Exploratories

The Expanding Universe

The purpose of this activity is to determine the age of the universe by examining its expansion. You will collect data with a simple model first, then repeat the process with astronomical data.

Materials: elastic, paper clips, meter stick

Procedure:

1. Have two group members hold your universe model (the elastic) horizontally so that it is not sagging but not stretched much.

2. Attach 7 paper clips, which represent galaxies, at random positions along the elastic. Choose any clip to represent the Milky Way, and make up names or numbers for the other "galaxies". Record this information in the data table.

3. We'll assign our "zero position" to the Milky Way. Determine the location of each of the other galaxies by measuring the distance from the Milky Way to each galaxy. It doesn't matter which direction they are along your universe model. Record these initial positons.

 Galaxy Name Initial Position (cm) Final Position (cm) Recessional Speed (cm/s) Milky Way

4. In one second, expand your universe by stretching the elastic--don't get carried away with this!

5. Measure the new distances between the Milky Way and the other galaxies. Record your data.

6. Calculate and record the recessional speeds using the formula below.

recessional speed .=. (final position - initial position)./. 1.00 second

7. Graph the initial position (on the y axis) versus the recessional speed (on the x axis). This is not the traditional way to graph the independent variables, but it will make our analysis easier.

8. Draw the best straight line through your data.

9. What does this data tell you about the relationship between how far a galaxy is from the Milky Way and the speed with which the galaxy is moving?

10. Would your answer to #9 be different if you had chosen a different clip to represent the Milky Way? Why or why not? You may wish to return to your elastic and clips to help you visualize this.

11. Find the slope of your line by choosing any two points which are on the line and are fairly far apart. Apply the slope formula

slope = (y2 - y1) ./. (x2 - x1)............. Slope = ___________

12. What does this slope mean? Consider looking backward in time with your universe model. Assume that your universe has been expanding uniformly prior to the time you began your measurements. If you simplify and examine the units of your slope, you'll find that the slope represents a time.... the age of your universe.

13. Use the analysis techniques you've just learned to analyze the actual data compiled by Allan Sandage at Mt. Wilson and Las Campanas Observatories given in table below.

 Galaxy Distance from Earth (Millions of Light Years-MLY) Speed (km/s) Milky Way 0 0 Virgo 78 1200 Ursa Major 980 15000 Corona Borealis 1400 21600 Bootes 2500 39000 Hydra 4000 61000 Perseus 350 5400 Hercules 650 10000 Ursa Major II 2700 41000

14. Draw the best straight line through the data.

15. Calculate the slope of the line (keep the units). Slope = _____________

16. To find the age of the universe from this data, multiply by 3.00 x 10^11. (this converts the units from MLY./.km/s to years).

Sandage/s value for the Hubble constant (age of the universe) = _______________

Note: Wendy Freedman and other researchers have found different ages for the universe by using different ways of measuring the distances to galaxies far away from the Milky Way. You may wish to explore some of these results through the Internet or an up-to-date astronomy textbook.