AST 101 Spring 2008
Chapter 17 Weekly Problems
from Astronomy: A Beginner’s Guide to the Universe 5/E
NOT TO BE TURNED IN!
Complete and understand the Review and Discussion questions and the Problems to
prepare for the quizzes.
Review and Discussion:
Q2, Q4, Q5, Q9, Q13
Q2. What is the cosmological principle?
The cosmological principle is made up of two assumptions fundamental to cosmology. They
are homogeneity and isotropy. At a large enough scale, the universe is homogeneous; one
part is pretty much like any other part. Isotropy means that it looks the same in all
directions. The cosmological principle tells us there can be no edge to the universe and there
is no center to it either.
Q4. Explain how an accurate measure of Hubble’s constant can lead to an estimate of the
age of the Universe.
Hubble’s law is a relationship between velocity of recession of objects in the universe and
their distance, v = H0d. Because we know that velocity is distance divided by time, Hubble’s
constant, H0, is a measure of 1 divided by time, the time of the expansion of the universe to
its present size. It turns out that this time gives a maximum age for the universe.
Q5. Why isn’t it correct to say that the expansion of the Universe involves galaxies flying
outward into empty space?
Although we appear to be at the center of the Hubble flow, it turns out that all other
locations in the universe appear to be at the center too. This is due to the fact that the
Hubble flow is not due to the motion of objects into the universe; rather, it is an expansion
of the universe itself. Space itself is expanding. Because the Hubble flow is an expansion of
space itself, galaxies are not rushing outward into unoccupied parts of the universe. The
universe is evenly filled with matter, but space is expanding, which gives rise to an
appearance of galaxies flying outward from us.
Q9. What is the cosmic microwave background, and why is it so significant?
Just after the Big Bang occurred, the universe was filled with X-ray and gamma-ray
radiation. Since that period, this radiation has traveled through the universe, its wavelength
expanding as the universe has expanded. It is now observed in the microwave part of the
spectrum. It provides us with information about the very early universe; it is the light from
the very oldest object visible in the universe—the universe itself!
Q13. What is cosmic inflation? How does inflation solve the horizon problem? The flatness
problem?
When the universe was 10-35 s old, the strong force froze-out or separated from the
superforce. The universe briefly entered a high-energy state called the false vacuum. Empty
space pulled the universe outward in an extremely rapid, but brief, period of expansion.
This period of time is referred to as the period of inflation. The universe expanded by a
factor of 1050 in size.
Problems:
P4. According to the standard Big Bang theory (neglecting any effects of cosmic
acceleration), what is the maximum possible age of the Universe if H0 = 50 km/s/Mpc?
70 km/s/Mpc? 80 km/s/Mpc?
In order for the units to work out for the age of the universe, the H0 Mpc part of km/s/Mpc
must be converted to Km as follows. 1 Mpc = 3.1 x 1019 km (See footnote 3 on page 458 of
BG5.)
For H0 = 50 km/s/Mpc, T = 1/H0 = 1/(50 km/s/Mpc) = 3.1 x 1019 km/50 km/s = 20 billion
years
For H0 = 70 km/s/Mpc, T = 1/H0 = 1/(70 km/s/Mpc) = 3.1 x 1019 km/70 km/s = 14 billion
years
For H0 = 80 km/s/Mpc, T = 1/H0 = 1/(80 km/s/Mpc) = 3.1 x 1019 km/80 km/s = 12 billion
years