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Homework #5 Solutions
Questions due at the beginning of lecture on April 11, 2000.


From Chapter 11.

Question 3. The greenhouse effect.
The greenhouse effect is a process by which heat from sunlight is trapped in a planetary atmosphere.  There are two properties of an atmosphere that contribute to the greenhouse effect.  First, the atmosphere must let some sunlight through to the surface of the planet, usually in the form of UV radiation.  Second, heat (infrared radiation) from the sun-warmed planet surface must be reflected downward by the atmosphere.  Both the atmospheres of Venus and Earth exhibit the greenhouse effect: temperatures on Venus are very high because of it.  Earth's temperature is raised by about 30 degrees C by the greenhouse effect.  Both planets would be much different places without the greenhouse effect.  Venus would be much more hospitable and the Earth much less so.

Question 6.  Evidence for active volcanos on Venus.  Changing levels of sulfurous compounds in Venus's atmosphere measured by Pioneer Venus are the primary evidence for current volcanic activity on Venus.  Sulfur and other chemicals detected by Pioneer Venus are known to come from volcanic eruptions on the Earth.  Also, lightening strikes similar to those seen during volcanic eruptions on  Earth have been detected on Venus.

Question 9.  Carbon dioxide in Venus's atmosphere.  Venus has so much more carbon dioxide in its atmosphere than Earth because there are currently no processes on Venus by which carbon dioxide can be absorbed.  On the Earth, CO2 is absorbed by plants during photosynthesis.  Also, CO2 is dissolved into liquid water and from there into carbonaceous rocks like limestone.  Venus currently has neither plants or liquid water.

Question 12.  Venus's continents compared to Earth's.  Venus has two continents, Aphrodite Terra and Ishtar Terra.  These continents are vertical displacements in Venus's relatively weak crust due to internal pressure.  The crust of Venus is probably too thin to beak up into independent plates the way Earth's crust has.  Thus, the Earth-like continents, formed by plate collisions or subductions are absent on Venus.

From Chapter 12.

Question 3.  The craters of Mercury, the Moon and Mars.  The craters of the Moon and Mercury are very similar.  There are no atmospheric processes on these bodies to weather the craters (other than nearby meteor impacts).  Mars, on the other hand has an atmosphere that blows dust around.  The dust naturally collects in the bottoms of craters (the effect of the crater rim is like that of a snow fence).

Question 5.  Meteor impact craters vs volcanic craters on Mars.  Volcanic craters are at the tops of mountains.

Question 6.  Comparing the volcanos of Venus, Earth, and Mars.  Venus and Mars have large shield volcanos.  These volcanos are formed by magma flowing to the surface in a weak point in the crust (a hot spot) and spilling out of the surface in the form of lava.  Olympus Mons on Mars and Theia Mons on Venus are two such volcanos.  Earth also has shield volcanos, but because the crust is broken up into plates that move, Earth's shield volcanos move away from the hot spot (or the vent closes due to other plate motion) before they get very big.  The islands of Hawaii are an excellent example of the effect of plate motion and hot spot volcanism,

Question 9.  The effect of Martian atmosphere on terrain.  Liquid water cannot exist on Mars now because it is too cold and the atmosphere it too thin.  The presence of river valleys and flood planes is clear evidence that liquid water did at one time flow, so it follows that the atmosphere was at least thicker, and probably warmer too.  The fact there there are so many craters on Mars indicates that Mars's atmosphere thinned out long ago.  Otherwise more craters would have been erased by wind and water erosion.

Question 18.  Mass of Mars from Phobos orbit data.  This is a problem for Newton's form of Kepler's 3rd law.  Let's solve it carefully.  I like to use a multi-column approach to keep my work organized.  In the first column, I write down the basic equation.  In the second column, I write down the values of the variables I need, putting a question mark for the variable I am trying to find.  It is helpful (but not essential) to think ahead about what units you want everything to be in.  Generally, we have been using MKS units, that is meters, kilograms, and seconds.  So on on lines 2 and 3, I convert the orbital period of Phobos to seconds.  G is Newton's universal constant of gravity, which was introduced in chapter 4.  Note that Newtons (N) can be converted to kg m/s2.  We are trying to find the mass of Mars and we don't know the mass of Phobos, but it is such a small moon, we can safely say it its mass is 0 compared to Mars.  In lines 10 and 11 I derive 'a', the semimajor axis of the orbit of Phobos.  You can get this from its altitude plus half Mars's diameter (line 10) or from the value of a given in the Appendix 3.  They are only slightly different.  Now that we have all of our numeric values, in column 2, we can solve the equation in column 1 for the variable we are looking for (m1).  Doing the algebra with the symbols takes a lot less writing than doing it with the numbers.  When you have an equation for the variable you want, then plug in.  Notice how nicely all the units cancel out in step 16 (step 19 for the other value a).  If units don't cancel, at this point, you can convert them.  make sure then cancel before your quote your final answer!  In this case, the final answer must be in units kilograms, since we are looking for a mass.  Generally, I carry lots of decimal places while I do the problem to avoid round off errors and then at the end, I look up column 2 and find the smallest number of significant digits of an variable value.  This is the maximum number significant digits that I am allowed to quote in my answer.

Question 21.  Mars at opposition.  The phase of Mars (as seen by Earth) when it is at opposition is "full."  The Earth's phase seen from Mars is "new."

Question 22.  Craters on Tharsis Rise.  The craters on Tharsis Rise are likely to have formed after the rise and the volcanos on the rise.  Otherwise, they would likely be covered in (or at least modified by) lava flows from the volcanos.
 



 
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