For this assignment you are going to practice some of the data analysis that astronomers have to do to look for evidence of extrasolar planets. You are given six example graphs of data that use three different methods: the astrometry method, the âwobbleâ or spectral method, and the transit method. I have provided some notes in the reading section on each of these methods, using the same types of diagrams I provide for the assignment. You will also be able to find a lot online about these methods and the discoveries made with them. There are two examples for each of three methods: Astrometry, Spectral, and Transit methods. For each example you are to determine if there is sufficient evidence to claim that there is an extrasolar planet orbiting the star. You are going to do this six times, once for each of the graphs. They are not connected to each other. Part 1 : For each graph answer (15% each) : Is there evidence of a possible extrasolar planet orbiting this star? (Yes or no)If there is not sufficient evidence to say there is an orbiting star, you should include a paragraph explaining why there is insufficient evidence of an extrasolar planet. There is no need to try to explain what could cause the patterns you do see in the data, but you have to explain why they are different than what you might see if there were a planet orbiting the star. (about 100 words)If there IS evidence of an extrasolar planet, you must include a paragraph about the evidence you used to come to that conclusion as well as the orbital period of the planet (how long it takes to make a complete orbit around the star). (about 100 words)Part 2 (3 pts): Answer the following question (10%) Are any of these graphs likely from the same star? Explain your answer. Remember to think about the orbit and the way we view the star. (about 100 words)version of .docx (MS word) to the DROPBOX area under COURSE ACTIVITIES on the top menu bar. Our TA will grade them and should return them within 2 weeks. If you have trouble submitting, please email a copy of the assignment before the due date to get full credit. 1 day ago ATTACHMENTS
Astronomy Assignment-make sure you can deliver the work on time
Searching for Extrasolar Planets The worlds orbiting other stars are called extrasolar planets (extra means beyond and solar means sun—planets beyond the sun). Because our equipment and methods are still fairly crude, most of the extrasolar planets discovered have had masses equal to or greater than Jupiter and are often very close to their star. As telescopes and technology continue to improve, we should be able to find planets that are the mass of Earth and smaller. With current technology, finding extrasolar planets directly is not possible. Our instruments lack the sensitivity to see extrasolar planets, but that will change with new technology. Planets are visible because they reflect the light of the star they orbit. Even so, they are only about one one-thousandth as bright as the star itself, or less. Currently, our telescopes are unable to distinguish this small amount of light from the tremendous amount radiated by the star itself. Also, because stars are so far away, the distance between the star and its planet appears very small—too small for current telescopes to resolve. The problem is similar to the way distant headlights appear as a single bright light, even though the light is being made by two distinct lights. Astronomers are developing techniques that one day may help them see enough detail to overcome the challenges posed by distance and differences in brightness. Currently, astronomers are restricted to using indirect techniques to locate an extrasolar planet. These techniques use changes in light coming from the star to infer a planet’s presence and orbit. In this session you will study two techniques astronomers currently use, transiting and spectral, and another, astrometry, that may be possible in the near future. How does the brightness of stars with transiting planets change over time? Finding transiting planets by measuring the variations in starlight is a very effective technique. Unfortunately, it is not possible for all stars. First of all, the orbit of the planet must be viewed edge-on, which enables us to see the planet clearly move in front of the star (Figure 1). If our view is face-on (Figure 2), the angle between our line of sight and the plane of the planet’s orbit will be too great. We will be unable to observe a transit. Figure 1 An edge-on view of a planet’s orbit Figure 2 A face-on view of a planet’s orbit In Figure 1, our vantage point lines up perfectly with the plane of the planet’s orbit. The planet clearly transits the star. In this case, we should observe a reduction in the brightness of starlight. In Figure 2, our view of the star-planet system is face-on. Because the planet orbits in a plane that is 90 degrees to our line of sight, the planet does not transit the star from our point of view. In this case, we will observe no reduction in brightness of starlight. In many cases, the planet will transit the star, but at an intermediate angle that makes it very difficult to observe a reduction in starlight. In Figure 3, the planet just skims the lower edge of the star, so the star’s brightness does not change very much from our vantage point. Astronomers take the angle between the