Chapter 25 The Milky Way Galaxy

# 25.8 Collaborative Group Activities, Questions and Exercises

# Collaborative Group Activities

- You are captured by space aliens, who take you inside a complex cloud of interstellar gas, dust, and a few newly formed stars. To escape, you need to make a map of the cloud. Luckily, the aliens have a complete astronomical observatory with equipment for measuring all the bands of the electromagnetic spectrum. Using what you have learned in this chapter, have your group discuss what kinds of maps you would make of the cloud to plot your most effective escape route.
- The diagram that Herschel made of the Milky Way has a very irregular outer boundary. Can your group think of a reason for this? How did Herschel construct his map? You might want to review the first section of this chapter.
- Suppose that for your final exam in this course, your group is assigned telescope time to observe a star selected for you by your professor. The professor tells you the position of the star in the sky (its right ascension and declination) but nothing else. You can make any observations you wish. How would you go about determining whether the star is a member of population I or population II?
- The existence of dark matter comes as a great surprise, and its nature remains a mystery today. Someday astronomers will know a lot more about it (you can learn more about current findings in The Evolution and Distribution of Galaxies). Can your group make a list of earlier astronomical observations that began as a surprise and mystery, but wound up (with more observations) as well-understood parts of introductory textbooks?
- Physicist Gregory Benford has written a series of science fiction novels that take place near the centre of the Milky Way Galaxy in the far future. Suppose your group were writing such a story. Make a list of ways that the environment near the galactic centre differs from the environment in the “galactic suburbs,” where the Sun is located. Would life as we know it have an easier or harder time surviving on planets that orbit stars near the centre (and why)?
- These days, in most urban areas, city lights completely swamp the faint light of the Milky Way in our skies. Have each member of your group survey 5 to 10 friends or relatives (you could spread out on campus to investigate or use social media or the phone), explaining what the Milky Way is and then asking if they have seen it. Also ask their age. Report back to your group and discuss your reactions to the survey. Is there any relationship between a person’s age and whether they have seen the Milky Way? How important is it that many kids growing up on Earth today never (or rarely) get to see our home Galaxy in the sky?

# Review Questions

**1:** Explain why we see the Milky Way as a faint band of light stretching across the sky.

**2:** Explain where in a spiral galaxy you would expect to find globular clusters, molecular clouds, and atomic hydrogen.

**3:** Describe several characteristics that distinguish population I stars from population II stars.

**4:** Briefly describe the main parts of our Galaxy.

**5:** Describe the evidence indicating that a black hole may be at the centre of our Galaxy.

**6:** Explain why the abundances of heavy elements in stars correlate with their positions in the Galaxy.

**7:** What will be the long-term future of our Galaxy?

# Thought Questions

**8:** Suppose the Milky Way was a band of light extending only halfway around the sky (that is, in a semicircle). What, then, would you conclude about the Sun’s location in the Galaxy? Give your reasoning.

**9:** Suppose somebody proposed that rather than invoking dark matter to explain the increased orbital velocities of stars beyond the Sun’s orbit, the problem could be solved by assuming that the Milky Way’s central black hole was much more massive. Does simply increasing the assumed mass of the Milky Way’s central supermassive black hole correctly resolve the issue of unexpectedly high orbital velocities in the Galaxy? Why or why not?

**10:** The globular 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 centre of the Galaxy? Why?

**11:** Shapley used the positions of globular clusters to determine the location of the galactic centre. Could he have used open clusters? Why or why not?

**12:** Consider the following five kinds of objects: open cluster, giant molecular cloud, globular cluster, group of O and B stars, and planetary nebulae.

- Which occur only in spiral arms?
- Which occur only in the parts of the Galaxy other than the spiral arms?
- Which are thought to be very young?
- Which are thought to be very old?
- Which have the hottest stars?

**13:** The dwarf galaxy in Sagittarius is the one closest to the Milky Way, yet it was discovered only in 1994. Can you think of a reason it was not discovered earlier? (Hint: Think about what else is in its constellation.)

