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# ES 1010 Unit VIII Assignment Worksheet

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ES 1010 Unit VIII Assignment WorksheetPart 1: Finding the Distance to Stars Using the Parallax AngleInstructions:Read Chapter 15 and Appendix D (pp. 543-545) in the textbook and the background information below.Answer the three questions at the bottom directly in this lab worksheet.This NASA web page provides additional explanation and allows you to check your answer:http://imagine.gsfc.nasa.gov/features/yba/HTCas-size/parallax3.htmlBackground:Stellar Parallax is the apparent shift in the location of a star due to the orbit of the Earth. In other words,the star will appear to be in a different place depending on the line of sight from the Earth. By knowing thediameter of Earth’s orbit and by measuring the angle of apparent shift (the parallax angle), astronomerscan calculate the distance to the nearby stars using trigonometry. This method has been used forcenturies. The ancient Greeks were able to measure some of the closest stars this way. Today,sophisticated telescopes have greatly enhanced this method. Figure 1 is a graphic from your textbookshowing how this works:Figure 1. Geometry of stellar parallax, (Lutgens, Tabuck, & Tasa, 2014)Assignment:For this assignment, you will determine the distance to a star, “HT Cas”, using the method of stellarparallax. Figure 2 and 3 below are photos of HT Case, taken six months apart: ES 1010 Unit VIII Assignment WorksheetFig 2. Image of HT Cas taken 06/96Fig. 3. Image of HT Cas taken 12/96When we super-impose these photos, we get the following image (figure 4):Fig. 4. Composite image of measurements ofHT Cas (shown in red) taken six months apart.You can see that the position of the star appears to have changed over the six-month time period.However, it is actually the angle from which the photos were taken that has changed. During that 6month period, the Earth moved from one side of the sun to the other.Using a stellar astrometric catalog, we find that the two stars closest to HT Cas are a distance of 0.01arcseconds apart. Based on this information, we can estimate that the angle of shift of HT Cas (theparallax angle) to be approximately 0.015 arcseconds apart.We also know that the radius of the Earth’s orbit is 1.0 A.U. (astronomical units).Using these two measurements, we can then determine the approximate distance to HT Cas using thefollowing equation:d= distance to HT Casa=radius of the Earth’s orbitp=parallax angle1. (10 points) Given the above equation and information provided, about how far away is HT Cas? ES 1010 Unit VIII Assignment Worksheeta.b.c.d.133 parsecs67 parsecs33 parsecs0.015 parsecsAnswer:2. (10 points) Your answer was calculated in parsecs. Given that 1 parsec = 3.2616 light years,about what is the distance to HT Cas in light years? (Your answer in parsecs X 3.2616 light years= The Distance to HT Cas in light years).a. 0.025 light yearsb. 217 light yearsc. 434 light yearsd. 219 light yearsAnswer:3. (30 points) Based on your answer, do you think this is a star that we might be able to send aspace probe to? Why or why not? Support your answer.Part 2: Using a Hertzsprung-Russell DiagramInstructions: After reading the Unit VIII lesson, click here to access the NASA web page “Stars” andanswer the questions below using Figure 5. You can also copy and paste the web address into

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