Student Exploration: Big Bang Theory – Hubble’s Law ALL ANSWERS 100% CORRECT FALL-2021 SOLUTION GUARANTEED GRADE A+

Vocabulary: absolute brightness, absorption spectrum, apparent brightness, Big Bang theory, blueshift, Cepheid variable, Doppler shift, Hubble constant, Hubble’s law, luminosity, megaparsec, period, redshift, spectrograph Gizmo Warm-up In 1912, an astronomer named Henrietta Swan Leavitt studied a class of stars called Cepheid variables. These stars change from bright to dim to bright again. Her discoveries led to a method of measuring distances to other galaxies and eventually helped to support the Big Bang theory of the origin of the universe. In the Big Bang Theory – Hubble’s Law Gizmo, select Region A. Look at the image of the Andromeda Galaxy, a galaxy relatively close to our own Milky Way galaxy. 1. Locate the two Cepheid variables, the stars that change in brightness over time. Star A-091 is the yellow star, and star A-171 is the white star. A. Which star reaches a greater apparent brightness? B. Which star takes longer to pulse? 2. Because both stars are in the same galaxy, they are about the same distance from Earth. Based on what you see, how is the brightness of the star related to how quickly it pulses? Activity A: Period and brightness Get the Gizmo ready: ● On the STARS tab, check that Region A: NGC 224 (Andromeda Galaxy) is selected. If not, click Return to map and select Region A. Introduction: Two factors determine how bright a star appears to an observer: its luminosity, or absolute brightness, and its distance from the observer. A star may appear bright because it is a large, luminous star, or because it is very close. It is only possible to use a star’s apparent brightness to determine its distance if you know the star’s luminosity. Henrietta Leavitt’s work on Cepheids provided the key to solving this problem. Question: How do Cepheids allow astronomers to measure intergalactic distances? 1. Collect data: Locate and select the yellow Cepheid variable star (A-091) in the lower left section of the Andromeda Galaxy. Click the Collect data button. You will see a graph of the apparent brightness of the star over time. A. How does the star’s apparent brightness change over time? B. Turn on Show time probes. Set the left probe at the first brightness peak, and the right probe at the second brightness peak. List the time represented by each probe: Left probe time 1.2 Right probe time 13.5 C. What is the time difference between the two brightness peaks? This difference is the period of the Cepheid. D. In the DATA tab, record the name of this star and its period. Do the same on your paper Data worksheet, located on the last page of this document. (Activity A continued on next page) Activity A (continued from previous page) 2. Collect data: The apparent brightness of the star is shown on the y-axis of the graph. The brightness is given as the ratio of the star’s brightness to the Sun’s brightness if viewed from a standard distance of one megaparsec (1 Mpc), which is about 3.26 million light years. For example, a brightness of “4,000” means that the star appears 4,000 times as bright as the Sun would appear if observed from a distance of 1 Mpc. A. What is your estimate of the mean apparent brightness of star A-091? B. Turn on Show mean brightness. What is the mean brightness of A-091? C. In the DATA tab, record this value. Do the same on your paper Data worksheet, located on the last page of this document. 3. Observe: Stars emit light at a variety of wavelengths. Just as white light is separated into a rainbow when it passes through a prism, starlight can be separated into its constituent colors when it passes through an instrument called a spectrograph. The result is a pattern of colors and black bars called an absorption spectrum. The bars represent wavelengths of light that are absorbed in the star’s atmosphere. Each star’s unique spectrum depends on the temperature and composition of its atmosphere. 4. Click Record spectrum to record the star’s spectrum. These will be saved under the Spectra tab for later use. Look at the spectrum of A-091. Notice the pattern of colors and black bars in the star’s absorption spectrum. 5. Record: Click Done. Select the other Cepheid variable star in the Andromeda Galaxy (A-171). Determine and record the period, mean brightness, and spectrum of this star. Then, click Return to map and select Region B. There are a total of ten Cepheids hidden in the nine regions of the Gizmo. Record the period, mean brightness, and spectrum of all ten stars both in the Gizmo data table and on your own data table. (Activity A continued on next page) Activity A (continued from previous page) 6. Compare: By comparing Cepheid variables that were all about the same distance away, Henrietta Leavitt discovered that larger, more luminous Cepheids had longer periods. Look at the periods of the ten stars in your data table. A. Based on the periods of the stars, which three stars are the most luminous? B. Find two stars with similar periods, and therefore similar size. List these stars, their periods, and their mean brightness below. Star: A-091 Period: 2 Mean Brightness: 7000 Star: A-171 Period: 2 Mean Brightness: 2499 C. Compare the apparent brightness of these two stars. Which star do you think is farther away? Explain with Details and supporting reasoning.