Name: Astronomy 102 Lab: Hubble Law Part of today s lab will involve the use of laptops. If you own one, please bring it to class. Pre-Lab Assignment: In this week's lab, you will study the expansion of the Universe. Hubble's law is often explained in terms of dots drawn on an expanding balloon. You will be doing such an experiment to see how well it corresponds to the actual Universe. You will then be using spectra to create a velocity vs. distance plot similar to the one first made by Edwin Hubble. Answer these questions before coming to lab. A) What were Edwin Hubble s contributions to astronomy? B) What is meant by "redshift?" C) If we see a redshift in the spectrum of a galaxy, what does this tell us about the galaxy? D) 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 of 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 an animation to model the expansion of the Universe and better understand the relationship of Hubble's law. In part B, we will use data from some galaxies to determine the age of the Universe. A. Modeling the expansion of the Universe: Begin at the following website. http://wittman.physics.ucdavis.edu/animations/hubblemodel/universalexpansion.html Read through the introduction before using the app. The screen shows several galaxies with arbitrary positions and names. The names are listed next to "Galaxy Name" at the bottom. The galaxy at the center is labeled "Milky Way." 1. Are galaxies similarly spaced everywhere, or are some galaxies closer to their neighbors than others? The bar next to "Expansion Factor" allows you to change the appearance of the Universe over an unspecified time. Slide the gray switch all the way to the right.
2. Describe how the image changed as you moved the switch from left to right. 3. Look carefully at the Milky Way galaxy. Does it get bigger? Are the other galaxies getting bigger? (If you're not sure, click on a galaxy and drag it over to the same galaxy shown in the background to compare them.) 4. Locate the galaxies G-15 (to the right of the Milky Way) and G-10 (lower left). Note how far each has moved from the Milky Way. Which galaxy, G-15 or G-10, appears to have moved farther from the Milky Way in this time interval? 5. How do all the galaxies appear to move relative to the Milky Way over this time interval? 6. Which groups of galaxies move the most with respect to the Milky Way in this time interval? This animation allows you to change your perspective to other galaxies. Click and drag the upper frame until G-10 is lined up with its original location. 7. How do all the galaxies appear to move relative to G-10 over this time interval? 8. 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? 9. Would your answer to Question 8 be true in general for all locations in the Universe? 10. Is there a "center" to the expanding Universe? 11. 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 looking at "before" and "after" photographs. 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. 12. The change in wavelength: The speed of light is 300,000 km/s. The velocity of the galaxy can then be found by the Doppler formula: vv = speed of light change in wavelength rest wavelength 13. 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. For example, if we know the apparent magnitude of the galaxy is 12.0, we can find the distance to the galaxy. By calculating the distance modulus, we can consult the table from the last lab and 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. The table is at this URL. http://natsci.parkland.edu/ast/102/labs/galaxydistance.html Find the spectra of eighteen galaxies including the Milky Way on your table. 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. Record the distance in millions of light-years, where 1 Mpc = 3.26 Mly. Round each distance to three significant digits. Galaxy m m M A 14.95 Distance (millions of light-years) Velocity (thousands of km/s) 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
14. Plot the galaxy velocities versus each galaxy's distance on the graph provided. Label each of the points with the galaxy name. Draw the best straight line you can through the data points. The line should run through the origin, (0,0) 15. How would you describe in words what the graph tells you? 16. What does Hubble's law imply about the how the Universe is behaving? 17. When a galaxy is farther away, does it appear to be moving faster or slower away from us? The Hubble law equation, vv = HH 0 dd, is analogous to the equation of a line, yy = mmmm, where the slope is the Hubble constant, HH 0. The next questions shall use your plot to estimate the Hubble constant. Find the coordinates of two points on the line. They should be far apart and do not need to be the plotted galaxies. Convert the distances to light-years from Mly by multiplying by 1,000,000 and convert the velocities from thousands of km/s to km/s by multiplying by 1,000. 18. Record the converted coordinates here. Include units. 19. Calculate the slope, i.e. the Hubble constant, using the following formula. Include proper units. HH 0 = vv 2 vv 1 dd 2 dd 1 20. Using your graph and the Hubble 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.