Homework Problem Set II
[59 points total]
 

Planetary surfaces & geologic processes.

1. Describe the history and current location of H2O, if any, on (a) Mars, (b) Venus, and (c) Io. [6 points]
 

2. Name at least one planet besides Earth and at least one satellite that could have once had large oceans of liquid water. Cite evidence. [4 points]
 

3. (a) What does the layered structure of the martian polar deposits imply about the history of martian climate?  (b) Cite 3 lines of evidence for climate change on Mars. [4 points]


4.  Consider the large sizes of some martian volcanoes.  Why are they present on Mars and absent on Mercury and the Moon?
[4 points] 

x

5. Assuming radiative equilibrium (see below):

(a) At which distances from the sun (in AU) will an icy body show cometary activity? [3 points]

(b) Can main belt asteroids, with semi-major axis a ~ 2 - 3.5 A.U., be made substantially of water ice? [4 points]

(c) Discuss implications for stable ground ice on Ceres (semi-major axis = 2.77 AU, albedo = 0.11), for which Dawn data indicate subsurface ground ice at polar latitudes. [3 points]

Show all calculations. HINT: For radiative equilibrium, set the incident flux (Fin) of light absorbed on a rotating planetary surface equal to the flux of light radiated from the planet (Fout). (This equality reflects conservation of energy.)  Assume that ice on the surface of this body will sublimate when temperatures reach 273 K or higher, and that this will result in apparent cometary activity.  For part (a), perform calculations for a representative mid-latitude (p = 30 degrees) on a rotating body with (a) an albedo A = 0.7 ( a comet with fairly clean ice exposed at the surface; take this as an upper limit to the albedo), and (b) with an albedo A = 0.03 (a comet mantled by dark carbonaceous material; take this as a lower limit to the albedo).  Formulas: Fout = (1-A)/pi * cos p * F/a2 where A = albedo, pi = 3.1415, p = latitude on rotating body, F = solar flux at 1 A.U. (solar constant) = 1.36 x 103 J/m2s, and a = distance from sun in A.U.; Fin = e S T4 where e = emissivity (assume 0.2), S = Stefan-Boltzman constant (= 5.67 x 10-8 J/m2K4s), and T = temperature in degrees K .  

 
Petrology

6. How would discovery of wide regions of granite on Venus imply a history different from that implied by discovery of a wholly basaltic or gabbroic crust? [2 points]
 

7. Why is Mars red, and what does this imply about the geologic history of Mars? [2 points]
 

8. Why might evaporite deposits be common on some outer solar system satellites if they had near-surface heat sources such as tidal heating or radiogenic heating? What surface material is most common on these bodies in the absence of such heating? In your answer, discuss Io.  [3 points]
 

Interplanetary worldlets.

9. (a) Assuming that manned space vehicles continue to evolve, what materials do meteorites suggest might be available in interplanetary space that would be useful in space exploration? (b) Depending on the destination, why might it cost less energy (hence money) to haul raw materials from a near-Earth asteroid (approaching Earth at, say, 5 km/s) than to haul the materials from Earth's surface? For part b, estimate the ratio of energy required to obtain material from the earth to the energy required to obtain material from the approaching asteroid. [6 points]
 

10. Describe some possible solutions to the paradox that most belt asteroids are C type, whereas only a small fraction of meteorites are carbonaceous chondrites. [2 points]
 

11. Give some lines of evidence that many asteroids melted very early in their histories but that the melting was not smoothly correlated with asteroid size. [3 points]
 

Planetary atmospheres.

12. Why is a cloudy night likely to be warmer than a clear night if other conditions are the same? Why is a night in a clear, high desert colder than a night on the beach if the noontime temperatures are the same? Relate these events to the greenhouse effect. [3 points]
 

13. Optical depth is a dimensionless quantity that expresses the amount of light intensity lost for a beam of light. For an optical depth of 1, light is dimmed by a factor of ~2.7 (i.e., a value of e1). Describe the surface climate on an imaginary planet in Earth's orbit with an atmosphere that has white clouds of optical depth 10 in the visual region of the spectrum but optical depth 0.1 in most of the infrared. [2 points]
 

Solar nebula and planet formation.

14. Why does Titan, which resembles a terrestrial planet, have a nitrogen-methane atmosphere when terrestrial planets have nitrogen-carbon dioxide-water vapor atmospheres (or volatile inventories)? [3 points]
 

15. You are traveling through space and come to a star of normal solarlike composition, but with planets composed of refractory silicate minerals rich in aluminum, titanium, and calcium, and containing no water or ice. What can you conclude about formation conditions? [2 points]
 

16. Citing their distance from the sun, temperature history, and gravity, give two reasons why the giants planets have so much more volatile and icy material and mass than do terrestrial planets. [3 points]
 
 



 
 

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