AY204 – Exam #2 Name: _____Key__________________
Multiple Choice: Circle the letter corresponding to the correct answer.
1) According to our present theory of solar system formation, which of the following
best explains why the solar nebula ended up with a disk shape as it collapsed?
A) The force of gravity pulled the material downward into a flat disk.
B) The law of conservation of energy.
C) It was fairly flat to begin with, and retained this flat shape as it collapsed.
D) It flattened as a natural consequence of collisions between particles in the
2) What is the primary basis upon which we divide the ingredients of the solar nebula
into four categories (hydrogen/helium; hydrogen compound; rock; metal)?
A) The locations of various materials in the solar nebula.
B) The atomic mass numbers of various materials.
C) The amounts of energy required to ionize various materials.
D) The temperatures at which various materials will condense from gaseous
form to solid form.
3) Among the planets in our Solar System, the planets closest to the Sun have the largest
A) rock and metal
B) hydrogen molecular compounds ("ices")
C) hydrogen and helium
D) liquid metallic hydrogen
4) Why are Mercury and the Moon geologically dead compared to Venus and Earth?
A) they are smaller than Earth, so they lost their internal heat faster
B) they are made only of crustal rock, which is geologically inactive
C) they have no atmospheres, so there is no greenhouse feedback
D) they lack an iron core
5) According to our present theory of solar system formation, which of the following
statements about the growth of terrestrial and jovian planets is not true?
A) The terrestrial planets formed inside the frost line of the solar nebula and the jovian
planets formed beyond it.
B) Both types of planet began with planetesimals growing through the process of
accretion, but only the jovian planets were able to capture hydrogen and helium gas
from the solar nebula.
C) The jovian planets began from planetesimals made only of ice, while the
terrestrial planets began from planetesimals made only of rock and metal.
D) Swirling disks of gas, like the solar nebula in miniature, formed around the growing
jovian planets but not around the growing terrestrial planets.
6) Suppose you find a rock that contains 10 micrograms of radioactive potassium-40, which
has a half-life of 1.25 billion years. By measuring the amount of its decay product (argon-
40) present in the rock, you conclude that there must have been 80 micrograms of
potassium-40 when the rock solidified. How old is the rock?
A) 3.75 billion years
B) 1.25 billion years
C) 2.5 billion years
D) 5.0 billion years
7) The choices below describe four hypothetical planets. Which one would you expect to
have the most features of erosion? (Assume the planets orbit a star just like the Sun and
that they are all the same age as the planets in our solar system.)
A) Size: same as Venus. Distance from Sun: same as Mars. Rotation rate: once every
B) Size: same as the Moon. Distance from Sun: same as Mars. Rotation rate: once every
C) Size: twice as big as Earth. Distance from Sun: same as Mercury. Rotation rate: once
every 6 months.
D) Size: same as Mars. Distance from Sun: same as Earth. Rotation rate: once every 24
8) Why did the solar nebula heat up as it first began to collapse?
A) Nuclear fusion occurring in the core of the protosun produced energy that heated the
B) As the cloud shrank, its gravitational potential energy was converted to kinetic
energy and then into thermal energy.
C) Radiation from other nearby stars that had formed earlier heated the nebula.
D) Collisions among planetesimals generated friction and heat.
9) Why are the inner planets denser than the outer planets?
A) The Sun's gravity pulled denser materials toward the inner part of the solar nebula,
while lighter gases escaped more easily.
B) Denser materials were heavier and sank to the center of the nebula.
C) In the inner part of the nebula only metals and rocks were able to condense
because of the high temperatures, whereas hydrogen compounds, although more
abundant, were only able to condense in the cooler outer regions.
D) In the beginning, when the protoplanetary disk was spinning faster, centrifugal forces
flung the lighter materials toward the outer parts of the solar nebula.
10) Why did the planets eventually stop accreting material in their growth process?
A) All material in the solar nebula was eventually consumed by the accretion process.
