Download ASTR 1110H – Fall 2004

ASTR 1110H – Fall 2004
Exam 2 – Solutions - November 4, 2004
Short answer questions (2 points each):
1. Which plays the greater role in determining the seasons on Earth, its location in its
orbit (e.g., perihelion vs. aphelion) or the tilt of its rotational axis?
The tilt of its rotational axis.
2. The “efficiency” of the Sun’s thermonuclear fusion process is 0.0071. What does that
mean?
0.71% of hydrogen is converted into energy (the rest goes into forming
helium).
3. Can the iron meteorites come from differentiated parent bodies? Why or why not?
Yes, because the irons are metals and it’s the metals of high density that sink
to the center of a differentiated body.
4. What are the two most prominent locations of asteroids in the solar system?
The asteroid belt and the Trojan asteroids.
5. How many tails does a comet have and what are they?
Two tails: the ion tail and the dust tail.
6. What is the source of the long-period comets? What is the source of the short-period
comets?
Long-period comets come from the Oort Cloud; short-period comets come
from the Kuiper Belt.
7. What is the explanation for why we experience meteor showers?
The Earth passes through the dust trail left behind by a comet.
8. How many astronauts have walked on the Moon?
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9. Is the crater density greater in the Moon’s highlands region or the lunar maria? Does
a higher crater density imply an older age or a younger age?
The crater density is larger in the highlands region. A higher crater density
implies an older age.
10. Suppose the Earth were closer to the Sun (let’s say at a distance of 0.9 AU instead of
1 AU). Would Mercury be seen more often or less often? Why?
Mercury would be seen more often because the angle between Mercury and
the Sun would be larger.
11. What physics principle is used to obtain rotational velocities of planets using radar?
The Doppler effect.
12. Suppose the radius of the Earth were smaller than it really is. Would the tides caused
by the Moon be larger or smaller? Why?
The tides would be smaller because the difference between the near side and
the far side of Earth would be smaller. Think of the Moon’s tidal effects on
you, for example. They are non-existent because the distance between your
head and your feet is so small compared to the distance between you and the
Moon.
13. As a result of tidal forces, the Moon’s distance from the Earth is slowly changing. Is
it getting closer or moving farther away? Will solar eclipses be more or less common in
the future?
The Moon is moving farther away and, as a result, solar eclipses will be less
common in the future (because the Moon won’t be able to cover up the Sun
anymore).
14. What is thought to be the source of the polar caps on Mercury?
Comet impacts.
15. What is the preferred explanation for the origin of the Moon?
The Collision-Ejection hypothesis.
16. How does the temperature in the Earth’s stratosphere change with altitude? Why
does it change that way?
It increases (unlike the troposphere). It does so because ozone absorbs much
of the Sun’s UV radiation.
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17. Provide a brief description of the way the Earth’s greenhouse effect works.
The Earth’s atmosphere is transparent to visible (and some UV) radiation
from the Sun. This radiation strikes the surface of the Earth, heating it. The
Earth then reradiates that heat as infrared radiation, but the Earth’s
atmosphere is opaque to those wavelengths, so the heat is retained.
18. Venus orbits the Sun in the same direction as every other planet, but rotates in a
retrograde direction. If its orbit were also in a retrograde direction, would the Sun rise in
the East or the West?
The Sun would still rise in the West, because orbital motion does not effect
sunrise or sunset.
19. Does tectonic activity occur on Venus? Do plate tectonics occur on Venus?
Tectonic activity (stretching and compression) does occur on Venus, but
plate tectonics do not.
20. Why is there a shortage of small craters in the Martian uplands?
They have been eroded by Martina dust storms.
Slightly longer answer questions (4 points each):
21. Suppose you lived on the Earth-facing side of the Moon and your best friend lived on
the Earth. When your friend was seeing a new moon, what would you see for Earth?
Would it be daylight or dark where you live?
You would see a “full-Earth.” It would be dark where you live.
22. The electron in a hydrogen atom jumps from the first excited state to the ground
state. Has the atom absorbed or emitted energy? Is the amount of energy greater than if
it had jumped from the first excited state to the second?
The atom has emitted energy. The amount of energy is greater in going from
the first excited state to the ground state (emission) than in going from the
first excited state to the second (absorption).
23. Will a comet last “forever”? If so, why? If not, why not?
No, because it loses about 0.01 to 0.1% of its dust and gas every trip through
the inner solar system. After a few thousand trips, there’s nothing left.
