Part 1: Parallax, Distance, and Magnitude
Below is a copy of the image shown on the screen of a field of distant stars. Work in pairs to demonstrate how astronomers use parallax to determine the distances to nearby stars. You will need a ruler and a nearby star.
Mark the locations where your “nearby star” appears to be against the distant star field when you observe it first with one eye, and then with the other. Hold your head in the same, fixed position when marking its location. Have your partner hold the artificial star at three different distances. Use the ruler to indicate the separation of the apparent positions of the stars at each distance. Use a yardstick to measure the distance to the nearby star. How does the apparent movement of the star depend on distance?

On the next page are two lists of stars. The first is a list of the brightest stars in the sky. The second is a list of the nearest stars – all the stars we know of within about 10 light years of the Sun. The tables give the distances to the stars in light years, as well as their apparent and absolute magnitudes and temperatures.
The stars Acrux and Altair appear to have nearly the same brightness in the sky, although Acrux is at a distance of 510 light years while Altair is only 16 light years distant. Use the inverse square law to determine how much brighter Acrux is intrinsically than Altair.
Of the two stars Hadar and Acrux, which has the larger radius? Describe your reasoning.
Betelgeuse and Rigel are at similar distances in the constellation Orion. Which has the larger radius?
(Remember the Stefan Boltzman Law – brightness is proportional to temperature to the 4 th power.)
Sirius and UV Ceti are at similar distances, but Sirius has an intrinsic brightness that is 4 x 10 5 times brighter than UV Ceti’s.
What is the ratio of their radii?

Sun
Sirius
Canopus
Rigil Kentaurus
Arcturus
Vega
Capella
Rigel
-
8.6
74
4.3
34
25
41
~1400
-26.72
-1.46
-0.72
-0.27
-0.04
0.03
0.08
0.12
4.8
1.4
-2.5
4.4
0.2
0.6
0.4
-8.1
Procyon
Achernar
Betelgeuse
Hadar
Acrux
11.4
69
~1400
320
510
0.38
0.46
0.50
0.61
0.76
2.6
-1.3
-7.2
-4.4
-4.6
Altair
Aldebaran
Antares
Spica
16
60
~520
220
0.77
0.85
0.96
0.98
2.3
-0.3
-5.2
-3.2
Pollux 40 1.14
The NEAREST STARS
– Stars within 10 light years of the Sun
0.7
Proxima Centauri 4.24 11.10 15.53
Alpha Centauri A
Alpha Centauri B
4.35
4.35
-0.01
1.34
4.37
5.72
Barnard's Star
Wolf 359
Lalande 21185
Sirius A
Sirius B
Luyten 726-8A
UV Ceti
Ross 154
5.98
7.78
8.26
8.55
8.55
8.73
8.73
9.45
9.54
13.46
7.48
-1.46
8.44
12.56
12.52
10.45
13.23
16.57
10.46
1.45
11.34
15.42
15.38
13.14
5800
9600
7600
5800
4700
9900
5700
11,000
6600
22,000
3300
25,000
26,000
8100
4100
3300
2600
4900
2800
5800
4900
2800
2700
3300
9900
12,000
2700
2600
3000

Part 2: The Nearest and Brightest Stars
Plot the stars from the two lists of brightest and nearest stars on the Hertzsprung-Russell diagram on the next page. Use the intrinsic brightness ( absolute magnitude ) on the y-axis and the temperature on the x-axis. Note that the y-axis has negative magnitudes (the brightest stars) at the top and positive magnitudes (the dimmest stars) at the bottom. The x-axis is also “backwards,” with hot stars on the left side and cool stars on the right side. Use a different color pen (or a pen and a pencil) for each group of stars to see how they differ.
What general trends do you see in the data in the plot? Draw a line following the main sequence defined by the nearest and the brightest stars together. Draw a circle encompassing any white dwarf stars and a circle encompassing any giant or supergiant stars. List the giants and supergiants below.
Also list any white dwarf stars.
Which star listed is the brightest intrinsically? Which is the intrinsically faintest?
Which star is furthest from the Sun? Why does it appear so bright in our sky?
Why does Alpha Centauri appear so bright in our sky?
How do the two groups of stars differ in the Hertzsprung Russell diagram? Where is each group preferentially found in the diagram? Why

