Chapter 73, Mass and Motions in the Milky Way Video Solutions, Pathways to Astronomy

Problem 1

Given that the Sun moves in a circular orbit of radius 8 kpc around the center of the Milky Way, and its orbital speed is $220 \mathrm{km} / \mathrm{sec},$ work out how long it takes the Sun to complete one orbit of the Galaxy.

Khoobchandra Agrawal

Numerade Educator

00:59

Problem 2

If the Milky Way were to double in mass, what would the Sun's velocity be?

Ashar Tanveer

Numerade Educator

01:17

Problem 3

Near the center of the Milky Way, the rotation speed climbs in proportion to the radius; so at 400 pc from the center, the speed is twice as fast as at 200 pc from the center.
a. What does this imply about the mass within 400 pc versus the mass within 200 pc?
b. Is there any differential rotation in this region? Explain.

Zachary Warner

Numerade Educator

01:47

Problem 4

Suppose there were no additional mass in the Milky Way beyond the distance of the Sun's orbit. What would the rotation speed be at a radius of $16 \mathrm{kpc}$ (twice as far from the center as the Sun)?

Sheh Lit Chang

University of Washington

01:15

Problem 5

What is the Schwarzschild radius of a black hole with the mass of the black hole thought to be at the center of the Milky Way? (See Unit $68 .)$

Narayan Hari

Numerade Educator

02:24

Problem 6

If spiral arms are about 2 kpc in width, how long does the Sun, at a distance of $8 \mathrm{kpc}$ from the Galactic center and an orbital speed of $220 \mathrm{km} / \mathrm{sec},$ spend inside a spiral arm on its motion around the Milky Way?

Cheryl Glor

Numerade Educator

01:55

Problem 7

Cut three circles of paper or cardboard whose diameters are 8 $10,$ and $12 \mathrm{cm} .$ Punch a hole in the middle of each and fasten them together through their centers. Fill in a circle near the edge of the $10-\mathrm{cm}$ disk that extends across the visible portion of this disk onto the two other disks. This dot represents a large region of star formation. To model the differential rotation of our Galaxy, assume the disks rotate with a "flat rotation curve." If the 8 -cm disk makes half a rotation, estimate how much the other two disks will have rotated in the same time. Draw how the star-forming region has become distorted. How does this relate to ideas for spiral structure in galaxies?

Matthew Miranda

Numerade Educator