**14:** Suppose three stars lie in the disk of the Galaxy at distances of 20,000 light-years, 25,000 light-years, and 30,000 light-years from the galactic centre, and suppose that right now all three are lined up in such a way that it is possible to draw a straight line through them and on to the centre of the Galaxy. How will the relative positions of these three stars change with time? Assume that their orbits are all circular and lie in the plane of the disk.

**15:** Why does star formation occur primarily in the disk of the Galaxy?

**16:** Where in the Galaxy would you expect to find Type II supernovae, which are the explosions of massive stars that go through their lives very quickly? Where would you expect to find Type I supernovae, which involve the explosions of white dwarfs?

**17:** Suppose that stars evolved without losing mass—that once matter was incorporated into a star, it remained there forever. How would the appearance of the Galaxy be different from what it is now? Would there be population I and population II stars? What other differences would there be?

# Figuring for Yourself

**18:** Assume that the Sun orbits the centre of the Galaxy at a speed of 220 km/s and a distance of 26,000 light-years from the centre.

- Calculate the circumference of the Sun’s orbit, assuming it to be approximately circular. (Remember that the circumference of a circle is given by 2π
*R*, where*R*is the radius of the circle. Be sure to use consistent units. The conversion from light-years to km/s can be found in an online calculator or appendix, or you can calculate it for yourself: the speed of light is 300,000 km/s, and you can determine the number of seconds in a year.) - Calculate the Sun’s period, the “galactic year.” Again, be careful with the units. Does it agree with the number we gave above?

**19:** The Sun orbits the centre of the Galaxy in 225 million years at a distance of 26,000 light-years. Given that

where *a* is the semimajor axis and *P* is the orbital period, what is the mass of the Galaxy within the Sun’s orbit? (See a worked out solution at the end of this section)

**20:** Suppose the Sun orbited a little farther out, but the mass of the Galaxy inside its orbit remained the same as we calculated in the question above. What would be its period at a distance of 30,000 light-years?

**21:** We have said that the Galaxy rotates differentially; that is, stars in the inner parts complete a full 360° orbit around the centre of the Galaxy more rapidly than stars farther out. Use Kepler’s third law and the mass we derived in the question above to calculate the period of a star that is only 5000 light-years from the center. Now do the same calculation for a globular cluster at a distance of 50,000 light-years. Suppose the Sun, this star, and the globular cluster all fall on a straight line through the centre of the Galaxy. Where will they be relative to each other after the Sun completes one full journey around the centre of the Galaxy? (Assume that all the mass in the Galaxy is concentrated at its centre.)

**22:** If our solar system is 4.6 billion years old, how many galactic years has planet Earth been around?

**23:** Suppose the average mass of a star in the Galaxy is one-third of a solar mass. Use the value for the mass of the Galaxy that we calculated in question 18 above, and estimate how many stars are in the Milky Way. Give some reasons it is reasonable to assume that the mass of an average star is less than the mass of the Sun.

**24:** The first clue that the Galaxy contains a lot of dark matter was the observation that the orbital velocities of stars did not decreases with increasing distance from the centre of the Galaxy. Construct a rotation curve for the solar system by using the orbital velocities of the planets, which can be found in Appendix. How does this curve differ from the rotation curve for the Galaxy? What does it tell you about where most of the mass in the solar system is concentrated?

**25:** The best evidence for a black hole at the centre of the Galaxy also comes from the application of Kepler’s third law. Suppose a star at a distance of 20 light-hours from the centre of the Galaxy has an orbital speed of 6200 km/s. How much mass must be located inside its orbit? (Answer: 6 million Suns. Kepler’s Law modified is P^{2}=a^{3}/(M total) where M is in Solar Masses. You have to convert P to Earth-years and a in AU). (See a worked out solution at the end of this section)

**26:** The next step in deciding whether the object in the question above, the supermassive object at the centre of the Milky Way Galaxy, is a black hole is to estimate the density of this mass. Assume that all of the mass is spread uniformly throughout a sphere with a radius of 20 light-hours. What is the density in kg/km^{3}? Remember that density = mass/ volume and the volume of a sphere is given by V = (^{4}/_{3}) π r^{3}. Explain why the density might be even higher than the value you have calculated. How does this density compare with that of the Sun or other objects we have talked about in this book?