B) The solar wind from the newly formed Sun blew away the remaining unaccreted
C) The Solar System became too cold to allow planets to accrete material.
D) Jupiter diverted all the remaining material to the Oort cloud.
11) Which of the following statements is false?
A) P-waves are longitudinal waves.
B) S-waves are side-to-side waves.
C) P-waves but not S-waves move through liquids.
D) S-waves but not P-waves move through liquids.
12) Today, the most significant source of internal heat in terrestrial planets is
A) radioactive decay
B) flexing from tidal forces of the Sun
C) gravitational contraction
D) absorption of the Sun’s radiation
13) Of the following, which lists all correct energy transport mechanism:location
relationships in terrestrial planets?
A) conduction: inner mantle; convection: lithosphere; radiation:surface
B) conduction: lithosphere; convection: inner mantle; radiation:surface
C) conduction: surface; convection: inner mantle; radiation:lithosphere
D) conduction: lithosphere; convection: surface; radiation:inner mantle
14) Which of the following is most important in determining how fast a planet or moon loses
its internal heat?
A) presence or absence of an atmosphere
B) distance from Sun
C) surface area-to-volume ratio
D) mean density of interior
15) Which of the flowing statements about cratering is false?
A) Most cratering occured in the early Solar System.
B) Craters are about 10 times wider than the object that made them.
C) Small craters greatly outnumber large craters.
D) The lunar maria are more heavily cratered than the lunar highlands.
16) The layer of the Earth’s atmosphere defined as where infrared radiation from the Earth’s
surface is most important is the
17) Aurora (Northern or Southern Lights) are caused by
A) charged particles from the Sun colliding with high air molecules
B) sunlight reflecting from the polar ice caps
C) internal heat from the Earth
D) geological features near the poles
18) Metallic hydrogen exists:
A) within all planets and moons
B) within all the planets
C) within all the gas giant planets
D) within only Jupiter and Saturn
Short Answer – 1-2 sentence explanations (3 pts each)
19) Suppose the Earth cools down somewhat. Describe how the CO2 cycle will eventually
drive Earth’s temperature back to its long-term average.
If Earth cooled down, then there would be less evaporation from the oceans leading to
less rainfall. With less rainfall, there would be less CO2 removed from the atmosphere
and the greater amount of CO2 in the atmosphere would lead to more heating, which
would heat the Earth back up.
20) Explain why determining cratering rates on planets and moons allows us to determine
how old the surface of the body is.
Craters are erased by erosion, tectonic, or volcanic activity. The fewer craters we see on
a surface, the younger the surface must be. Following the period of Great
Bombardment, the cratering rate decreased significantly. By counting craters on a
given part of a planetary surface, we know how long it has been since erosion, tectonic,
or volcanic activity has erased the craters made before the activity.
21) Name two specific Solar System anomalies that are not explained simply by the nebular
Earth’s large moon
Venus’s retrograde rotation
Uranus’s 90° rotation axis (rotates on its side)
22) Name two pieces of evidence that imply liquid water used to flow on the surface of Mars.
Highly eroded craters
Apparent dry riverbeds
23) Describe what is meant by the “frost line” of a solar system. Between which two planets
is the frost line in our Solar System?
The distance from the Sun dividing the region where hydrogen compounds can and
cannot condense into ices. Planets inside the frost line will be made only of metal and
rock, while planets outside the frost line will also have frozen ices. This line occurs
between Mars and Jupiter.
24) Explain why some lava is runny while other lava is very thick. Which kind of lava are the
lunar maria made of, runny or thick?
If gases are trapped in the molten rock as it cools, the lava will have higher viscosity,
and the lava will be thicker. The lunar maria lava was made of runny lava.
Problem Solving (10 pts each). Please show all work to receive full credit.
25) By what factor would Jupiter’s radius need to expand such that the escape velocity from
its cloud tops would be equal to the escape velocity from the surface of Earth? Assume
the mass of Jupiter is 319 Earth masses and its radius is currently equal to 11.2 Earth radii.
