Download Astronomy 1400: Homework 9

Astronomy 1400: Homework 9
Due in class, Friday, November 21
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) Using data in Appendix E, identify the orbital resonance relationship between Titan and Hyperion. [Hint: If the orbital period of one were 1.5 times the other,
we would say that they were in a 3:2 resonance.] Which medium-sized moon is in a 2:1
resonance with Enceladus?
We can get the orbital periods from Appendix E. Titans period is 15.945 days while
Hyperions is 21.277 days. Taking a ratio of the two periods will give us an idea of the
21.277 days
= 1.33 which is 4/3, so Titan and
resonance they are in. The ratio is:
15.945 days
Hyperion are in a
4 : 3 resonance.
From Appendix E, Enceladus has a period of 1.370 days. A moon with a 2-to-1 resonance
with Enceladus would have to have either twice the period or half the period. Twice
this period is 2.740 days, while half the period is 0.685 day. Looking down the list of
orbit periods of the moons in Appendix E, we see that Dione has a period of about 2.737
days. No medium moons have periods around 0.685 day, so Dione is the moon that
is in the 2-to-1 resonance with Enceladus.
2. (10 points) Suppose someone announced they had discovered that a previously unknown
moon around Jupiter had been discovered in an orbit outside other known moons which
was the smallest of Jupiter’s moons and had several active volcanoes. Is this claim
credible? Why or why not?
This is not plausible. Tidal forces are too weak on objects so far away, and they are not
forced into elliptical orbits by resonances. It would also be too small to have volcanoes
from radioactive heating.
3. (10 points) Briefly describe Jupiter’s weather patterns. What is the Great Red Spot?
Jupiter has bands of alternating winds like Earth, but Jupiter has many more bands
because of the planets rapid rotation and great size. Jupiter also features powerful
storms. These include the famous Great Red Spot, a spinning storm system that is rather
like Earths hurricanes, except that it spins in the wrong direction. Unlike terrestrial
hurricanes, the Great Red Spot has lasted for several centuries.
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4. (10 points) Why is Jupiter so much denser than Saturn? Could a planet be smaller in
size than Jupiter but greater in mass?
Jupiter is denser than Saturn due to the pillow effect. As extra mass is added to the
planets, the lowest layers of gases compress more under the added weight. So as we add
gas to the jovian planets, they can grow denser as Figure 11.2 indicates. Figure 11.2
also shows that if a planet were to grow more than about three times more massive than
Jupiter, adding more gas would actually result in making the planet shrink in radius in
order to accommodate the extra weight.
5. (10 points) How do clouds contribute to Jupiter’s colors? Why do color bands on Jupiter
rotate in different directions?
The different cloud layers are made of different chemicals and therefore apparently reflect
light differently. This explains why Jupiter has different-color clouds in its atmosphere.
Each of these bands exists at a different depth of the atmosphere, and so are at different
temperatures. Coriolis effects split the convection cells into many stripes, and are also
responsible for their alternating rotations as convection to the north is diverted one way,
and to the south, the other.
6. (10 points) What evidence is there for liquid water on Europa beneath the surface ice?
The evidence for a Europa ocean is strong, but all indirect: Strictly speaking, we have
not directly detected liquid water because it would be too far below the ice. We have
observed the following indirect evidence:
• The fractured surface ice shows there is tidal heating as on Io which could provide
a heat source to melt some of the ice.
• There are few impact craters on the surface, so the ice must be fairly young, i.e.
replenished by liquid water flows analogous to geologic activity.
• Maps of the gravitational field of Europa indicate a low density layer of ice or water
100 km thick around the rocky core and mantle. Modeling the interior suggests
that tidal heating will melt the lower layers into either liquid water or convecting
“mushy ice”.
• Finally, Europa has a strong magnetic field induced by the rotation of Jupiter’s
magnetic field, which is only possible in the presence of a conducting layer of liquid
such as a salt water ocean beneath the surface. Evidence of salt on the surface
supports this idea.
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7. (15 points) You have discovered two new asteroids and named them Albert and Isaac.
Both lie at the same distance from the Sun and have the same optical brightness when
you look at them through a telescope, but Albert is twice as bright as Isaac at infrared
wavelengths. What can you deduce about the relative reflectivities and sizes of the two
asteroids? Which would make a better target to mine metal? Which would make a
better target for a mission to collect a sample of a carbon rich planetesimal? Explain.
Because Albert emits a higher proportion of thermal emission (infrared) than of reflected
light (visible), it must be warmer than Isaac. This means it must be darker (in order
to be warmed by the Sun). Because Albert has a lower reflectivity than Jordan, it must
be larger in order to appear as bright. Isaac would make a better candidate for mining
metal, and Albert a better candidate for carbon-rich material.
8. (10 points (bonus)) A relatively small impact crater 20 kilometers in diameter (as large
as a city!) could be made by a comet 2 kilometers in diameter travelling at 30 kilometers
per second (30,000 m/s). Assuming typical densities for a comet made of ice and rock,
it would have a mass around 4.2 × 1012 kg. What is it’s total kinetic energy in Joules?
What is this in terms of tons of TNT? [Hint: 1 megaton of TNT releases 4.2 × 1015
Joules of energy.]
1
1
KE = mv 2 = × (4.2 × 1012 kg) × (3 × 104 m/s)2 =
2
2
1.9 × 1021 J¢
=
4.2 × 1015 J¢ /megaton
450, 000 megatons
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1.9 × 1021 J
Multiple Choice: Choose the best answer.
9. (5 points) Which of the following does not yield information on jovian planet interiors?
A.
B.
C.
D.
E.
Earth-based observations of the mass and size of the planets
spectroscopy of the cloud layers
spacecraft measurements of magnetic and gravitational fields
laboratory studies and theoretical models
detailed observations of planetary shapes
10. (5 points) The belts and zones of Jupiter are
A.
B.
C.
D.
E.
alternating bands of rising and falling air at different latitudes
cyclonic and anticyclonic storms.
names for different cloud layers on Jupiter.
alternating regions of charged particles in Jupiters magnetic field.
the thermosphere and stratosphere respectively.
11. (5 points) What mechanism is most responsible for generating the internal heat of Io
that drives the volcanic activity?
A.
B.
C.
D.
E.
accretion
radioactive decay
differentiation
tidal heating
bombardment
12. (5 points) When we see a meteor shower, it means that
A. the solar wind is unusually strong.
B. an Earth-approaching asteroid has recently come very close to our planet.
C. you should duck and run for cover to avoid being blasted on the head by a rock from
space.
D. Earth is crossing the orbit of a comet.
13. (5 points) Why are Saturns rings so thin?
A. Saturns gravity prevents particles from migrating upwards out of the rings.
B. Thegapmoons shepherd the particles and maintain its thin profile.
C. Any particle in the ring with an orbital tilt would collide with other ring
particles, flattening its orbit.
D. Solar radiation pressure keeps particles pressed into the rings.
E. The current thinness is a short-lived phenomenon that is special to this time.
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