Pre-Lab Assignment: In this week's lab, you will study the expansion of the Universe. The Hubble–Lemaître law is often explained in terms of dots drawn on an expanding balloon. You will do such an experiment to see how well it corresponds to the actual Universe. You will then use spectra to create a velocity vs. distance plot similar to the one first made by Edwin Hubble. Answer these questions before coming to lab.
1. What were Edwin Hubble's contributions to astronomy?
2. What is meant by "redshift?"
3. If we see a redshift in the spectrum of a galaxy, what does this tell us about the galaxy?
4. Let's say that you graph two quantities, such as distance and time. You find that the change in distance is constant with respect to time. What will your graph of distance versus time look like? Explain your answer or draw an example graph.
Introduction: In the early 20th century, astronomer Vesto Slipher, having studied the spectra of over forty galaxies, discovered that nearly all those galaxies were moving away from us. He did this by looking at the redshift in the spectral lines. By the end of the 1920s, Edwin Hubble had measured the distances to the receding galaxies and noticed something odd. The farther away the galaxy was from us, the faster it was receding. Today, we look at Hubble's discovery as evidence for the expansion of the universe. This lab exercise has two parts. In part A, we will use a simulator to model the expansion of the universe and better understand the relationship of the Hubble–Lemaître law. In part B, we will use data from some galaxies to determine the age of the universe.
A. Simulation of the motion of galaxies: We will use the interactive simulation at this website: astro.unl.edu/mobile/Galaxies/GalaxiesStable.html The screen shows several galaxies with arbitrary positions. One galaxy is designated as the observer, and the other galaxies have arrows, which show what direction they move in relation to the observer galaxy. The length of the arrows show how fast the other galaxies move.
1. Are galaxies similarly spaced everywhere, or are some galaxies closer to their neighbors than others?
2. How do all the galaxies appear to move relative to the observer galaxy?
3. Which galaxies appear to move fastest compared to the observer galaxy?
Click on another galaxy to choose a new observer.
4. How do all the galaxies appear to move relative to the new observer galaxy?
5. What is the relationship between an object's distance away from you in the Universe and the speed it would appear to move away from you?
6. Would your answer to Question 5 be true in general for all locations in the universe?
7. Is there a "center" to the expanding universe?
8. Considering your answers to these questions, what's really moving, the galaxies or space?
B. The "real" universe: In reality, measuring the expansion of the universe isn't as easy as seeing which way the galaxies are all moving. We need to measure the velocity of a galaxy by looking at the calcium absorption lines in the galaxy's spectrum. For example, the measured wavelength of the calcium "K" line for a specific galaxy is 4240Å. The wavelength measured in a laboratory, the rest wavelength, for the K line is 3933.67Å.
9. Calculate the change in wavelength:
The speed of light is 300,000 km/sec. The velocity of the galaxy can then be
found by the Doppler formula:
10. For this galaxy, we get a velocity of __________________ kilometers/second.
From many observations of galaxies, we can assume that the absolute magnitude of a galaxy is -22. If we know the apparent magnitude of the galaxy is 12.0, we can find the distance to the galaxy. Applying the distance modulus used in previous labs, we find that the distance to this galaxy would be 63,095,000 parsecs (63 Mpc) or over 200,000,000 light years (200 Mly)! Now you can see how we get both the velocity and distance for each galaxy.
In lab you will find the spectra of eighteen galaxies, including the Milky Way. Since we reside within our galaxy, the Milky Way will serve as our lab spectrum. Using the velocity numbers at the top, determine the recession velocity of each galaxy by comparing its spectrum to the Milky Way's spectrum. Record these velocities in the table. Use the given apparent magnitude to find the distance modulus and the distance to the galaxy in light years. Round to three significant digits.
| Galaxy | m | m – M | Distance (millions of light-years) |
Velocity (thousands of km/s) |
|---|---|---|---|---|
| A | 14.95 | |||
| B | 13.44 | |||
| C | 16.71 | |||
| D | 15.32 | |||
| E | 16.94 | |||
| F | 16.16 | |||
| G | 14.66 | |||
| H | 14.83 | |||
| I | 16.71 | |||
| J | 16.59 | |||
| K | 14.81 | |||
| L | 16.16 | |||
| M | 16.94 | |||
| N | 15.21 | |||
| O | 16.00 | |||
| P | 16.59 | |||
| Q | 14.95 |
Plot the galaxy velocities versus each galaxy's distance on the graph below or linked here. Draw the best straight line you can through the data points.
11. How would you describe in words what the graph tells you?
12. What does the Hubble–Lemaître law imply about the how the universe is behaving?
13. When a galaxy is farther away, does it appear to be moving faster or slower away from us?
The Hubble–Lemaître law equation, v = H0d, is analogous to the equation of a line, y = mx, where the slope is the Hubble constant, H0.
14. Use the graph to estimate the Hubble constant. Find the coordinates of two points on the line and calculate the slope, i.e. the Hubble constant, using the following formula. Include proper units.
m = (y2–y1)/(x2–x1)
18. Using your graph and the Hubble–Lemaître law equation, estimate what the distance of a galaxy would be if its spectrum shows it to be receding from us at a rate of 120,000 km/s.
This lab was adapted from Lecture-Tutorials For Introductory Astronomy, third edition, by E.E. Prather, et al.
