Extrasolar Planets Worksheet

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Clemson University *

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1020

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Physics

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Jan 9, 2024

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Name ______ Extrasolar Planets Worksheet These lab activities have evolved over years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Lea Marcotulli, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. 1) If you plot a star’s radial velocity versus date, what do you expect to see if a planet is perturbing the star?. Describe what you expect to see and what information could be gained from the graph. If you plot a star’s radial velocity versus date, it would be expected to see a periodic curve because of the effect that the planet’s mass has on its orbit. 2) Copy and paste your graph here and then briefly describe your graph in your own words. 3) How is what you obtained different from your expectation?
What I obtained is not much different from my expectations for what I thought the ups and downs of the graph were going to be. 4) Does your graph say that there isn’t a planet? Explain Yes, the graph does say that there isn’t a planet due to its ups and downs. 5) Based on your graph at this point, can you put any upper or lower limits on the orbital period of a possible planet? Explain. Yes, you can put both upper and lower limits once the data points are plotted on the graph. Return to the instructions prior to answering the next set of questions. 6) What is 11.1 modulo 4 [ =mod(11.1,4) in google sheet syntax ]? 3.1 7) For what value of the period does the graph show clear periodic motion? 4.4 8) Why does plotting the phased date vs velocity and setting the period work better than the first plot of raw data? Plotting the phased date vs velocity is more effective in visualizing periodic motion since it aligns the date points based on their phase, allowing you to see repeating patterns. 9) Compare this to, for example, Mercury’s period around the Sun (88 days.) What does this tell you about the planet compared to Mercury? (Think about keplers 3rd law) It is much greater than Mercury's period. Return to the instructions prior to answering the next set of questions.
10) Convert the period to years and calculate A recording your results here. P = 0.012 years a = 0.053 A.U. 11) If we know how far the planet is from its star and its period, we know its circular velocity: v planet = 27.403 A.U./year v planet = 129471.12 m/s 12) Velocity of the star from your graph: v star = 55.45 m/sec 13) Why might the maximum positive velocity not be equal in magnitude to the minimum negative velocity? This is due to the fact that the data for maximum positive velocity was not collected continuously. There is no max or min velocity. 14) Solve for the mass of the planet: m planet = 0.0042 solar masses m planet = 8.566*10^26 kg m planet = 0.451 M J m planet = 143.478 M E 15) Summarize what you learned about the planet. Discuss its orbital period, mass and how it compares to the planets in our solar system. The orbital period is 4.4 which is more than mercury, and about 143.478 times the mass of Earth. 16) Can you think of complications that we did not consider in our analysis? We may have come across some complications, but I don’t think I have.
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17) Using the uncertainty in the maximum positive velocity measurement, find the percent error in our velocity calculation for the star. percent error = 100 × uncertainty measurement Percent error = 9.581% 18) If the percent error in the velocity carries to our calculation of the mass of the planet, what are the bounds on the planet’s mass? Upper bound of planet mass= .494 M J Lower Bound of planet mass= 2.486 M J Return to the instructions prior to completing the final questions. Star HD 10697 (109 Pisces) Repeat the process using the data in the “HD10697 data” google sheet and record the information about the planet here. You will not need to calculate the phased date, just look carefully at the graph of velocity vs date. 19) Period of planet= 908 days Period of planet = 2.487 years 20) Distance planet is from the star (A) = 1.835 AU 21) Velocity of planet = 0.738 AU/year Velocity of planet = 3485.38 m/s 22) Velocity of Star= 105.25 m/s 23) Mass of the planet = 142.62 solar masses Mass of the planet = 150121.239 M J Mass of the planet = 47777278.4 M E
24) Percent uncertainty in star velocity= 5.416 % 25) How does this planet compare to those in our solar system and the planet around 51 Pegasi? Explain. This planet is much larger than most of the planets in our solar system and 51 Pegasi.