Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 16, Problem 12RQ
To determine
Whether the classification helped one to understand the evolution of galaxies.
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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.
How astronomers determine the distance of a galaxy? Explain.
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
determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of
the Solar mass.
250 km s-1. Using Kepler's 3rd Law,
Chapter 16 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 16 - Prob. 1RQCh. 16 - Prob. 2RQCh. 16 - Prob. 3RQCh. 16 - Prob. 4RQCh. 16 - Prob. 5RQCh. 16 - Prob. 6RQCh. 16 - Prob. 7RQCh. 16 - Prob. 8RQCh. 16 - Prob. 9RQCh. 16 - Prob. 10RQ
Ch. 16 - Prob. 11RQCh. 16 - Prob. 12RQCh. 16 - How would you respond to someone who said, Oh,...Ch. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - Prob. 10PCh. 16 - Arrange the following in order of increasing size:...Ch. 16 - If the diameter of the Milky Way Galaxys visible...Ch. 16 - Prob. 1LTLCh. 16 - Prob. 2LTLCh. 16 - Prob. 3LTLCh. 16 - Prob. 4LTL
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- What evidence can you give that we live in a galaxy?arrow_forwardWe 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.)arrow_forwardIf the diameter of the Milky Way Galaxys visible disk, 80,000 ly, is represented in a model by a dinner plate with a diameter of 10 inches, what is the model distance to galaxy M31, 2.6 millionly away? What is the model distance to the Virgo galaxy cluster, 16 Mpc away? (Convert answers to feet.)arrow_forward
- Suppose the Sagittarius dwarf galaxy merges completely with the Milky Way and adds 150,000 stars to it. Estimate the percentage change in the mass of the Milky Way. Will this be enough mass to affect the orbit of the Sun around the galactic center? Assume that all of the Sagittarius galaxy’s stars end up in the nuclear bulge of the Milky Way Galaxy and explain your answer.arrow_forwardSuppose the average mass of a star in the Galaxy is one-third of a solar mass. Use the value for the mass of the Galaxy that we calculated in Exercise 25.19, and estimate how many stars are in the Milky Way. Give some reasons it is reasonable to assume that the mass of an average star is less than the mass of the Sun.arrow_forwardAssume that the Sun orbits the center of the Galaxy at a speed of 220 km/s and a distance of 26,000 lightyears from the center. A. Calculate the circumference of the Sun’s orbit, assuming it to be approximately circular. (Remember that the circumference of a circle is given by 2pR, where R is the radius of the circle. Be sure to use consistent units. The conversion from light-years to km/s can be found in an online calculator or appendix, or you can calculate it for yourself: the speed of light is 300,000 km/s, and you can determine the number of seconds in a year.) B. Calculate the Sun’s period, the “galactic year.” Again, be careful with the units. Does it agree with the number we gave above?arrow_forward
- Why didnt astronomers before Shapley realize how large our Galaxy is?arrow_forwardUsing the information provided in Table 18.1, what is the average stellar density in our part of the Galaxy? Use only the true stars (types OM) and assume a spherical distribution with radius of 26 light-years. Stars within 21 Light-Years of the Sunarrow_forwardDoes an elliptical galaxy rotate like a spiral galaxy? Explain.arrow_forward
- Suppose three stars lie in the disk of the Galaxy at distances of 20,000 light-years, 25,000 light-years, and 30,000 light-years from the galactic center, and suppose that right now all three are lined up in such a way that it is possible to draw a straight line through them and on to the center of the Galaxy. How will the relative positions of these three stars change with time? Assume that their orbits are all circular and lie in the plane of the disk.arrow_forwardThe 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?arrow_forwardOne way to calculate the size and shape of the Galaxy is to estimate the distances to faint stars just from their observed apparent brightnesses and to note the distance at which stars are no longer observable. The first astronomers to try this experiment did not know that starlight is dimmed by interstellar dust. Their estimates of the size of the Galaxy were much too small. Explain why.arrow_forward
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