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24. Planetary scientists believe that there must have been a period of heavy bombardment
early in the Moon’s history, after which the rate of impacts dropped precipitously and
became nearly constant. If, instead, the impact rate had declined steadily from a high rate
to a low one, would our estimate of the lunar maria’s age be older or younger than our
current estimate? Why?
Our estimate would be that the maria are younger. This is because the
impact rate required to give rise to the number of craters seen in the maria
would have occurred much later (i.e., more recently).
25. Why do planetary scientists think that the Moon has maria (but no scarps) and that
Mercury has scarps (but no maria)?
The Moon has maria because the Moon expanded enough for fissures to
form, permitting volcanic lava to flow and give rise to the maria. Mercury
has scarps because Mercury contracted, causing the surface to compress and
buckle, forming the hilly regions known as scarps.
26. Why do we think that the Earth’s core is partially molten or liquid?
Two reasons: (1) the Earth has a magnetic field, which arises because of the
currents that are created in its hot liquid or molten core that is rapidly
rotating (period = 24 hours) and (2) seismological studies tell us that shear
waves, generated by earthquakes and not capable of traveling through liquid
or molten material, are not traveling through the Earth’s center.
27. How does the process of plate tectonics work?
The continental plates, located in the Earth’s lithosphere, move laterally,
driven by slow convection in the underlying mantle.
28. Provide one explanation of why plate tectonics do not occur on Venus.
Two possible explanations are: (1) The surface temperature of Venus is so
hot that its crust is too soft to move as a rigid plate and (2) the absence of
water may limit convective motions in the underlying mantle.
29. Why is Mars’s Olympic Mons so big?
It sits on top of what used to be an active mantle plume and, since there were
never any plate tectonics on Mars, just continued to grow until the plume
became inactive. Also, Mars’s gravity is relatively small, allowing volcanic
features to grow much larger than they would on, say, Venus or Earth.
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30. Which occurred earlier, Mars’s runoff channels or its outflow channels? What is the
evidence for your conclusion?
Mars’s runoff channels occurred first. The runoff channels were probably
similar to rivers on Earth. In order for them (and surface water in general)
to have existed on Mars, its atmosphere must have been thicker, which is
what occurred long ago in Mars’s past. The outflow channels are thought to
have arisen from surface collapse (chaotic terrain) that melted and unleashed
massive amounts of subterranean permafrost. Also, the runoff channels only
appear in the old southern hemisphere, while the outflow channels stretch
from the south to the north.
Problems (10 points each):
31. Suppose an astronomer discovers a new planet in our solar system. And, after a
while, it is determined that the planet has a synodic period of 2 years.
(a) Can you determine from this information alone whether the planet is an inferior
(closer to the Sun than the Earth) or superior (farther from the Sun than the Earth) planet?
If yes, how? If no, what else might you want to know?
No, you need more information. One thing you’d want to know is whether
the planet can be seen at midnight – if so, then it must be a superior planet.
(b) Calculate the new planet’s orbital period, in either case.
If the planet is inferior, then 1/PInner = 1/POuter + 1/PSynodic = 1/1 + 1/2 = 3/2 and
the inferior planet’s orbital period is 2/3rds of a year. If the planet is
superior, then 1/POuter = 1/PInner – 1/PSynodic = 1/1 – 1/2 = 1/2 and the superior
planet’s orbital period is 2 years.
32.
(a) Suppose Venus still has its atmosphere (and its high Bond albedo of 0.75), but that it
does not provide a greenhouse effect. Calculate its expected surface temperature in this
case. Venus’s semi-major axis is 0.72 AU.
You need to use the equation I gave you in class: Tp = To (1 – A)1/4 ÷(Ro/2D).
In this equation, To is the surface temperature of the Sun (5800K), Ro is the
radius of the Sun (7 x 108 m [On the test, I gave you the value for the
diameter; sorry]), A is the Bond albedo, and D is the distance of Venus from
the Sun (0.72 AU x 1.5 x 1011 m/AU). Plugging all of those values in gives a Tp
= 233 K.
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(b) Now suppose Venus has no atmosphere and that its surface is as black as coal (and
thus has an albedo of 0). What is its surface temperature in this case?
The only thing that’s changed between this question and the previous
one is the value of the albedo; now it’s set equal to zero. Again plugging in
the values, we get Tp = 330 K.
(c) Explain why your answers to parts (a) and (b) are self-consistent.
The two answers are self-consistent because a lower albedo means less light is
reflected and more is absorbed. If more is absorbed, then the surface
temperature should be higher (and it is, 330 K vs. 233 K).
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