**27:** Suppose the Sagittarius dwarf galaxy merges completely with the Milky Way and adds 150,000 stars to it. Estimate the percentage change in the mass of the Milky Way. Will this be enough mass to affect the orbit of the Sun around the galactic centre? Assume that all of the Sagittarius galaxy’s stars end up in the nuclear bulge of the Milky Way Galaxy and explain your answer.

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Answers to Problem 19

Problem: If the sun is 4.6 billion years old, how many times has it orbited the galaxy? Assume our Sun is 8.2 kpc (kilo parsecs) from the centre of the galaxy and it is moving at 240 km/s (kilometres per second.)

a) First convert 8.2 kpc to metres.

Remember that 1 parsec = 3.09 x 1016 metres

8.2 kpc = 8.2 x 1000 parsecs x (3.09 x10 ^{16} m / 1 parsec) =

b) Assuming a circular orbit then the distance the Sun travels as it orbits once around the galaxy is:

distance = circumference = 2 π r =

c) So how long (what time) in seconds does it take to cover the distance you found in part (a) assuming that the Sun is moving at 240 km/s = 240 000 metres / second.

Remember that speed = distance / time

So time = distance / speed

Time = ( ) /(240,000 m/s) =

d) One year = 3.16 x 10^{7} seconds, so the time you found in part c) is how many years?

( sec) x 1 year

———————————————————- = years

3.16 x 10 7 seconds

- e) What is the number of times the Sun has orbited the galaxy? Find the ratio of your answer to 4.6 billion years. Remember that one billion is 1,000,000,000.

4.6 x 10 ^{9} years

number of times = ——————————- =

Answers: a) 2 kpc = 2.53 x 10 20 m

b) distance = 2 π r where r = 2.53 x 10 ^{20} m so distance = 1.59 x 10 ^{21} meters

c) time = distance / speed = ( 59 x 10 ^{21} meters ) / ( 240,000 m/s) = 6.6 x 10 ^{15} seconds

d) time = 6.6 x 10 ^{15} seconds x ( 1 year / 3.16 x 10 7 seconds) = 2.1 x 10^{8} years

e) ratio number of times = (4.6 x 10^{9} years) / ( 1 x 10^{8} years ) = 22 times

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Answers to Problem 25

Use the Modified Kepler’s Law. P^{2} = a^{3} / (M total) (Note that for our Sun M=1 so you get Kepler’s Law)

But you need to convert P to earth years and a to AU. You will get a huge mass.You will get a mass in Solar mass units

a = 20 light hours = 20 (7.2143 AU) = 144 AU

1 light hour = 7.2143 AU Google the conversion or work it out from 3 x 10 ^{8} m/s x 3600 s / hour = 1.08 x 10 ^{12} m and then 1 AU = 1.5 x 10^{ 11} m.

a = 144 AU or a = 20 light hours x (1.08 x 10 ^{12} m) = 2.16 x 10 ^{13} m

Now for the period you can do this all in years from the start, or all in metres and seconds then convert to years.

Period = time to go around once = travel one circle = 2 π r

speed = distance / time so time = distance / speed = 2 π r / speed = 2 π a / speed

Again, see above or google the conversion factor r = a = 20 light hours = 20 x 1.079 x 10 ^{12} m = 2.158 x 10^{ 13} m = 2.158 x 10 ^{13} m

r = a = 2.158 x 10 ^{10} km. I am going to stick to metres speed = 6,200 km/s = 6,200,000 m/s

time = period = distance / speed = 2 π (2.158 x10 ^{13} m ) / ( 6, 200,000 m/s)

time = period = 2.186 x 10 ^{7} seconds. 1 year = 3.154 x 10 7 second. time = period = 0.694 years

so back to the mass which is what we were looking for P^{2} = a^{3} / (M total)

M total = a^{3} / p^{2} = ( 144 AU )^{3} / ( 0.694 years )^{ 2} = 6.23 x 10 ^{6} solar mass = 6 million solar masses.

1 solar mass = 1.99 x 10 ^{30} kg So M total at the centre of the galaxy = 1.23 x10 ^{37} kg