Foundations of Astronomy (MindTap Course List)
Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 15, Problem 2RQ
To determine

The reason behind the exact dimension of the Galaxy’s disk and visible halo are hard to determine.

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A 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 Gyr
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?
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.)
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