Download STUDY QUESTIONS #10 The MILKY WAY GALAXY diameter face

STUDY QUESTIONS #10
The MILKY WAY GALAXY
diameter
face-on view
edge-on view
two views of our Galaxy, the Milky Way
1. What is the diameter of our Galaxy, the Milky Way?
2. How far from the center of the Galaxy is the solar system? What else besides stars are in the Galaxy?
3. Label the following where appropriate: spiral arms, disk, halo, bulge, globular clusters, galactic center
4. What is the evidence for a massive black hole in the center of the Galaxy?
5. According to Kepler's laws, the velocity of one object orbiting a second object depends on the mass of
the second object and on the distance between them. For example, in the solar system if the sun were
more massive that it is, the earth would orbit the sun much faster. The plot on the next page shows
the orbital velocity of each planet and its distance from the sun. You can calculate the mass of the
Sun using:
2
V orbital
Rdistance from sun
Msun =
G
for example, using the values for the planet Mercury:
Msun =
(47829.6)2 ! (5.79 ! 101 0)
6.67 ! 10 –11
Using the table on the right
and the formula above,
verify that the orbit of
each planet gives the same
mass for the Sun (round to
one digit, as shown for
Mercury). Since the
formula measures the total
mass interior to each orbit,
why do you get the same
values for the Mass in the
last column?
distance from the
sun in meters
mercury
venus
earth
mars
jupiter
saturn
uranus
neptune
pluto
5.79 × 1010
1.082 × 1011
1.496 × 1011
2.279 × 1011
7.783 × 1011
1.427 × 1012
2.869 × 1012
4.497 × 1012
5.900 × 1012
orbital velocity in Mass of the Sun in
meters/sec
kilograms
47829.6
34993.9
29763.1
24107.3
13048.3
9636.6
6794.1
5429.3
4738.8
2 × 1030
velocity around the sun [km/s]
6. The plot below shows the data from question 5. It tells us that for a large central mass like the sun, the
orbital velocity becomes smaller and smaller the farther out you go from the sun. Use the plot to
estimate the orbital velocity of the asteroids in the asteroid belt.
50
mercury
40
venus
30
earth
mars
20
10
center of 0
the sun
jupiter
saturn
uranus
neptune
1
2
3
4
5
distance from the center of the sun [billions of km]
.
pluto
7. Just as in the solar system with planets, you can find the central mass of the Galaxy by plotting the
velocities of stars versus their distance from the galactic center and obtain a rotation curve. Using the
formula from question 5 and the data from the plot below, calculate the total mass interior to the orbit of
the Sun. (Be sure to use meters/s for the velocity and meters for the distance. One thousand light-years is
9 × 1018 m.)
velocity of the stars at a given
distance from the galctic center [km/s]
inner Galaxy
outer Galaxy
300
200
galactic
center
100
0
10
20
sun
very few stars
beyond here
30
40
50
60
70
80
90
100
distance from the center of the Galaxy [thousands of light-years]
.
8. According to the measurable light in the whole Galaxy, almost all stars are located within 50,000 lightyears of the galactic center. Then, what would you expect the rotation curve to look like in the outer
Galaxy, out to 100,000 light years? Draw it on the plot above. (hint: compare this plot with the plot from
question 7.)
9. Using the rotation curve above, astronomers have calculated a mass for the whole Galaxy, out to about
50,000 light-year radius where there are no more stars, to be about 2 × 1011 M , yet by measuring light
at all wavelengths, they only measure one sixth of that mass (3 × 1010 M ). Using the orbital velocity
equation, how much mass does the rotation curve predict at 100,000 light-years from the galactic center?
(divide your answer by 2 × 1030 kg to put your answer in solar masses (M ). How much mass is
unaccounted for? (This is "dark matter".)
10. Name three ways to find the distance to stars. How far can we measure with each method?
11. Cepheids are special variable stars with pulsation periods that are correlated with luminosity.
Therefore, if you measure how the light from a Cepheid varies with time to get its period of light
variation, you can use that information to learn its luminosity. Measure the period of the Cepheid
HR3343 from its light curve below. (Each point represents one observation.)
12. The plot below is called a Period-Luminosity diagram. Every point on the plot represents a different
Cepheid variable star. Astronomers found the distances to each of these 15 stars using the method of
parallax (the most reliable way to measure distance), so we know the luminosity of each star with
good accuracy. Find the luminosity of the star in the question 11 above (HR 3343) by consulting the
Period-Luminosity diagram below.