0
5
-10
-5
10
15
20
30000 25000 20000 15000 10000
5000 0

Part 3: The Jewels of the Night
Work with a partner on this assignment. We will use a color image of the Jewelbox star cluster, and a
“star gauge” to measure brightness and color. The goal is to construct a Hertzsprung-Russell diagram of the Jewelbox cluster to estimate the age of the cluster.
Examine the print of the Jewelbox Cluster. Can you tell the approximate boundary of the cluster in space? Outline where you think the boundaries of the cluster are with the marker. Use a ruler to draw a square about 5 cm square on a side around the center of the cluster.
1. What property of the stars in the image gives you information about the brightness of the star?
2. What property of the stars in the images gives you information about the temperature of the star?
Use the star gauge to measure the brightness and temperature of each star in square you have drawn. Be systematic - start in one corner and mark off each star you measure as you plot it in the graph.
3. When you have plotted all the stars in the 5 cm box, draw a line on your graph indicating the location of the main sequence of the Jewelbox cluster. Label the line "main sequence."
Stars in front of or behind the Jewelbox which are not part of the cluster may also appear in the image.
4. Circle any stars in your HR diagram that might be "field" stars and not part of the Jewelbox cluster.
5. Estimate the age of the Jewelbox cluster by comparing your HR diagram with the sample diagrams shown below the graph. Age: ________________________
6. Describe the reason that led you to your estimate of the age of the Jewelbox.
7. If our Sun were a member of the Jewelbox cluster, where would it fall in the graph? Plot and label the Sun in the graph.

Part 4: The Ages of Star Clusters
Take a look at the Hertzsprung-Russell (HR) diagrams for six star clusters in the Milky Way. The clusters range in age from less than 20 million years (2x10 7 years) to 5 billion years (5x10 9 years).
The HR diagrams are plots of the brightness of stars (their apparent or absolute magnitude) on the yaxis versus (here we use apparent magnitude), the temperature (or color) of stars on the x-axis. In the attached diagrams, the color of the star is indicated by the “ B-V color ,” which is the difference in brightness in Blue and yellow (Visual) filters.

Hotter stars are brighter in blue light than in yellow light, have low values of B-V color, and are found on the left side of the diagram.

Cooler stars are brighter in yellow light than in blue light, have larger values of B-V color, and are found on the right side of the diagram.
Since brighter stars are designated with a smaller number for apparent magnitude, magnitudes are plotted in reverse order to put the brighter stars at the top.
Investigating Stellar Evolution - For each cluster, identify the main sequence, and sketch in a line that follows the main sequence from its brightest point to the bottom of the diagram. For some clusters, you will need to extrapolate the main sequence to magnitudes fainter than have been plotted. Sometimes astronomical photographs don’t reach faint enough stars to detect the bottom portion of the main sequence.
Using the HR diagrams, answer the following questions.
1. Which cluster contains stars with the brightest apparent magnitudes?
2. Which cluster contains the stars with the brightest absolute magnitudes?
3. Which cluster contains the most red giants?
4. In which cluster have white dwarf stars been detected?
5. For the cluster in question 4, what is the difference in magnitude between white dwarfs and main sequence stars of the same temperature (color)?

Estimating Distances: The Sun has a B-V color of about 0.6. For each cluster, estimate the apparent magnitude of stars like our Sun.
NGC 752
M67
__________
__________
Pleiades
M34
__________
__________
Hyades __________ Jewelbox __________
6. Based on the apparent magnitudes of Sun-like stars, which cluster is the nearest to our Sun?
7. Based on the apparent magnitudes of Sun-like stars, which cluster is the farthest from our Sun?
Sun-like stars have an absolute magnitude of about 5. The difference between the apparent magnitude and the absolute magnitude of a star is called the distance modulus .
From the chart below, estimate the distance to each cluster in light years.
Distance
Modulus
0
2.5
5
7.5
10
12.5
15
17.5
20
Distance in
Light Years
30 ly
100 ly
300 ly
1,000 ly
3,000 ly
10,000 ly
30,000 ly
100,000 ly
300,000 ly
Cluster Distance
NGC 752
Modulus
M 67
Hyades
Pleiades
M 34
Jewelbox
Distance in
Light Years
Estimating the Ages of Star Clusters - Massive stars burn their nuclear fuel faster than lower mass stars and leave the main sequence sooner. In a cluster in which all the stars formed at the same time, the stars “peel off” the main sequence from the top, leaving only progressively less and less massive stars remaining on the main sequence as time goes by. The main sequence turnoff is the point on the main sequence for which more massive stars have evolved away, but less massive stars still remain. Over time, the turnoff point moves down the main sequence to lower and lower mass stars. By measuring the turnoff point, astronomers can determine the age of a star cluster.
For each cluster, estimate the “color” of the main sequence turnoff in the HR diagram and determine the cluster’s age from the chart below.

3000000000
2500000000
2000000000
1500000000
1000000000
500000000
0
-0.5
-0.3
-0.1
0.1
B-V Color
0.3
0.5
0.7
Cluster
NGC 752
M 67
Hyades
Pleiades
M 34
Jewelbox
Turnoff
Color
Age
8. Which cluster is the youngest?
9. Which cluster is the oldest?
10. Why has a cluster with a turnoff color of B-V=0.9 never been discovered?

