t tectonically changed in over 4 billion years, so it carries the scars of all the impacts on its surface, while the Earth basically resurfaces itself within ¼ of a billion years.

Question 8. - #9. A picture is worth a thousand words: see Figure 9.15.

Question 9. - #11. Mercury died geologically very quickly. Its surface is covered with impact craters and what little volcanism there was before the crust became too thick produced small lava plains. There is tectonic evidence of planetary shrinking in the form of vertical cliff faces of 3 or more km in height. This was caused by a buckling of the crust as the massive interior core shrunk a bit while the planet cooled. There is no atmosphere so there is no erosion and the planet looks pretty much like it did 4 billion years ago.

Question 10. - #12. 1) The Tharsis Bulge was produced by volcanism. 2) Tectonics produced Valles Marineris. 3) Impact craters are evident in the southern hemisphere, so this part of the surface is older. 4) Eroded craters are evident in some of the southern regions (see Fig. 9.29a). 5) Windblown dust is evident in Fig. 9.28.

Question 11. - #13. There are lots of photos from the martian surface that show clear evidence of being made by a fast-moving liquid. The only liquid that makes any sense given the temperatures and likely atmospheric pressures on an early Mars is water. Today, the atmospheric pressure is too low for water to exist on the martian surface. If any subterranean water was released (by some subterranean volcanic-type heating) it would quickly freeze or sublimate. Remember there is lots of frozen water on Mars.

Question 12. - #14. 1) Volcanic peaks on Venus are produced much like shield volcanoes on Earth. These contrast with the stratovolcanoes (see Fig. 9.34) which were built from thicker lava. 2) Some tectonic features (not plate tectonics like on the Earth) produced twists and fractures on the crust. 3) Impact craters are present, though rare because Venus does resurface itself (though not as quickly as the Earth) and the thick atmosphere plays a role in eroding and preventing some craters.

Question 13. - #15. Crater counts indicate that the surface of Venus is about 750 million years old. Venus’ lithosphere is not cracked into plates like that of the Earth because it may be thicker and stronger than that of the Earth…but we don’t really know.

Question 14. - #16. Take a look at Figure 9.39. Seafloor crust is younger than the continental crust.

Question 15. - #57. Kinetic energy is just ½ mv² . We know the velocity (2 x 10⁴ m/s), but we don’t know the mass. We can get the size and volume of the asteroid…but to get the mass, we still need to know the density (because mass = density times volume). We are going to have to guess the density. Let’s assume the asteroid was rocky. Then, its density is 3000 kg/m³. If it was made of metal, then its density would be about 6000 kg/m³, so we would be off only by a factor of 2 which in this type of problem is unimportant. Now, the volume is (4/3)pr³ so we need to plug in half the diameter for r, and, with that, we get 5.2 x 10⁸ m³ . The mass is then 1.6 x 10¹² kg. So, the kinetic energy is ~ 3 x 10²⁰ Joules. This is 750 times more energy than is released in a 100 megaton blast.

Question 16. - #58. Three trillion watts is 3 x 10¹² J/s. This has to leak out through the Earth’s surface area. So, over 1 square meter, we have 3 x 10¹² / (4pr²) . For the radius, use 6.4 x 10⁶ m. The radiation due to radioactive decay leaking out of each square meter of the Earth’s surface is thus about 0.006 J s^-1 m^{-2 .} Internal heating drives internal activity because in the lower mantle it’s the only source of heat. Sunlight, only heats the top of the lithosphere.

Question 17. - #60. One centimeter is 1 x 10^-5 km . Thus, the area produced in one year is 1 x 10^-5 km times 2000 km = 0.02 km² . This is a rate of 0.02 km² /yr , so in a 100 million years, this would be 2 million square km. This is 0.004 of the Earth’s surface.