planet’s orbit and their line of sight into account when inferring the actual orbit from changes in star brightness. Figure 3 Some planets orbit their star in a way that makes viewing a transit difficult when observing it from Earth When a planet transits a star, the dip in brightness can be seen on a graph of brightness vs. time. A regularly repeating dip in brightness can be a good indicator of a transiting planet. The graph would look something like this: The total brightness of the star is also important in determining whether a planet’s orbit could be detected by the transit method. A fully transiting planet will reduce the starlight brightness by anywhere from 0.1% (1/1000th) to 1% (1/100th). With bright stars, a 0.1% change in brightness is detectable by sophisticated telescopes. But with dim stars, such a subtle change is undetectable, even by the most powerful telescopes currently available. How Is Gravity Related to Planetary Orbits? It is said that Sir Isaac Newton discovered the law of gravity when an apple fell on his head as he sat under an apple tree. Of course, people already knew that objects fall to Earth, but Newton was the first to describe this force mathematically, in a formula called Newton’s Law of Gravitation. It states that any two masses will exert an equal force on each other, pulling the two objects toward one other. One of Newton’s most profound realizations was that gravity not only caused the apple to fall to Earth, but it causes the moon to stay in orbit around Earth and the planets to stay in orbit around the sun. There is a point around which both the star and planet orbit that does not wobble. This point in space, called the center of mass, remains fixed in position. Like two figure skaters who spin while holding hands, the planet and star spin around the center of mass, which is located at the exact center of the forces keeping them together. There is a point, the center of mass, between the two skaters around which both skaters spin. If the masses of the two skaters are considerably different, the center of mass will be significantly closer to the heavier skater, keeping the heavier skater more stationary while the lighter skater seems to skate around him or her. To understand the concept of center of mass, imagine putting the star and the planet on each end of a seesaw. The center of mass would be the point where you would need to put the support so they would balance. In a solar system, this point is usually well inside the star because of the great difference in mass between the star and planet. In fact, with most star-planet systems, the center of mass is so close to the center of the star that it is not within our current capabilities to detect any influence of the planet upon the star at all. However, when a very massive planet is close to the star, astronomers may see the star wobble around the center of mass. By observing this motion, they can infer the path of the planet’s orbit, the mass of the planet, and how long it takes the planet to orbit the star. One complete, back-and-forth wobble corresponds to one complete orbit by the planet. While this technique, called astrometry, is currently beyond our capabilities for extrasolar planets, it is a promising one. When astronomers are able to detect small wobbles directly, they will be able to survey the sky, possibly finding new solar systems . Here is an example of what astrometry data might look like, notice that the star appears to move on the grid at each different observation. By recording periodic motion (when the star makes a complete cycle back to the same position), one can measure the orbit of the planet around the star. 1. Observation date: March 27, 1988(star is located at x=5, y=4) 2. Observation date: September 30, 1990(star is located at x=5, y=5) 3. Observation date: March 26, 1993(star is located at x=5, y=6) 4. Observation date: September 28, 1995(star is located at x=5, y=5) 5. Observation date: March 28, 1998(star is located at x=5, y=4) This star takes approximately 10 years (from March 27, 1988 to March 28,1998) to complete a full cycle. So the period of its extrasolar planet is 10 years. The Spectral Line Detection Method for Extrasolar Planets: You have probably noticed that when a car blowing its horn passes by, the horn’s pitch changes. This is because as the car comes toward you, the sound waves arriving to your ear include both their normal speed plus the car’s speed. With these two speeds added together, the number of waves arriving at your ear is more than usual. For you, the frequency of the sound—the number of waves per second—has increased, resulting in a slightly higher pitch than usual. The opposite happens when the horn moves away from you. Again, the sound waves arriving at your ear include both their normal speed and the car’s speed. However, since the car is moving in the opposite direction of how the waves travel, the number of waves arriving at your ear is fewer than usual. For you, the frequency of the sound has decreased, resulting in a slightly lower pitch than usual. This apparent change in frequency caused by the motion of a source or observer is called the Doppler Effect. Both sound and electromagnetic waves experience Doppler shifts. You can visualize a Doppler shift by imagining you are standing at one end of a swimming pool. Every two