Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 25, Problem 10E
The 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?
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Observations indicate that each galaxy contains a supermassive black hole at its center. These black holes can be hundreds of
thousands to billions of times more massive than the Sun. Astronomers estimate the size of such black holes using
multiple methods.
One method, using the orbits of stars around the black hole, is an application of Kepler's third law. The mass of the black hole
can be found by using the given equation, where a is the semi-major axis in astronomical units, P is the period in years, and k is
a constant with a value of 1 Mo X year²/ AU³.
a³
M = k-
p²
What is the mass of a supermassive black hole if a star orbits it with a semimajor axis of 959 AU and a period of 13.3 years?
mass:
Another method measures the speed of gas moving past the black hole. In the given equation, v is the velocity of the gas (in
kilometers per second), r is the distance of the gas cloud from the black hole (in kilometers), and G is Newton's gravitational
constant. In this equation, G = 1.33 ×…
The 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.
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)
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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- The Sun orbits around the center of the Milky Way on a circular orbit with a radius of 8 kpc, and at a speed of about 200 km/s.Suppose that the gravitational field of the Milky Way is dominated by a spherical dark matter halo. What is the mass of the halo within the radius of the solar orbit?arrow_forward(a) Estimate the height (z) above or below the Galactic plane for the globular cluster M13 (1,b = 59°, 40.9°) and the Orion Nebula (1,b = 209°, -19.4°). M13 and the Orion Nebula are 7 kpc and 450 pc away from Earth respectively. (b) To which components of the Galaxy do these objects probably belong? Explain your answers.arrow_forwardn(r) = 1ge where r represents the distance from the centre of the Galaxy, Ro is the distance of the Sun from the centre of the Galaxy, Ra is the typical size of disk and no is the stellar density of disk at the position of the Sun. All distances are expressed in kpc. An astronomer observes the center of the Galaxy within a small field of view. We take a particular type of Red giant stars as the standard candles for the observation with approximately constant absolute magnitude of M = -0.2, (a) A telescope has a limiting magnitude of m = 18. Calculate the maximum distance to which this telescope can detect these red giant stars. For simplicity we ignore the presence of interstellar medium so there is no extinction. (b) Assume an extinction of 0.7 mag/kpc for the interstellar medium. Repeat the calculation as done in the part 5a and obtain a rough number for the maximum distance these red giant stars can be observed. (c) Give an expression for the number of these red giant stars per mag-…arrow_forward
- The best evidence for a black hole at the center of the Galaxy also comes from the application of Kepler’s third law. Suppose a star at a distance of 20 light-hours from the center of the Galaxy has an orbital speed of 6200 km/s. How much mass must be located inside its orbit?arrow_forwardThe first clue that the Galaxy contains a lot of dark matter was the observation that the orbital velocities of stars did not decreases with increasing distance from the center of the Galaxy. Construct a rotation curve for the solar system by using the orbital velocities of the planets, which can be found in Appendix F. How does this curve differ from the rotation curve for the Galaxy? What does it tell you about where most of the mass in the solar system is concentrated?arrow_forwardObservations of the central region of the galaxy M87 indicate that stars which are 60 light years from the centre are orbiting the central supermassive black hole at speeds of 730 kms‑1. Estimate the mass of the black hole, in solar masses. (You can assume circular motion.arrow_forward
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