Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
expand_more
expand_more
format_list_bulleted
Concept explainers
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.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
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...
Additional Science Textbook Solutions
Find more solutions based on key concepts
In which extrasolar planet system(s) (A–D) is the planet closest to the star?
Lecture- Tutorials for Introductory Astronomy
(II) Calculate the relative probabilities, when you throw two I dice, of obtaining (a) a 7, (b) an 11, (c) a 4....
Physics for Scientists and Engineers with Modern Physics
Explain all answers clearly, with complete sentences and proper essay structure if needed. An asterisk (*) desi...
Cosmic Perspective Fundamentals
Calculate the total thermal energy in a liter of helium at room temperature and atmospheric pressure. Then repe...
An Introduction to Thermal Physics
What is the role of “loose” electrons in heat conductors?
Conceptual Physics (12th Edition)
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective (8th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 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_forwardThe best parallaxes obtained with the Hipparcos satellite have an uncertainty such that we believe measurements as low as 0.005 arc-seconds. What is the farthest distance a star can be to have an accurate distance from Hipparcos?200 parsecs The disk of our Galaxy is 100,000 light-years in diameter. Using the results from the previous problem, what fraction of the diameter of the Galaxy's disk is the distance for which we can measure accurate parallaxes?arrow_forwardThe best parallaxes obtained with the Hipparcos satellite have an uncertainty such that we believe measurements as low as 0.005 arc-seconds. What is the farthest distance a star can be to have an accurate distance from Hipparcos? 200 Parsecs The disk of our Galaxy is 100,000 light-years in diameter. Using the results from the previous problem, what fraction of the diameter of the Galaxy's disk is the distance for which we can measure accurate parallaxes? 0.0065 The Gaia satellite has greatly improved precision over Hipparcos, measuring parallaxes that are as small as 0.00025 arcseconds. How many times farther away is Gaia be able to measure distances to than Hipparcos?arrow_forward
- 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.arrow_forward(Astronomy) White Dwarf Size I. The density of Sirius B is 2×106 g/cm3 and its mass is 1.95×1030 kg. What is the radius of the white dwarf in km? (Hint: Density = mass/volume, and the volume of a sphere is 4/3πr3) Please round your answer to two significant digits.arrow_forwardIndicate whether the following statements are true or false. (Select T-True, F-False. If the first is T and the rest F, enter TFFFFF). A) If we find an O type star in our galaxy, it must be in the disk. B) The nearest large spiral Galaxy, similar in size to the Milky Way, is the Andromeda Galaxy (M31). It is located about 2 million light years from Earth. C) The disk of the Milky Way galaxy is about 100,000 light years in diameter. D) On very large scales, matter in the Universe is distributed in clumps and voids. E) Distances to most stars in the Milky Way are measured by parallax. F) RR Lyrae and Cepheid variable stars are used to measure the distance to nearby galaxies.arrow_forward
- If the active core of a galaxy contains a black hole of 106?Θ (1 million solar masses), what will the orbital velocity be for matter orbiting the black hole at a distance of 0.33 AU? (Hint: use the formula for orbital velocity: ?=√???; where ?=6.67×10−11 ?3?? ?2 and ?Θ= 2.0×1030 ??. Note: 1 ??=1.50×1011 ?)arrow_forwardSuppose that the outer stars of a galaxy have an orbital velocity of 150 km/s. If the radius of the galaxy is 4.0 kpc (1??? = 3.1 × 1016 ??), what is the orbital period of the outer stars in years?arrow_forwardSuppose you observe a star orbiting the galactic center at a speed of 1100 km/s in a circular orbit with a radius of 14 light-days. Calculate the mass of the object that the star is orbiting. Express your answer in solar masses to two significant figures.arrow_forward
- The difference in absolute magnitude between two objects is related to their fluxes by the flux-magnitude relation: FA / FB = 2.51(MB - MA) A distant galaxy contains a supernova with an absolute magnitude of -19. If this supernova were placed next to our Sun (M = +4.8) and you observed both of them from the same distance, how much more flux would the supernova emit than the Sun? Fsupernova / FSun = ?arrow_forwardYou observe the H-alpha line of Hydrogen in a distant galaxy to have a wavelength of 754.4 nm. What is the radial velocity of the galaxy? Hint: The rest wavelength of H-alpha is 656 nm. I have to use the forumla mentioned in the photo I shared with this post.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 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,arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
AstronomyPhysicsISBN:9781938168284Author:Andrew Fraknoi; David Morrison; Sidney C. WolffPublisher:OpenStax
Stars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage Learning
Foundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning
Astronomy
Physics
ISBN:9781938168284
Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher:OpenStax
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning