Using the Transit Method to detect extrasolar planets

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User Generated

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ZvxrUneevatgba24

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Science

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Astro 115

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University of Michigan - Ann Arbor

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Would love to these questions regarding the transit method answered. Deals with transit method of detecting planets to answer questions about them. Few files will explain the details.

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Astronomy 115: Weekly Project 08 Due on: Thursday, March 29th 2017 (in lecture) If you have any questions about these homework problems, you can attend my office hours (Ben) on Tuesday 3/27 from 5:30 to 6:30 pm, or you may post on the class piazza site (link on canvas). Please print your homework neatly. For any numerical problems, you must write down the formula you are using and show intermediate steps of your calculation, to receive full credit. While you may work with other students, all answers must be your own. When handing in your work, multiple pages should be stapled. Not adhering to the above requirements could result in point deductions. This assignment will discuss chapter 11 of the book. We will specifically look at a newly discovered exoplanet, and calculate some of its main features using the transit method. Finally, armed with our calculations, we will inquire about the potential habitability of this newly discovered exoplanet. Problem 1 Detecting Exoplanets: Transit Method Figure 1 - This is the "Kepler light curve" of the transit flux. The black dots are the measurements; Dark blue dots are the averages over 30 min intervals. The red curve is the best fit to the data (what you should use!!!) Figure 2 – Plot shows the velocity of the star (NOT THE PLANET) with respect to its center of mass. The black dots are the measurements; The dark curve is the best fit model, and is what you should use!! The above figures represent a real exoplanet detected by the Kepler and the Keck Telescopes, orbiting a ! − !"#$$ star just like our sun. Our goal in this problem is to use the available information from the plots above and our knowledge of the star to calculate the density and surface temperature of this newly discovered exoplanet (again, we want the planets density, not the stars density, so make sure your variables reflect that). This is a multipart calculation, and is split up in the following parts. Continued on Next Page 1 A. In figure 1, we see that when our exoplanet passed in front of the star (so it was between our telescopes and the star), the stellar flux or brightness “dipped”. Use this information to find the radius !! of the planet, given the following equation: ∆! !!! ≈ ! ! !∗ Where !∗ is the radius of the Sun, 6.957x108 meters. B. Using figure 2 to find the orbital period, find the orbital distance !! of our exoplanet to its host star. Use Kepler’s law to do this (use the approximate method: cosmic calculation 7.1). C. Using figure 2 to find the stellar velocity, find the mass of the planet using conservation of momentum. Refer to cosmic calculation 11.1 as a guide, and report how our exoplanet’s mass compares to Jupiter’s mass. Some (but not all) variables you will need include the mass of the Sun (1.989*1030 kg) and the velocity of a star which can be !"# ! !"# determined from the curve in Figure 2: = !∗ ! D. Using results from A and B, report the density of our newly discovered exoplanet. Make sure your final units are kg/m3. Based on this density, what might the composition of the planet be? E. The surface temperature of this planet is ~760 K. Based on this surface temperature of the planet and the density calculated in part D, do you think this planet could be earth 2.0? In part B you calculated the orbital distance of the exoplanet: Is it in the habitable zone for a sun-like star? Explain. 2 The x-axis in Figure 2 is in units of days. Too much information: BJD = Barycentric Julian Days. Day O is Monday, January 1, 4713 BCe on the proleptic Julian calendar e (November 24, 4714 BC, in the proleptic Gregorian calendar 2). "Julian" = Julius Caesar, who instituted that calendar. So the Julian date is just a total count of days from some zero point, ignoring years and avoiding confusion about which calendar is being used. Since 4713 BC (or 4714 BC) was a long time ago, one usually subtracts a large number of days (like 2.5 million, for example), to make a readable number without having to have 7+ decimal places. Astronomical phenomena don't care about our years (except for solstices, equinoxes, etc.) Barycentric time is corrected to the center of mass of the solar system, because as the Earth moves in its orbit there is a time delay due to the finite speed of light. This correction can be as much as 8 minutes - the light travel time from Sun to Earth. Astronomers used use Heliocentric time, referred to the center of the Sun, but the Sun makes small wobbles around the center of mass of the Solar System, making shifts of up to 4 seconds in timing. (The wobble of a star due to its planets is something we use to detect extrasolar planets, as discussed in the upcoming chapter 11.)
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Tags: astronomy life in the universe Astrobiology