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Astronomy 10: Introduction to General Astronomy
Instructor: Tony Piro, [email protected]
Homework #5: Solutions
Chapter 15
(1) page 364, question 5
If you see a red nebula around a blue star, then it is an emission nebula . The red color comes from
the absorption and re-emission of light from the blue star, which is dominated by the 2 to 3 transition in
hydrogen (also called Hα emission). If the cloud were instead a reflection nebula, then the nebula would
appear blue, similar to the color of the light is was reflecting from the star.
(2) page 364, question 6
Harlow Shapley noticed that the positions of globular clusters where not distributed uniformly in the sky.
Instead they appear to have a common center that is away from the Sun. By assuming that the globular
clusters orbited around the center of the galaxy, he was able to derive the distance between the Sun and the
galactic center.
(3) page 364, question 7
The Sun is 8 kpc (8000 pc) away from the center of our Galaxy. Since 1 pc ≈ 3.1 × 1013 km, one orbit
around the galaxy is a distance of
d = 2πr = 2π × 8000 pc × 3.1 × 1013 km/pc = 1.6 × 1018 km
Using the relationship d = V t, we can solve for the time it takes for one orbit
v = d/t = 1.6 × 1018 km/(200 km/s) = 7.8 × 1015 s = 250 million years
(4) page 364, question 14
The brightness of car headlights is instinctively thought to follow the inverse-square law. In this way you
can judge the brightness of an oncoming car. In the fog, the apparent brightness can be decreased, making
a car look further away than you would guess from instinct. In the same way, stars in the plane of the Milky
Way can look farther than they really are because of gas and dust.
Chapter 16
(5) page 394, question 1
The Shapley-Curtis debate centered around the question of whether spiral nebulae are clouds within the
Milky Way or distinct systems, separate and distant from the Milky Way galaxy. Once it was realized that
these nebulae are distant galaxies like our own Milky Way, it greatly increased the understood size of the
Universe.
(6) page 394, question 6
Trigonometric parallax is only used for measuring the distance to nearby stars. For distant stars, the
amount of parallax is just too small to measure. For galaxies, such a measurement is even more difficult
because of there immense distance. Instead we use other distance indicators, such as Cepheid variables to
measure the distance to galaxies.
(7) page 394, question 8
The rotation curve of the Milky Way Galaxy is essentially flat. In contrast the rotation curve of the Solar
System decreases with distance from the Sun. In the latter case, this is because the gravitational pull of the
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Sun dominates the planet’s orbits. In the case of the Milky Way, dark matter is required to explain why the
outer stars are orbiting at such great velocities.
(8) page 394, question 23
The redshift of the galaxy is
z=
144
∆λ
6707 Å − 6563 Å
=
=
= 0.022
λ0
6563
6563 Å
Such a galaxy is moving at 0.022 times the speed of light.
(9) page 394, question 24
The speed of the galaxy is 0.03 times the speed of light, or V = 0.03 × 3 × 105 km/s = 9000 km/s. The
distance is
d=
9000 km/s
V
=
= 130 Mpc
H0
71 km/s/Mpc
Chapter 18
(10) page 451, question 5
(a) When we say that “the Universe is expanding,” we mean that space itself is expanding.
(b) Although galaxies appear to be flying apart from each other, they are not actually moving through
a preexisting space. They are moving apart because of the expansion of space itself.
(c) Objects that are bound (for example, gravitationally like a galaxy or star, or electromagnetically like
humans) do not actually expand. The space is expanding underneath these things, but these forces still hold
them together at the same size. It is space between non-bound objects that is seen to be expanding.
(11) page 451, question 15
The cosmological constant is an energy that fills space with a constant density of energy. It acts like an
“anti-gravity” causing space to actually accelerate its expansion.
(12) page 451, question 18
The critical density of the Universe is the critical amount of material needed in the Universe to determine
eventual contraction or expansion forever. If the critical density is greater than one, then the Universe is
over dense, and will eventually collapse on itself. If the critical density is less than one, then the Universe will
expand forever, always with a positive expansion. If the critical density is exactly one, then the expansion
of the Universe asymptotes to zero infinitely in the future.
(13) page 452, question 22
Supernovae are used as standard candles to measure distances to distant galaxies. This is then compared
to the redshift of these galaxies, which provides their velocities. By comparing changes in the velocities at
different distances (which corresponds to different times) we can infer whether there is acceleration (changes
in the velocities).
The expectation was that the velocities should be decreasing (deceleration) because of the attractive force
of gravity. In fact, what the supernova measurements showed was that the Universe is now accelerating,
consistent with the repulsive aspect of the cosmological constant.
Chapter 19
(14) page 479, question 3
The cosmic microwave background (or CMB) corresponds to the photons that decoupled from matter
when the electrons and protons combined into atoms 400,000 years after the Big Bang. Before this time,
the photons could easily be absorbed and re-emitted by the electrons (like in a black body) because the free
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electrons could absorb any energy photon. Once the electrons were bound in hydrogen atoms, only certain
energies could be absorbed and emitted, so most photons were left unaffected.
The temperature that corresponds to when this happened was about 3000 K, so the Universe was filled
with black body radiation at this temperature. Over time, the expansion of the Universe stretched the
wavelength of these photons and now it corresponds to a temperature of 2.7 K.
(15) page 479, question 6
The cosmic microwave background is full of tiny ripples. These small temperature (and density) inhomogeneities correspond to the overdensities that eventually became the superclusters that we see today.
Furthermore, the size of the ripples can be used to measure the shape of the Universe, demonstrating that
the Universe has a flat geometry.
(16) page 479, question 11
The original Big Bang theory did not explain the incredible uniformity of the Universe nor its flat
geometry. By uniformity we mean that when we look at the CMB in opposite directions in the sky, they
have the same temperature (with small differences in ripples), but these two regions could never have been
casually connected (because even light is not fast enough to pass information between them). By flatness we
mean that Ω = 1. This is somewhat surprising because this is an unstable situation. What I mean by this is
that if Ω were slightly greater than 1, then the Universe would collapse and Ω would be much much greater
than 1. If Ω were slightly less than 1, then the Universe wold expand and Ω would become much much less
than 1 (nearly zero). Ω can only be 1 if it has always been exactly 1. The original Big Bang theory did not
explain why this should be so finely tuned.
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