Download Astronomy 1400: Homework 7

Astronomy 1400: Homework 7
Due in class, Friday, November 7
Name:
Instructions: To receive partial/full credit you must show your work or explain your answer thoroughly. Please circle your final answer to each problem
if it is a number.
1. (10 points) What is the frost line and how does it explain the formation of the inner
and outer planets?
The frost line marked the key transition between the warm inner regions of the solar
system where terrestrial planets formed and the cool outer regions where jovian planets
formed. Inside it, only metal and rock could condense, but outside of it, it was cold
enough for hydrogen compounds to condense into ices. This meant that the outer planets
could grow faster and even get massive enough to keep a hold of light elements (hydrogren
and helium), enabling runaway accretion. This is why the inner planets are mostly made
of rock and the outer planets are mostly made of the same elements contained in the
Sun.
When astronomers first started looking for planets around other stars, the first type of planets
they found were systems with hot Jupiters. These are planets with the size and composition
of Jupiter orbiting so close to their parent star (many inside the orbit of Mercury) that their
atmospheres are heated to very high temperatures.
2. (10 points) Does the nebular theory naturally explain/predict these planets? How/Why?
No, they were a surprise.
3. (5 points (bonus)) Do a little research on hot Jupiters and explain one way how these
planets could be so close to their parent stars.
Planetary migration - Hot Jupiters form far out and migrate towards the star by interacting with material in the disk
Gravitational interaction - Gas giants are forced close to their star by interacting with
another gas giant in the system, sending one inward and the other outward.
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4. (10 points) A lot of archeological dating uses 14 Carbon (5700-year half life) to date bone,
cloth, wood and plant fibers created by ancient humans. Your friend, who happens to
be into dinosaurs, suggests that you should use 14 Carbon to date dinosaur bones. Is this
a good idea? Why or why not? What about using 14 Carbon to estimate the age of the
solar system from a meteorite?
No, it is not a good idea to use 14 Carbon to date either because they half life is much
smaller than the timescales you are probing. There will be so little 14 Carbon to compare
to that you will not be able to make a measurement in either case.
5. (15 points) What is the leading hypothesis for the Moons formation? Name two pieces
of evidence that support this hypothesis.
The Earth would have a really hard time capturing an object so massive. The Moon
orbits in the same direction (and about in the same plane) that the Earth rotates. The
average density is low (the metal content of the core is low). The chemical makeup of
the Moon rocks matches the mantle makeup extremely well.
6. (5 points (bonus)) Name a third piece of evidence.
See the list in the problem above.
7. (9 points) About how much more quickly/slowly should Mars cool off than Mercury?
We know the planets’ interiors cool at a rate proportional to their surface area to volume
ratio, which scales with 1/r. So we just compare the radii of Mars and Mercury.
rmoon
rM ercury
So Mercury cools off at
71.2%
=
1740 km
= 0.712
2440 km
of the rate that the Moon cools off. An alternate
but equally valid way of saying it is that the Moon cools off
Mercury.
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1.40
times faster than
8. (16 points) What are the four major processes that shape the surface of a planet and
give examples of a feature created/shaped by each.
• Cratering by impacts of meteors, asteroids, or comets
Ex. Tycho crater on the Moon, Crater Lake in Oregon, Meteor Crater in Arizona...
• Erosion - wearing away of solid material by some fluid, either gaseous (wind) or
liquid (rain, rivers, etc)
Ex. The Grand Canyon, river deltas, many other possible examples
• Volcanism
Olympus Mons, Mount St. Helens, Vesuvius, Kilauea, the Hawaiian Islands, etc.
• Tectonics
San Andreas Fault, Pacific “Ring of Fire”, Himalayas, etc. Example must be from
Earth, as Earth is the only planet with tectonic plates in the solar system.
9. (10 points) Internal versus External Heating In daylight, Earth’s surface absorbs about
400 W/m2 . Earth’s interal radioactivity produces a total of 30 × 1012 W that leak out
through our planet’s entire surface. Calculate the amount of heat from radioactive decay
that flows outward through each square meter of Earth’s surface (your answer should
have units of W/m2 ). Compare quantitatively to solar heating, and comment on why
internal heating drives geological activity.
To get the energy flux of heat from radioactivity inside the Earth, we need to divide the
total power produced (30 × 1012 W) by the area through which it escapes - the surface
2
)
area of the Earth (A = 4πrEarth
A = 4π(6.378 × 106 m)2 = 5.11 × 1014 m2
There is a typo in the amount of heat produced through radioactivty - it should be
3.0 × 1012 W instead of 30 × 1012 W, but we will work it through with the numbers you
were given as it does not change the conclusion. The energy flux through the Earth’s
surface from radioactivity is then
F lux =
Power
3 × 1013 W
=
= 5.87 × 10−2 W/m2
14
2
Area
5.11 × 10 m
So 5.87 × 10−2 Watts per square meter of internal heat energy escape Earth. That’s
much smaller than the power received by the Sun! This means that the temperature of
the surface must be set by incoming radiation from the Sun, not from internal energy
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sources. This energy has to work it’s way out of the Earth, though, while incoming Solar
energy does not; it is already at the surface when it gets here. Volcanic activity starts
below the surface, out of the reach of the Solar energy. Because of this placement, even
though the number is smaller, tectonic activity must be driven by Earth’s interior heat.
10. (10 points) Typical motion of one plate relative to another is 1 cm/yr. At this rate, how
long would it take for two continents 3000 km apart to collide? What are the global
consequences of motion like this?
©
3000 ©
km
d
×
t= =
»
v
1»
cm/yr
µ
»
100, 000 »
cm
©
1©
km
¶
= 300, 000, 000 yr
Multiple Choice: Choose the best answer.
11. (5 points) Which of the terrestrial worlds has the strongest magnetic field?
A.
B.
C.
D.
E.
Mars
Earth
the Moon
Venus
Mercury
12. (5 points) What is differentiation in planetary geology?
A. the process by which gravity separates materials according to density
B. the process by which different types of minerals form a conglomerate rock
C. any process by which a planet’s surface evolves differently from another planet’s
surface
D. any process by which one part of a planet’s surface evolves differently from another
part of the same planet’s surface
E. any process by which a planet evolves differently from its moons
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