PTYS/ASTR 206 – Section 2 – Spring 2007
Homework #3 (Page 1/4)
NAME:____KEY________________________________________________________
Due Date: start of class 3/1/2007
 5 pts extra credit if turned in before 9:00AM (early!)
(To get the extra credit, the assignment must be placed the box outside of room 330!)
 5 pts taken off if turned in after the start of the class period and before 5PM of the due
date (late!)
 The assignment will not be graded if turned in later than 5PM 3/1/2007 (too late!)
Turn in your own work. It is not acceptable to turn in work that is identical to that of another
student. You may work together to understand the material, but the work you turn in must be in
your own words.
There are 3 parts, plus an extra-credit part. Please put your answers to all questions to PARTS 12 in the space provided (you may use the back of the page if necessary).
PART 1 (25 pts total): Conceptual. Please provide a concise short answer (not more than a few
sentences) for each of the following.
# 1. (5 pts) (Chapters 9) Describe the greenhouse effect. What is the difference between the natural and
human-induced greenhouse effects? What is a runaway greenhouse effect? What planet has an
atmosphere that is an example of this phenomenon?
The greenhouse effect occurs when a planet’s atmosphere contains certain gasses that make the
atmosphere act as a thermal blanket. Incident solar radiation, accounting for most of the heating
of Earth’s surface, peaks in the visible part of the spectrum. Radiation emitted by Earth’s surface
peaks in the infrared and is absorbed by greenhouse gasses (e.g. CO2, H2O) in the atmosphere and
cannot escape directly. Because of the absorption of Earth’s emitted energy by these gasses, the
resulting equilibrium is at a higher temperature than if the greenhouse gasses were not present.
Such gasses have existed long before humans because of volcanic outgassing; however, humans
have increased the amount of greenhouse gasses in the atmosphere since the industrial revolution
– this increases the greenhouse effect and warms the planet further (this is global warming).
When there is no way to remove greenhouse gasses from the atmosphere and they are continually
increased at the same time (such as volcanic outgassing), a “runaway” greenhouse effect occurs.
This process is believed to have happened on Venus. Note that on Earth, the presence of water
(and rain!) leads to the removal of much of the atmospheric CO2, which then becomes locked into
the rocks on the surface (which is where you will find most of the CO2 on Earth).
# 2. (5 pts) (Chapter 9) Describe three ways in which the Earth is unique among the planets of our solar
system
1. Earth has liquid water – other planets do have water, but none of them are in liquid
form as it can be on Earth because of Earth’s thick atmosphere, which provides
pressure, and warm temperatures
2. Earth has plate tectonics – no other planets show evidence for this which is a result of
Earth’s rigid crust and “plastic” asthenosphere
3. Earth has an oxygen-rich atmosphere – no other planets have O2 in a significant
amount. This is a result of life on Earth.
4. Earth has life –we keep looking, but haven’t found life on any other extraterrestrial
body!
PTYS/ASTR 206 – Section 2 – Spring 2007
Homework #3 (Page 2/4)
# 3. (5 pts) (Chapter 9, #8) The deepest wells and mines go down only a few kilometers. What, then, is
the evidence that iron is abundant in the Earth’s core? What evidence is there that the Earth’s outer core
is molten but the inner core is solid?
First, because of the analysis of the propagation of seismic waves, we know that Earth’s interior is
differentiated and has a solid inner core (we know this because of a slight P signal in the shadow
zone due to refraction through the solid core), a liquid outer core (we know this because the shear,
or S, waves do not propagate through liquid and there is a “shadow” zone created on the opposite
side of the planet from where the Earthquake occurred), a mantle, and a rigid crust. We also
know that Earth’s mean density is much more than the density of rocks on the surface. Thus,
there must be a substance that is very dense in the interior. Iron is a good candidate because it is
the most abundant heavy ion in the solar nebula (see figure 8-3 of the textbook). It also has some
nickel mixed in because this is another abundant element. Also, the presence of Earth’s magnetic
field indicates that the metal must be electrically conducting, which iron is, hence we are quite
certain that our core is made of iron.
# 4. (5 pts) (Chapter 9) How has Earth’s atmosphere changed over time, in both the short (i.e.
centuries) and long term (i.e. geologic eras)?
In the last 100 years or so, humans have affected our atmosphere by increasing the amount
of greenhouse gasses which leads to global warming. Moreover, humans are also
responsible for the ozone hole over the southern pole, but this seems to be decreasing in size
(again because humans recognized what they were doing and stopped it – lets hope that it
isn’t too late for global warming too!). Earth’s first atmosphere was probably mostly HHe, but these gasses were lost because they are light and Earth is rather hot. Because of
volcanic outgassing, Earth’s second atmosphere probably had a lot of water vapor and
CO2. Disassociation of these gasses by solar UV led to a small amount of free oxygen in the
atmosphere which was used by the first organisms on the planet. As more life evolved,
more O2 was created until it reached the level that it is presently. Note that nitrogen is also
outgassesd by volcanoes, in the form of NO2, but nitrogen is inert, so it stays in the
atmosphere – this is why N2 is the dominant component of Earth’s atmosphere today.
# 5. (5 pts) (Chapter 9) Explain how Earth’s volcanoes play a vital role in keeping our planet
warm.
Volcanoes put greenhouse gasses (like carbon dioxide, water vapor, etc.) into the atmosphere and,
in fact, replenish the CO2 that is washed out of the atmosphere by rain. The greenhouse effect
only works if there are greenhouse gasses present in the atmosphere. Having more greenhouse
gasses in the atmosphere increases the effect. The rain, in fact, removes a portion of the
greenhouse gasses, and volcanic outgassing replenish them. As we will see when we discuss Venus,
this is an important component to the cycle that exists on Earth.
PTYS/ASTR 206 – Section 2 – Spring 2007
Homework #3 (Page 3/4)
PART 2 (15 pts total): Quantitative
# 1. (5 pts) (Chapter 9: #25 of the textbook) On average, the temperature beneath the Earth’s crust
increases at a rate of 20oC per kilometer. At what depth would water boil? (Assume the surface
temperature is 20oC and ignore the effect of the pressure of overlying rock on the boiling point of
water).
Water boils at 100ºC; starting at the surface, we need 80ºC more. At the rate of 20ºC per km, this
would require 4 km depth.
D
100C  20C
 4km
20C / km
# 2. (5 pts) (Chapter 9: #30 of the textbook) Africa and South America are separating at a rate of about
3 cm per year. Assuming that this rate has been constant, calculate when these two continents must have
been in contact. Today, the two continents are 6600 km apart.
The time required for Africa and South America to separate by 6600 km equals that distance
divided by the speed of separation (3 cm/yr):
6600 km 6.6  103 km

3cm/yr 3  10 –5 km/yr
 2.2  108 yr
So Africa and South America began moving apart about 220 million years ago. The text states 200
million years ago, which is close enough.
# 3. (5 pts) (Chapter 9 and lecture #12) Earth’s atmospheric pressure decreases by a factor of one-half
for every 5.5 km increase in altitude above sea level. At about what altitude is the pressure in Earth’s
atmosphere equal to that at the surface of Mars (0.007 bar, where 1 bar is the pressure at sea level on
Earth)? What region of Earth’s atmosphere (troposphere, stratosphere, etc.) is this?
Height above surface
0 km
5.5 km
11 km
16.5 km
22 km
27.5 km
33 km
38.5 km
44 km
Air pressure
1 bar
0.5 bar
0.25 bar
0.125 bar
0.0625 bar
0.0313bar
0.0156 bar
0.0078bar
0.0039bar
By inspection of this table, it appears that the
altitude at which Earth’s atmospheric pressure
is that same as that at the Martian surface is
about 40 km, which is in the stratosphere.
Note that we could also arrive at the answer with
the formula P = 2-h/5.5, where h is the height in
km. This equation is solved by taking the log of
both sides to give logP = -h/5.5 log2, which gives
h = -5.5km log(P)/log(2)
Inserting P = 0.007 bar, we get
h = -5.5 log(0.007)/log(2) = 39.4 km.
PTYS/ASTR 206 – Section 2 – Spring 2007
Homework #3 (Page 4/4)
PART 3 (10 pts total): Starry Night Backyard Observing Problems
Please provide your answers on a separate sheet of paper and attach it to the rest of your homework.
# 1. (5 pts) Ch 7, #42 of the textbook
Mercury: blotchy. The features are definitely not clouds are are probably craters (we know that
they are, but from Earth this is hard to see)
Venus: very hard to see any features. What can be seen seems banded, most likely is clouded over
entirely. The surface cannot be seen.
Mars: reddish with dark brown blotches and white polar caps. These features are definitely not
clouds and are probably mountain ranges, and other rough terrain. Large craters (like Mare) can
also be seen.
Jupiter: Banded with 2 conspicuous dark brown bands and a giant red spot and many other small
ovals and similar features embedded within the bands. These are definitely clouds. The surface
cannot be seen.
Saturn: Obviously a ringed planet, banding can also be seen. This is definitely cloud cover. The
surface cannot be seen.
Uranus: Dull green color. This is certainly cloud cover, but with no noticeable features. The
surface cannot be seen.
Neptune: Bluish color with a noticeable dark spot. This is also cloud cover. The surface cannot be
seen.
Pluto: Too small to see any detail.
# 2. (5 pts) Ch 9, #51 of the textbook
(a) you can see evidence for plate tectonics in that there are clearly mountain ranges as well as
continents that would seem to have once been in contact with one another
(b) you can see evidence for life in that there are large green areas indicating plant life. There is
also indirect evidence of life in the huge oceans indicating liquid water.
It would be difficult (but not impossible) to see such evidence from remote observations alone.
That is why sending spacecraft is very important.
PART 4: Extra Credit
Points available: 2 for one, 5 for both
Please provide your answers on a separate sheet of paper and attach it to the rest of your homework.
E.C. #1 Chapter 9, #27 of the textbook
According to Table 9-3, the inner core has an average density of 13,000 kg/m3 (1.3x104 kg/m3) and a
radius of 1300 km (1.3x106 m). The volume of the inner core is
v
3
4 3 4
πr  π 1.3  106 m   9.2  1018 m3
3
3
The mass of the inner core is therefore
M   9.2  1018 m3   1.3  104 kg/m3 
 1.2  1023 kg
The mass of the entire Earth is 5.974  1024 kg, so the inner core fraction is
1.2 10
23
5.974 10
kg 
24
kg 
 .02 or 2%
E.C. #2 Chapter 9, #24 of the textbook
The temperature is related to the total emitted flux by the Stefan-Boltzmann law. The problem
gives the total radiated flux as 0.06 W/m2. Thus, using the Stefan-Boltzmann law and solving for
the temperature, we get
T
4
F 4
.06 W/m2

 32 K  241o C
8
2
4
σ
5.67  10 W/m  K