For Wednesday, April 1
Part 5: Where is the Center of the Milky Way? (From Anna Larson, U. Washington)
The globular star clusters are bright, and can be seen for a long distance. Their distances can be estimated accurately from their main sequence turnoffs, as well as by measuring the periods of variable stars that belong to each cluster. In the table below are listed several dozen Galactic globular clusters with their distances (in kiloparsecs) and their directions in galactic longitude. Most of the globular clusters fall above or below the plane of the Milky Way. They have been projected down to the plane, with their distances foreshortened accordingly.
 A “’kiloparsec” is 1000 parsecs. A parsec is 3.26 light years.

Galactic longitude is like longitude on Earth, but measured along the plane of the Milky Way.
Plot each cluster on the plot below, at its correct projected distance and direction from the Sun, which is located at the center of the plot.
NGC
#
Projected
Gal.
Long.
Distance
(kpc)
NGC
#
Projected
Gal.
Long.
Distance
(kpc)
NGC
#
Projected
Gal.
Long.
Distance
(kpc)
NGC
#
Projected
Gal.
Long.
Distance
(kpc)
104 306 3.5
362 302 6.6
2808 283 8.9
6273 357 7
6287 0
6333 5
16.6
12.6
288 147 0.3
1904 228 14.4
Pal 4 202 30.9
6284 358 16.1
6293 357 9.7
6341 68 6.5
4147 251 4.2
5024 333 3.4
6356 7 18.8
6397 339 2.8
4590 299 11.2
5053 335 3.1
6366 18 16.7
6402 21 14.1
5139 309 5
5634 342 17.6
Pal 5 1
5904 4
24.8
5.5
6121 351 4.1
O
1276
22 25
6638 8 15.1
6171 3 15.7
6218 15 6.7
6235 359 18.9
6266 353 11.6
6535 27
6712 27
6723 0
6864 20
6981 35
15.3
5.7
7
6760 36 8.4
Pal
10
53 8.3
Pal
11
32 27.2
31.5
17.7
7089 54 9.9
Pal
12
31 25.4
5272 42 2.2
5694 331 27.4
5897 343 12.6
6093 353 11.9
6541 349 3.9
6626 7 4.8
6144 352 16.3
6205 59
6229 73
6254 15
4.8
18.9
5.7
6656 9 3
6717 13 14.4
6752 337 4.8
6779 62
6809 9
6838 56
6934 52
7078 65
7099 27
7492 53
10.4
5.5
2.6
17.3
9.4
9.1
15.8

Mark a clear “X” at the location of the Galactic Center. Estimate the distance to the Galactic Center and the constellation where the center is found.
Distance _____________________________ Constellation ___________________________
Our knowledge of globular clusters on the far side of the disk of the Milky Way is incomplete. How might this affect a measurement of the distance to the Galactic Center based on the globular clusters?

Part 6: Weighing the Milky Way
Below is a plot of the velocity of stars orbiting around the center of the Milky Way, as a function of distance from the Galactic Center. Astronomers call a plot like this a “rotation curve.” Stars orbit the
Galaxy following Newton’s laws. Their orbital speed depends on the total mass contained inside their orbit.
The orbital velocities of stars rise quickly from the center as we move out in radius. This is because the center of the Galaxy is dense, so that the mass inside a circle rises quickly with increasing orbital radius. Further out, the density of stars is less, so the mass contained inside a given radius increases more slowly, and the rotation curve flattens out. The wobbles in the curve are due to the spiral arms of the Milky Way. Beyond a distance of about 16 Kpc from the Galactic Center, there are very few stars or gas clouds – effectively, nearly all of the stars and gas of the Milky Way are within 16 Kpc of the center.
Using Newton’s laws, the relationship between rotation velocity, distance from the Galactic Center, and mass within radius R can be expressed as follows.
M
 v
2 r
G
G is the gravitational constant, "v" is the rotational velocity, and "M" is the mass contained inside of radius
“r.” Here, we are using astronomical units. Mass is measured in solar masses, radius is measured in kiloparsecs (Kpc), and velocity is measured in km s -1 .
Using these units, the gravitational constant has a value of 4.31 x 10 -6 Kpc km 2 M
☼
-1 s -2 .
Estimate the mass of the Milky Way contained within a radius of 16 Kpc from the Galactic Center.

Estimated mass: ___________________________________________________________
Based on the observed distribution of stars and gas in the Milky Way, and the mass within 16 KPC of the Galactic Center, compute the rotation curve for the extreme outer regions of the Galaxy. Compute the orbital speed for stars at distances of 20,000, 25,000, and 30,000 Kpc from the center of the Milky
Way. (These correspond to distances of 65,000, 82,000, and 98,000 LY from the Galactic Center. Plot these points on the chart below.
How do your calculated orbital speeds compare to the observed orbital speeds for distant stars in the extreme outreaches of the Milky Way? How does the discrepancy change with distance?
What explanation can you suggest for the discrepancy?

Part 6: Reflection a) Write a short statement describing what you learned from these activities. Which activities were the most helpful for learning about the properties of stars and the Milky Way and which were not helpful? Which were too easy, and which were too difficult? b) Draw a sketch of the Milky Way, including and labeling the various components that make up our galaxy.