Mindtap Astronomy, 1 Term (6 Months) Printed Access Card For Seeds/backman's Foundations Of Astronomy, 14th
14th Edition
ISBN: 9781337399975
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 16, Problem 6P
To determine
The mass of the galaxy.
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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.)
Among the globular clusters orbiting a distant galaxy, one is moving at 417 km/s and is located 16 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, V, = V
GM
; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 x 1016 m.)
solar masses (M.)
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 16 Solutions
Mindtap Astronomy, 1 Term (6 Months) Printed Access Card For Seeds/backman's Foundations Of Astronomy, 14th
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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- If 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_forwardA given star orbits the center of its galaxy at an average speed of v_star, at a distance of r_star from the center. The galaxy has 2 spiral arms, and the arms themselves orbit slower than the star -- at the same radius, they orbit at a speed of v_arm (in the same direction as the star). The galaxy's age is t_gal. In the history of this galaxy, how many times did this star cross through a spiral arm? Values: v_star = 200 km/s, r_star = 9 kpc, v_arms = 46 km/s, t_gal = 4 Gyrarrow_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_forward
- Given an image of a disk galaxy, you have measured that the average surface brightness at two radii (R = R1 and R = R2) are I1 and I2 respectively. The disk surface brightness profile has the exponential form of I(R) = I0 e(-R/Rd). What are the values of I0 and Rd for this disk?arrow_forwardFigure 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…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
- Suppose you want to observe the molecular gas in a galaxy with redshift z using the rotational transition of CO J=4-3. What frequency would you observe this transition at? (Hint: the CO J=1-0 emits a photon at 115.27 GHz, and higher order transitions emit photons with frequencies in multiples of J, e.g., use the knowledge you gained from the problem above). Express your answer as an integer. Values: z = 1.3arrow_forwardIf the active core of a galaxy contains a black hole of 106 M, what will the orbital period be for matter orbiting the black hole at a distance of 0.23 AU? Hint: Use the formula for circular velocity, V. GM V hrarrow_forwardGlobular 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)arrow_forward
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