Download Homework Solutions: Chapter 17: The Earthlike Planets

Homework Solutions: Chapter 17: The Earthlike Planets
[RQ- 1,4, 7,12,&15. Problems: 1,3,&7]
RQ 17-1
What are the four stages in the development of a terrestrial planet?
Answer:
The four stages of evolution in the development of a planet are differentiation, cratering,
flooding, and slow surface evolution. Differentiation is the process of heavier elements
sinking to the core of a planet while its interior is molten. Cratering occurs by impacts
with asteroids or planetesimals. There appears to have been an era of intense cratering in
the inner solar system in the past. Flooding occurs when magma from under the surface
oozes from cracks or craters in the planet’s surface. This molten material forms relatively
smooth plains over the surface. Also condensed water from the cooling atmosphere can
produce flooding. Slow surface evolution can include plate tectonics, volcanism, and
wind and water erosion.
RQ 17-4
Why do we suspect that Earth’s primeval atmosphere was rich in carbon dioxide?
Answer:
There are two reasons that we believe that Earth’s primeval atmosphere was rich in
carbon dioxide. First it appears that the terrestrial planets formed in a hot environment.
This means that only fairly heavy atoms and molecules would have been held to the
planet by gravity. The lightweight elements like hydrogen and helium would have been
moving so fast that they would easily escape from the surface. Secondly, Earth grew from
accreting planetesimals, which were rich in volatiles like water and carbon dioxide.
Therefore CO2 was added to the atmosphere during this phase of evolution. In addition to
this, it is known that the Earth’s mantle contains large amounts of CO2, which is still
brought to the surface by volcanoes. The young and cooling Earth must have out gassed a
lot of this gas during its first two stages of development.
RQ 17-7
Discuss the evidence and hypotheses concerning the origin of Earth’s moon.
Answer:
There are basically four hypotheses concerning the origin of the moon. The fission
hypotheses suggest that the moon broke from a rapidly spinning proto-Earth. This break
would have had to have occurred after Earth differentiated or the moon would have about
the same mean density as Earth, which is not so. The condensation hypothesis is based on
Earth and the moon forming simultaneously in the solar nebula as sister planets, this
predicts that the composition and mean density of the two should be identical but this is
not so. The capture hypotheses proposes that the moon was formed somewhere else in the
solar system and was captured by Earth’s gravitational field. However, if the moon got
close enough for Earth to capture it, Earth’s gravitational field would have torn it apart.
Finally, the large-impact hypothesis proposes that the moon formed as a large
planetesimal and collided with Earth. The impact was glancing and shattered the
planetesimal and put much of the debris from the collision in orbit around Earth. Such an
impact would have melted the protomoon, and the material falling together to form the
moon would have been heated hot enough to melt. This fits our expectation that the moon
formed as a sea of magma.
RQ 17-12
Q: Why is the atmosphere of Venus rich in carbon dioxide? Why is the atmosphere of
Mars rich in carbon dioxide?
A:
The atmosphere of Venus is rich in carbon dioxide because it outgassed much CO2 from
the rocks while it was hot. Since Venus is relatively close to the sun and never formed
extensive liquid water oceans, the CO2 remained in the atmosphere. Mars, like Earth and
Venus, outgassed a significant amount of carbon dioxide, as well as oxygen and nitrogen.
There is evidence that Mars did form liquid water on its surface. Ultraviolet radiation
from the sun would have broken up the water molecules, because Mars did not form an
ozone layer to absorb the ultraviolet radiation. The hydrogen from the broken up water
molecules could easily escape from Mars. As a result, Mars was without water oceans for
a long time and the new CO2 (from volcanoes) did not dissolve out of the atmosphere as
it did on Earth.
RQ 17-15
Q: What evidence do we have that there has been liquid water on Mars?
A:
There are two types of erosion on the surface of Mars that indicate the presence of liquid
water at some point in Mars’ past. The first consists of large flood plains that appear to be
created by large scale flooding of a region. The second is the presence of meandering
drainage valleys. These valleys show long-term erosion due to flowing liquid. Also,
within the last months the mars landers have found direct evidence of salt deposits on the
surface. These could only have been deposited as the result of evaporated water.
Problems:
Problem 17-1
If the Atlantic seafloor is spreading at 3 cm/year and is now 6400 km wide, how long ago
were the continents in contact?
Solution:
Converting the speed of 3cm/year to km/year and using the formula:
6400 km
= 213x10 6 years
km
3x10 −5
year
Which is about 213 million years ago, the continents were in contact.
t=
D
=
v
Problem 17-3
The smallest detail visible through Earth-based telescopes is about 1 second of arc in
diameter. What size is this on Earth’s moon? (Hint: See By the Numbers 3-1)
Solution:
Using the small-angle formula:
θ
d
=
206,265 D
Here, θ = 1 arc sec.
Average distance between the Earth and moon is D= 3.84 X 108 m
Putting these numbers in the above formula we get
1
d
=
206,265 3.84 x10 8
3.84 x10 8
⇒d =
= 1861.7 m ≈ 1.86 km
206,265
Hence the smallest detail visible through Earth based telescopes is 1.86km in size.
Problem 17-7
Imagine that we have sent a spacecraft to land on Mercury, and it has transmitted radio
signals to us at a wavelength of 10 cm. If we see Mercury at its greatest angular distance
west of the sun, to what wavelength must we tune our radio telescope to detect the
signals? (Hints: See Data File 4 to find Mercury’s orbital velocity, and then see By the
Numbers 6-2.)
Solution
At its greatest angular distance west of the sun, we see Mercury receding from us with a
radial velocity equal to its orbital velocity:
V
Mercury
Sun
Earth
The average orbital velocity of Mercury is v=47.9km/sec and this is in our case also the
speed at which Mercury recedes from us. With the Doppler formula (Numbers 6-2.) one
can calculate the red shift of the λ=10 cm radio signal as it reaches us:
km
v
s = 1.60 × 10 −3 cm
Δλ = λo r = 10cm
km
c
300000
s
47.9
Therefore, the wavelength at which we have to search for the signal is
λ = λo + Δλ = 10cm + 0.0016cm = 10.0016cm ≈ 10.002cm
REMARK:
This problem is different from the problem in your Astronomy lab (Rotation of
Mercury)! In that lab, you calculate the Doppler shift of a wave that was emitted from
Earth towards Mercury and then reflected by Mercury back to Earth. In such a case, one
gets double the Doppler shift than when the wave was emitted directly by a spacecraft on
Mercury.