# H205 – Cosmic Origins Exploration Packet 3: Exploring the Neighborhood Your Name Due April 1, 2009 Part 1: Parallax, Distance, and Magnitude

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H205 – Cosmic Origins Exploration Packet 3: Exploring the Neighborhood
Your Name _____________________________ Due April 1, 2009

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.

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 4th power.)

## The Brightest Stars in the Northern Sky

Name

Distance (light years)

Apparent Magnitude

Absolute Magnitude

### Temperature

Sun

-

-26.72

4.8

5800

Sirius

8.6

-1.46

1.4

9600

Canopus

74

-0.72

-2.5

7600

Rigil Kentaurus

4.3

-0.27

4.4

5800

Arcturus

34

-0.04

0.2

4700

Vega

25

0.03

0.6

9900

Capella

41

0.08

0.4

5700

Rigel

~1400

0.12

-8.1

11,000

Procyon

11.4

0.38

2.6

6600

Achernar

69

0.46

-1.3

22,000

Betelgeuse

~1400

0.50

-7.2

3300

320

0.61

-4.4

25,000

Acrux

510

0.76

-4.6

26,000

Altair

16

0.77

2.3

8100

Aldebaran

60

0.85

-0.3

4100

Antares

~520

0.96

-5.2

3300

Spica

220

0.98

-3.2

2600

Pollux

40

1.14

0.7

4900

The NEAREST STARS – Stars within 10 light years of the Sun

Name

#### (light years)

Apparent

Magnitude

Absolute Magnitude

Temperature

Proxima Centauri

4.24

11.10

15.53

2800

Alpha Centauri A

4.35

-0.01

4.37

5800

Alpha Centauri B

4.35

1.34

5.72

4900

Barnard's Star

5.98

9.54

13.23

2800

Wolf 359

7.78

13.46

16.57

2700

Lalande 21185

8.26

7.48

10.46

3300

Sirius A

8.55

-1.46

1.45

9900

Sirius B

8.55

8.44

11.34

12,000

Luyten 726-8A

8.73

12.56

15.42

2700

UV Ceti

8.73

12.52

15.38

2600

Ross 154

9.45

10.45

13.14

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

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

## Jewelbox

1. Which cluster is the youngest?

1. Which cluster is the oldest?

1. 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 # Gal. Long. Projected Distance (kpc) NGC # Gal. Long. Projected Distance (kpc) NGC # Gal. Long. Projected Distance (kpc) NGC # Gal. Long. Projected Distance (kpc) 104 306 3.5 6273 357 7 288 147 0.3 6284 358 16.1 362 302 6.6 6287 0 16.6 1904 228 14.4 6293 357 9.7 2808 283 8.9 6333 5 12.6 Pal 4 202 30.9 6341 68 6.5 4147 251 4.2 6356 7 18.8 4590 299 11.2 6366 18 16.7 5024 333 3.4 6397 339 2.8 5053 335 3.1 6402 21 14.1 5139 309 5 6535 27 15.3 5272 42 2.2 6656 9 3 5634 342 17.6 6712 27 5.7 5694 331 27.4 6717 13 14.4 Pal 5 1 24.8 6723 0 7 5897 343 12.6 6752 337 4.8 5904 4 5.5 6760 36 8.4 6093 353 11.9 6779 62 10.4 6121 351 4.1 Pal 10 53 8.3 6541 349 3.9 6809 9 5.5 O 1276 22 25 Pal 11 32 27.2 6626 7 4.8 6838 56 2.6 6638 8 15.1 6864 20 31.5 6144 352 16.3 6934 52 17.3 6171 3 15.7 6981 35 17.7 6205 59 4.8 7078 65 9.4 6218 15 6.7 7089 54 9.9 6229 73 18.9 7099 27 9.1 6235 359 18.9 Pal 12 31 25.4 6254 15 5.7 7492 53 15.8 6266 353 11.6

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.

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 km2 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.

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