By what factor would its density change if this occurred?
vescape = sqrt(2GM/R), so if we want the escape velocity from an inflated Jupiter to be the
same as on the surface of Earth, we simply want M/R to be the same for the two planets.
Since Jupiter is 319 times more massive than Earth, Jupiter’s radius will need to increase to
319 times that of Earth. So, Jupiter must increase in size by 319/11.2 = 28.5 times.
If Jupiter’s radius increases by 28.5 times while keeping the same mass, its density will
decrease by a factor of (28.5)3 = 23,150
26) Calculate the escape velocity from a location 500 km above the cloud tops of Saturn
(M = 95 MEarth, R = 9.5 REarth). If Saturn were suddenly moved to the location of Earth,
would it be able to retain 4He in its atmosphere? Assume that the temperature in Saturn’s
atmosphere would rise to 300 K, and assume that an atmosphere is eventually lost if the
average thermal velocity of a particle is 20% or greater of the escape velocity.
vescape = sqrt(2GM/R)
= sqrt[(2*6.67 x 10-8 cgs * 95 * 6.0 x 1027 g/(9.5*6.4 x 108 cm + 5 x 107 cm)]
= 3.52 x 106 cm/s = 35.2 km/s
average thermal velocity of 4He = sqrt(3kT/mHe)
= sqrt(3 * 1.38 x 10-16 ergs/K * 300 K/4 * 1.67 x 10-24 g )
= 1.36 x 105 cm/s = 1.36 km/s
Clearly, the average thermal velocity is less than 20% of the escape velocity at an
altitude of 500 km, so the 4He will not escape in appreciable amounts.
27) It’s very well known (to woo-woos) that the planet Nibiru is on a highly elliptical orbit
around the Sun that brings it close to Earth once per orbit. During this close approach, the
alien race known as the Annunaki visit Earth to make humans mine for gold to put in
Nibiru’s atmosphere to reflect sunlight to keep Nibiru warm when it is far from the Sun.
Recently, NASA scientists secretly found an Annunaki wool scarf left on Earth from the
last time our Annunuki overlords visited. The scarf has 64.5% of its original 14C
remaining (which has a half-life of 5700 years). Given that Nibiru is certain to return in
2012, what is the semi-major axis of Nibiru? Assume Annunaki sheep have the same
isotopic abundances as Earth sheep. Extra credit (2 points): What is wrong with the
argument about gold in Nibiru’s atmosphere?
For radioactive decay, N(t)=N(0)* (1/2)t/t_half-life, so log10(N(t)/N0)= t/t_half-life * log10 (1/2),
t = -t_half-life * log10(N(t)/N0)/log10 (1/2) = 5700 years * log10(0.645)/log10 (1/2) =
3605 years for the age of the scarf.
Since Nibiru returns in 2 years, this means the period of Nibiru is 3607 years.
Since this is a Solar System object, we can use Kepler’s simplified 3rd law:
P2 = a3, so a = P2/3 = (3607 years)2/3 = 235 AU semimajor axis for Nibiru.
28) The Earth absorbs about 247 Watts/m2 from the Sun. Since we know that the amount of
heat from radioactivity is negligible compared to this, the Earth must be radiating away
like a blackbody in the infrared at the same rate if 247 Watts/m2. Using this value,
derive the temperature on the surface of the Earth in the absence of greenhouse heating.
What is the peak wavelength that the Earth is emitting? Determine the reflectivity
(albedo) of the Earth.
From Stefan-Boltzmann Law, the energy density is given as:
E = σT4 T = (E/σ)1/4 = (247 Watts/m2/5.67 x 10-8 MKS)1/4 = 257 K
From Wien’s displacement law, λpeakT = 0.29 cm K λpeak =0.29 cm K /257 K
= 1.1 x 10-3 cm
Tno greenhouse = 280 K * [(1-albedo)/d2 (AUs)]1/4
albedo = 1 - (Tno greenhouse /280 K)4 * d2 (AUs)) = 1 – (257 K/280 K)4 * 12 AU2