1. Interstellar extinction: the farther you look through the ISM, the more difficult it is to see things (because of the dust) -- see page 457. In fact, look far enough, and you won't be able to see anything at all.
Astronomers thought that we were at the center of the Galaxy because they saw the same number of stars in every direction (when looking along the galactic plane). However, in reality, the dust in the ISM restricted their vision to the same number of light-years in every direction -- and this limiting distance was not large enough to allow them to see all the way to the edge of the galactic disk.
(We are at the center of the region of our Galaxy that we can see through the dust. It's just that this region is not the entire Galaxy.)
2. The globular clusters lie in the galactic halo, which contains very little gas and dust. Thus, in contrast to the situation with stars in the galactic disk, we can see globular clusters clear out to the edge of the halo. Astronomers noticed that most globular clusters lay on one side of the sky. This indicated that we were not at the center of the Galaxy, but off to one side. By measuring the distances to all the globular clusters, astronomers like Harlow Shapley were able to construct a three-dimensional map, allowing them to see where the Galactic Center was (at the center of the distribution of globular clusters) and where we were in relation to it.
4. Recently-formed stars contain metals in their outer layers; these metals were created in the cores of previous generations of stars. Thus, we see that stars in the disk of our Galaxy (which are mostly metal-rich Population I stars) must have formed more recently than stars in the halo (which are nearly all metal-poor Population II stars).
11. In our solar system, planets that lie farther from the Sun travel more slowly in their orbits. In the galactic disk, however, stars orbit at roughly the same speed (220 km/s), regardless of how far they are from the Galactic Center.
The difference arises from the fact that orbital speed is determined by mass contained within an orbit, as well as the radius of the orbit. For the planets in our solar system, every orbit contains the same amount of mass (1 Mo), so orbital speed drops off with increasing radius. But in the galactic disk, larger orbits contain more mass, and this added mass compensates for the fact that the star is farther from the Galactic Center, so orbital speed is more or less constant as the radius increases.
12. If all of the Galaxy's mass was contained within the galactic disk, then hydrogen gas clouds orbiting outside the disk would obey the following rule: the farther one is from the Galactic Center, the slower it travels in its orbit (just like the planets in our solar system). However, this is not the case: the orbital speed of these clouds (regardless of their distance from Galactic Center) is the same as the orbital speed of the stars within the disk: roughly 220 km/s. This implies that there must be invisible matter outside the disk of visible matter, so that larger orbits continue to contain more mass (thus canceling out the fact that these larger orbits are farther from Galactic Center).
17. When gas and dust pass into a spiral arm (a density wave), stars of all classes (O, B, A, F, G, K, and M) are created simultaneously. These newly-formed stars pass out of the density wave, and continue around the Galaxy. However, they have not gone far before the O and B stars (which have the shortest lifetimes) have died and disappeared. Thus, we can only find O and B stars in or near the spiral arms.
However, that is not to say that the spiral arms contain only O and B stars, and no other classes of stars. As stated above, stars of all classes are formed in the spiral arms. (However, since the O and B stars are the most luminous ones, they will be the only ones that you can see from a great distance. This is why the spiral arms of galaxies look bluish.)
19. There is an object called Sagittarius A* that resides in the exact center of our Galaxy. Astronomers observe stars close to Sagittarius A* orbitting it at enormously high speeds. By measuring the semimajor axes and periods of these orbits, we can calculate the mass of Sagittarius A*: 3 million solar masses. However, one nearby star gets as close as 60 AU to Sagittarius A*; thus, this central object must be smaller than 60 AU in radius. The only thing that could be this small and yet have such a high mass is a supermassive black hole.
28. (a) If you drive 100 miles at 50 miles per hour, how long will it take you? Right, 2 hours. How did you get that answer? Time equals distance divided by velocity: t = d / v . (This will work as long as the units are consistent. If I had asked how long it takes to drive 100 kilometers at 50 miles per hour, then you would have had to convert 100 kilometers into miles before using the equation.)
In this problem, we want to determine the period, which is the time that it takes for the gas cloud to complete one orbit. The distance that it will travel during that time is the circumference of the orbit, which is 2p times the radius: (2)(3.14)(20,000 pc) = 126,000 pc. The velocity at which it travels is given as 400 km/s. To get the period, we simply divide the distance traveled by the velocity. However, we first need to convert the distance from parsecs to kilometers, so that the units will be consistent. There are 3.09 x 1013 km in 1 pc.
This answer is correct as it stands, but we might as well convert it into years, since we'll need it in that form for part (b). There are 3.16 x 107 s in 1 y.
So it takes 310 million years for the gas cloud to make one orbit around the galaxy.
(b) To find the mass contained within the gas cloud's orbit, use the version of Kepler's Third Law given on page 441 of your book. (We can ignore the mass of the gas cloud, since it will be tiny compared to the mass contained within its orbit.) However, in order to use this formula, we must first convert the radius of the gas cloud's orbit (20,000 pc) into AU. There are 2.1 x 105 AU in 1 pc.
Thus, the mass within the cloud's orbit is 770 billion times the Sun's mass.
35. (a) Again, use the version of Kepler's Third Law found on page 441 of your book. The masses of the two stars are inconsequential compared to the mass of the black hole, so we can ignore them in the formula.
The average distance between the star called S0-1 and Sagittarius A* is 2,300 AU, while the average distance between S0-2 and Sagittarius A* is 950 AU.
Last edited 27 Apr 04 M. A. Weinstein.