lecture_tutorial_12_rv_exoplanets

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New Mexico State University *

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ASTR-305

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Astronomy

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Apr 30, 2024

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11 WOBBLING STARS: HOW EXTRASOLAR PLANETS ARE DISCOVERED GOALS = Discover how Doppler shift is used to detect the presence of extrasolar planets = Analyze graphical data to interpret extrasolar planet motion = Compare the orbital distance and mass of extrasolar planets PART A: THE MOTION OF THE SUN Astronomers have made astounding progress in discovering planets orbiting stars outside our solar system. In fact, they have identified a vastly larger number of these planets, called extrasolar planets, than currently exist in our own solar system. There is more than one technique for detecting extrasolar planets. But with current technology, the most effective technique for detection has been the radial velocity of Doppler shift technique. In this activity, you will learn how astronomers use this technique to infer the presence of planets around other stars. Let’s begin by looking at the radial velocity technique applied to our own solar system. In Figures I and 2, there are two different depictions of our solar system. Since the Sun and Jupiter account for nearly all the mass of our solar system, our solar system is modeled here as a two-body problem involving only the Sun and Jupiter. Note that these representations are not drawn to the proper scale for the size or distance of the objects shown.* Our solar system as seen from above (not to scale) Our solar system as seen edge-on or from the side (not to scale) Center of Mass Center of Mass Sun Jupiter Figure 1 Figure 2 *The center of mass of the solar system is located within the Sun. We 've exaggerated the Sun's orbit about the center of mass. Prather, Offerdahl, and Slater 131 Life in the Universe — Activities Manual, 2nd Edition

Activity 11 1. Is Jupiter coming toward or going away from you in Figure 27 2. Is the Sun coming toward or going away from you in Figure 2? 3. Draw a stick figure in Figure 1 to indicate where an observer would need to be in relationship to the solar system to see the view shown in Figure 2. Now examine the four drawings in Figure 3 below. Each of the four drawings shows the positions of the Sun and Jupiter at a different time during a single orbit. March 1985 Observer . Observer March 1991 Observer Observer March 1988 s Jupltfy Figure 3 4. In Figure 3, does the Sun always appear to remain in the same position? If not, describe its motion. Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater

Extrasolar Planeis What form of interaction or force causes the orbital motions of the Sun and Jupiter? Estimate the time (in Earth years) for the Sun to complete one orbit (this time is known as the orbital period). How does this time compare to the orbital period of Jupiter? use the boxes below to draw what the For each of the four drawings in Figure 3, he or she was observing the solar system observer would see at each time period if edge-on. See the example in Figure 2. March 1985 March 1988 March 1991 March 1994 Life in the Universe _ Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 133 —4

Activity 11 8. Make two sketches below (using representations in Figures 1 and 2) depicting what you would see in September 1992 from the observer location. Your drawings need to include the positions of the Sun and Jupiter. September 1992 September 1992 When studying motion it is useful to consider the object’s velocity as being made of two parts or components. The component of velocity that is directed toward (negative) or away from (positive) the observer’s line of sight is known as the radial velocity. 9. Jmagine that you are at the observer location shown in the drawings you made in Question 8 for September 1992, and that you are located much farther away from the Sun and Jupiter’s orbital paths than is depicted in your drawing. a. From your point of view and line of sight at the observer location, would the Sun appear to be moving with a radial velocity? If so, is it positive or negative? Explain your reasoning. b. From your point of view and line of sight at the observer location, does Jupiter appear to be moving with a radial velocity? If so, is it positive or negative? Explain your reasoning. 10. Now consider the entire interval shown in Figure 3 from March 1985 all the way through March 1994. a. During which range of dates would the Sun appear to be moving with a radial velocity? When is the radial velocity positive and when is the radial velocity negative? b. During which range of dates would Jupiter appear to be moving with a radial velocity? When is the radial velocity positive and when is the radial velocity negative? Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 134 '

4 Extrasolar Plarnets If an observer and a star being studied are both stationary then the wavelength of the light traveling from a star to an observer will remain unchanged. However, if the star is moving toward an observer (with a negative radial velocity), then the light’s wavelength will appear to be shifted to a shorter wavelength (or blue shifted). Furthermore, if a star is moving away from an observer (with a positive radial velocity), the light’s wavelength will appear to be shifted to a longer wavelength (or red shifted). This shifting in the wavelength of light due to the motion toward or away from a light source (like a star) is known as the Doppler shift. 11. During which range of dates would the light from the Sun have a Doppler shift to a longer wavelength? Explain your reasoning. 12. During which range of dates would the light from the Sun have a Doppler shift to a shorter wavelength? Explain your reasoning. 13. If, instead of viewing the solar system edge-on (like in Figure 2), an observer was very far away from the solar system and looking directly down on the solar system, during what time interval, if ever, would the observer see the Sun have a Doppler shift to shorter wavelengths? Explain your reasoning. PART B: DISCOVERING NEW PLANETS Astronomers measure the change in radial velocity using the Doppler shift of the light coming from a star. They can graph this change in radial velocity versus time. Figure 4 shows a radial velocity versus time graph for a star that has an extrasolar planet orbiting it. A 50 + 2 Q L o J| Il 1 1 ! 4> B 1 3 5 7 9 = t; .50 4 Time (days) Figure 4 Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 135

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