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PHYS 175, FALL 2014
HW #4 S OLUTION
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8.4 What is the evidence other stars existed before our Sun was formed?
About 98% of the entire solar system’s mass (Sun, planets, moons, asteroids, debris,
etc.) is H and He. Since the Sun’s mass limits it ability to fuse elements together, it is
only capable of making He out of H. Only much more massive stars and energetic
events like supernovas can manufacture the heavier elements. So any elements in
the solar system heavier than He must have been produced elsewhere, in other stars
that are now long gone.
8.9 The half-life for uranium-238 in Box 8-1 is 4.5 billion yr. There is plenty of
uranium-238 in Earth, and much of Earth’s heat comes from the radioactive decay of this isotope. Compared to today, about how much more uranium-238 was
there when Earth formed? (Hint: See Box 8-1)
The solar system (and, hence, the Earth) is about 4.54 billion years old, and this is
roughly the same as the half-life of 238 U (4.5 billion years). That means that there
was approximately twice as much 238 U was present when the Earth formed. In another 4.5 billion years, we’d expect only a quarter of the original 238 U to be present,
or half of what we observe today.
8.16 Why are terrestrial planets smaller than Jovian planets?
There are two primary drivers for this difference: temperature and abundance. The
farther away from the protosun at the center of a solar nebula, the cooler it gets.
For a given substance, there is a distance which marks the transition from solid to
gaseous phases of that substance (since temperature falls off with distance). Given
the substances in the nebula that gave rise to the solar system, only about 0.6% of
them can exist in solid form within about 2 AU of the center of the solar system –
these are the constituents of rocks and the base metals. So the rocky planets will be
the smallest, because there was less material available to build them.
8.34 What does it mean for a planet to transit a star? What can we learn from such
events?
In some cases, the alignment of the Earth-star-exoplanet may be such that the exoplanet passes directly in the line of sight between the Earth and star. While these
alignments are relatively rare, we can learn four important things from the transit
technique. First, we can deduce the actual mass of the exoplanet (not just a lower
bound). We can also learn the diameter, atmospheric composition and temperature
by analyzing the differences in light during various phases of the transit.
PHYS 175, FALL 2014
HW #4 S OLUTION
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9.23 Describe Earth’s magnetosphere. If Earth did not have a magnetic field, do you
think auroræ would be more or less common than they are today?
Earth’s magnetic field is similar to the dipole field of a bar magnet, but is induced
by currents in a liquid metal core in motion (the dynamo). Unlike the field of a bar
magnet, the Earth’s magnetic field is distorted by interactions between the Sun’s
magnetic field and the solar wind (a stream of charged particles constantly given
off by the Sun). This causes the field to be compressed on the sunward side, and
stretched into a tail on the anti-sunward side. The region inside this field, where
charged particles are dominated by the Earth’s magnetic influence, is called the
magnetosphere. Arouræ require a body with a magnetosphere (strong magnetic
field) and an atmosphere. The former concentrates field lines near the magnetic
poles, and hence charged particles which strike the constituents of the latter, giving
rise to auroral emissions. Without a magnetic field you would not really have what
we call auroræ, but rather what is technically known as a non-organized aurora
over the entire atmosphere. It would pretty much be optical background noise from
a visual perspective. Saturn’s large satellite, Titan, has such non-organized auroræ
– it has no magnetic field, but a dense atmosphere (it’s the only moon in the solar
system with one).
10.3 Why does the sky look black from the Moon even during daytime?
Since the Moon has no atmosphere, there is no scattering of light. This means that
if you’re not looking at the Sun directly, there is nothing to cause the sunlight to
be deflected to your eyes, so you see only the black of space (or other stars). On
Earth, blue light scatters more easily than red, so we see blue even when we are
not looking at the Sun. At high altitudes, where there dis less atmosphere to scatter
light, you begin to see the darker type of sky, even on Earth.
10.9 Describe the differences between the near and far sides of the Moon. What is
thought to be the likely explanation for these differences?
Both the near and far sides are characterized by older, heavily cratered highlands
which are relatively light in color. The near side has many smooth (few craters)
maria that are dark in color, but the far side has almost none. This is thought to
stem from the difference in the crust on the near and far sides. The crust on the far
side is thought to be thicker than the near side, so even major impacts failed to crack
it and allow lava to flow. Since lava flows form the younger maria, there are only a
very few small ones to be found on the far side.
PHYS 175, FALL 2014
HW #4 S OLUTION
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10.20 On the basis of Moon rocks brought back by the astronauts, explain why the
maria are dark-colored but the lunar highlands are light-colored.
Maria rocks are composed of mare basalt, a darker, denser igneous rock. The highland rocks are made up of anorthosite, a lighter colored and less dense rock. The
less dense rocks would have come to the surface more quickly as the Moon formed
and cooled, so they comprise most of its visible surface.
10.28 In a whimsical moment during the Apollo 14 mission, astronaut Alan Shepard hit
two golf balls over the lunar surface. Give two reasons why they travelled much
farther than golf balls do on Earth.
There is no lunar atmosphere, so there is no drag (wind resistance) on the ball. Secondly, the gravitational force of the Moon on the ball is less than that it would have
been on Earth. So due to a combination of these effects, the ball carries farther.
10.30 How much would an 80-kg person weigh on the Moon? How much does this
person weigh on Earth?
On both Earth and Moon the person would have 80 kg of mass. Their weight is the
same as the gravitational force exerted by the Earth (or Moon) on the person. On
Earth, that would be W = 80 kg · 9.8 m/s2 ≈ 780 N (or about 175 lb). The Moon’s
gravitational acceleration is about 1/6th that of Earth, so WM = W /6 ≈ 130 N (or
about 30 lb).