Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 16: The Milky Way Galaxy

Problems

1
Make a scale diagram of the Galaxy looking down from above. Let 1 inch = 4 kpc (about 17,000 ly), and draw a 7.5 -inch diameter circle to represent the 30 kpc wide disk of the Galaxy (see fig. 16.6). The Sun is about 8 kpc out from the center, so place a small dot 2 inches out from the center. The most distant stars visible to the naked eye would be no more than about 3000 pc (3 kpc) from the Earth, and most bright naked-eye stars are less than 1200 pc away. Draw circles around the Sun at distances corresponding to 1200 pc and 3000 pc. Are any of the stars in the night sky outside the Milky Way Galaxy?
2
How long does it take light from the center of the Milky Way, 8 kpc away, to reach the Solar System?
3
On average, a hydrogen atom emits a 21-cm photon once every 15 million years. How many 21-cm photons does a 100-M. gas cloud emit per second?
4
The dust in an interstellar cloud blocks blue light in the following way: For every 1 pc light travels through the cloud, only 90% of the light continues. Thus, after 2 pc, 90% of the remaining 90%, or 81% (0.9 × 0.9 = 0.81), remains. (a) You might initially expect that after 10 pc, the ten 10% reductions would have removed all of the blue light. How much blue light actually remains? (b) The same cloud removes about 7% of the red light every parsec, so after 1 pc, the ratio of blue to red has dropped to 90/93 ≈ 97% of its unreddened value. What is the ratio of blue to red after 5 pc? after 10 pc?
5
Given that the Sun moves in a circular orbit of radius 8 kiloparsecs around the center of the Milky Way and that its orbital speed is 220 kilometers per second, work out how long it takes the Sun to complete one orbit of the Galaxy. (Hint: Remember to convert kiloparsecs to kilometers and convert your final answer to years, not seconds.)
6
According to figure 16.26, the Milky Way's rotation speed is about 230 km/sec at a distance of about 16 kpc from its center. Using the equation from Figure 16.25, estimate the mass of the Milky Way. Is this an upper or a lower limit? Compare with the mass of the Andromeda Galaxy, where the rotation speed is 230 km/s at a radius of 35 kpc.
7
How long is the period for a star orbiting the black hole at the center of our Galaxy that is about 2800 AU from the black hole at the farthest part of its orbit, but that gets as close as 1200 AU at the nearest? Take the mass of the black hole to be 4 × 106 solar masses. Compare your answer to the path of star S0-20 in figure 16.26.
8
Calculate the Schwarzschild radius of the black hole at the center of the Galaxy using 4 × 106 solar masses for its mass. How many AU is the Schwarzschild radius?
9
The 4 × 106 solar mass black hole at the center of the Galaxy may have gained its first million solar masses in the first billion years of the Milky Way's existence. How much mass must it have absorbed on average each year since then to reach 5 million solar masses today?
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