Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 25, Problem 21E
We have said that the Galaxy rotates differentially; that is, stars in the inner parts complete a full 360° orbit around the center of the Galaxy more rapidly than stars farther out. Use Kepler’s third law and the mass we derived in Exercise 25.19 to calculate the period of a star that is only 5000 light-years from the center. Now do the same calculation for a globular cluster at a distance of 50,000 light-years. Suppose the Sun, this star, and the globular cluster all fall on a straight line through the center of the Galaxy. Where will they be relative to each other after the Sun completes one full journey around the center of the Galaxy? (Assume that all the mass in the Galaxy is concentrated at its center.)
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Students have asked these similar questions
Figure 2 shows the "rotation curve" of
NGC 2742. It plots the “radial velocity
(V)" (how fast material is moving
either toward or away from us) that is
measured for objects at different
distances (R = radius") from the
center of the galaxy. The center of the
galaxy is at 0 kpc (kiloparsecs) with a
speed of 9 km/sec away from us.
(These velocities have been corrected
for the observed tilt of the galaxy and
represent true orbital velocities of the
stars and gas.)
200
100
U4779
-100
As you can see, one side of the galaxy
is moving with a negative velocity
(spinning toward us), while the other
side has a positive velocity (spinning
away from us). Using Newton's
gravity equation, we will be able to
determine the gravitational mass of the
entire galaxy and how the mass varies
versus distance from the galaxy's center.
-200
-8
8
-4
Radius (kpc)
Read the following text carefully and follow the instructions:
Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…
Globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why? (If you would like to learn more about globular clusters, read Section 22.2 of the book, though it is not necessary to answer this question)
A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance
from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen-
tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe
dark matter exists. Let's work out why!
Assuming that each star in a given galaxy has a circular orbit, we know that the accelera-
tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and
equal to v?/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected
relationship between ve and r due to the stellar halo (p(r) xr-3.5) does not produce a flat
rotation curve. (b) Show that a p(r) ∞ r¯² density profile successfully produces a flat ro-
tation curve and must therefore be the general profile that dark matter follows in our galaxy.
Chapter 25 Solutions
Astronomy
Ch. 25 - Explain why we see the Milky Way as a faint band...Ch. 25 - Explain where in a spiral galaxy you would expect...Ch. 25 - Describe several characteristics that distinguish...Ch. 25 - Briefly describe the main parts of our Galaxy.Ch. 25 - Describe the evidence indicating that a black hole...Ch. 25 - Explain why the abundances of heavy elements in...Ch. 25 - What will be the long-term future of our Galaxy?Ch. 25 - Suppose the Milky Way was a band of light...Ch. 25 - Suppose somebody proposed that rather than...Ch. 25 - The globular clusters revolve around the Galaxy in...
Ch. 25 - Shapley used the positions of globular clusters to...Ch. 25 - Consider the following five kinds of objects: open...Ch. 25 - The dwarf galaxy in Sagittarius is the one closest...Ch. 25 - Suppose three stars lie in the disk of the Galaxy...Ch. 25 - Why does star formation occur primarily in the...Ch. 25 - Where in the Galaxy would you expect to find Type...Ch. 25 - Suppose that stars evolved without losing...Ch. 25 - Assume that the Sun orbits the center of the...Ch. 25 - The Sun orbits the center of the Galaxy in 225...Ch. 25 - Suppose the Sun orbited a little farther out, but...Ch. 25 - We have said that the Galaxy rotates...Ch. 25 - If our solar system is 4.6 billion years old, how...Ch. 25 - Suppose the average mass of a star in the Galaxy...Ch. 25 - The first clue that the Galaxy contains a lot of...Ch. 25 - The best evidence for a black hole at the center...Ch. 25 - The next step in deciding whether the object in...Ch. 25 - Suppose the Sagittarius dwarf galaxy merges...
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- Among the globular clusters orbiting a distant galaxy, one is moving at 534 km/s and is located 14 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? Convert your answer to solar masses. (Hint: Use the formula for circular velocity, Vc = GM r ; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 ✕ 1016 m.)arrow_forwardI answer is not 100, I also tried 21. I need help! Thank you!arrow_forwardThe Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot = 250 km s−1. Using Kepler’s 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.arrow_forward
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