seconds, swimmers at the other end dive in and swim the length of the pool at a constant speed, arriving every two seconds. However, if you walk toward the other end, you will encounter a swimmer more than once every two seconds. In fact, the faster you walk, the more rapidly the swimmers pass you. Their frequency has increased as a result of your motion, not because there are more swimmers. If you turn around and walk the other way, you will encounter a swimmer less often than once every two seconds. For you, their frequency has decreased. When a train whistle blows, or a star emits light, waves are sent out in all directions from the source. (Figure 1). When such a source is motionless relative to an observer, the observer receives the waves just the way they left the source. However, when the source of the waves moves toward an observer, such as Observer B in Figure 2, the waves appear to bunch. Though the source still emits the waves equally as shown in Figure 1, Observer B receives them more rapidly. For Observer A, the waves are stretched out as the source and observer move apart. Thus, when either a wave source or observer are moving, the observer experiences a change in the frequency of the waves emitted by the source. With light, the Doppler Effect produces a color shift. When an object moves toward an observer and the frequency of its light increases, its color shifts toward the blue end of the color spectrum. This is called blue-shifting, because blue light has a higher frequency than red, and increasing the frequency of light shifts it to the blue end of the spectrum. Similarly, if the source and the observer are moving apart, the light waves appear stretched to the observer. This is called red-shifting, because the longer wavelength shifts the color toward the red end of the spectrum. Figure 1: Red light has a longer wavelength than blue light does. If a source emitting yellow light moves toward an observer, its wavelength will be compressed, making it look greener. If the source is moving away from the observer, the wavelength will be stretched, making the light look more orange.     With light, the Doppler Effect produces a color shift. When an object moves toward an observer and the frequency of its light increases, its color shifts toward the blue end of the color spectrum. This is called blue-shifting, because blue light has a higher frequency than red, and increasing the frequency of light shifts it to the blue end of the spectrum. Similarly, if the source and the observer are moving apart, the light waves appear stretched to the observer. This is called red-shifting, because the longer wavelength shifts the color toward the red end of the spectrum. Using Absorption Lines from Stars to Detect Motion Stars typically emit light at all wavelengths—a complete, continuous spectrum. However, a star’s atmosphere absorbs certain wavelengths of light. When we look at light that has passed through a star’s atmosphere, some light at very specific wavelengths is missing—it was absorbed and never escaped the star. To us, the star’s spectrum shows dark lines at the wavelengths where the light was absorbed. Scientists call these lines absorption lines. Each element present in the star’s atmosphere absorbs specific wavelengths of light, creating absorption lines. Figure 3 shows absorption lines produced by calcium, sodium, and hydrogen atoms. Because each element produces a unique set of absorption lines, astronomers use them to determine the composition of a star’s atmosphere. They also use them to measure the motion of the star by observing blue- and red-shifting of the lines. When the lines are shifted toward the red end of the spectrum, we can infer that the object is moving away from the observer. When the lines are shifted toward the blue end of the spectrum, it is because the object is moving Suppose a star has a spectrum that shows these absorption lines when it is at rest: When that star is moving towards us its spectrum would appear blue-shifted like this: When it is moving away from us its spectrum would appear red-shifted like this: By watching any regularly repeating patterns in the shifting of the spectral lines, we can infer the motion of the star towards and away from us by the tug of an orbitting planet. Determining the Period of a Planet’s Orbit The time a planet takes to trace a full orbital path around its central star generally stays the same orbit after orbit is called the orbital period. The period is determined by the mass of the central star and the distance between the planet and the star. Mercury’s orbital period is approximately 88 days, Earth’s is approximately 365 days (one year), and Pluto’s is approximately 249 years. Since the stars currently being observed when searching for extrasolar planets are very similar to the Sun, we can assume that a planet taking one year to orbit its star has the same distance from its star as the distance between the Earth and Sun. Planets with longer periods are farther from their sun and planets with shorter periods are closer to their sun.
Astronomy Assignment-make sure you can deliver the work on time
Astrometry Graph 1    Astrometry Graph 2 Spectral Graph 1    Spectral Graph 2      Transit Graph 1                                   Transit Graph 2




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