Keplers Laws Worksheet Aiden Yeruva

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Apr 3, 2024

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Kepler’s Laws Worksheet These lab activities have evolved over many years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include, in chronological order, Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Steven Bromley, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. Student Name: Aiden Yeruva Section: _______ I. Read the introductory information on the instructions page for a reminder of the terms used in this lab. II. Kepler's First Law Comet name Semi Major Axis (AU) Periapse/ Perihelion distance (AU) Eccentricity Aphelion Distance (AU) [see instructions on how to calculate] P/2010 H2 (Vales) 3.831868 3.076097 0.197233 4.587639 125P/Spacewatch 3.129373 1.526693 0.512141 4.732053 96P/Machholz 1 3.011873 0.123794 0.958890 5.899952 For each comet, describe the comet's orbit within the solar system. Discuss the orbits shape based on its eccentricity. Does it cross any planetary orbits? Which planetary orbits does it lie between? Does its distance from the Sun change dramatically? 1) P/2010 H2 (Vales) The orbit is very circular because it has a low eccentricity and it does not intersect with any planets. 2) 125P/Spacewatch The orbit is pretty circular because the eccentricity is in the middle of 0 and 1 and it does not intersect with any planets, but it gets very close to the orbit of Mars. 3) 96P/Machholz 1 The orbit of 96P is more like an elliptical orbit because its eccentricity is very close to 1, and because of its orbit, it also goes around the Sun and interrupts the orbit of Mercury, Venus, Earth, and also Mars.

4) Which comet has the most similar orbit shape to the planets and what does this tell you about the eccentricity of the planet’s orbits? 125P has the most circular orbit and since it is almost a perfect circle the eccentricity is very similar to that of the planets in our solar system. 5) Which comet will have the largest changes in temperature? Explain 96P/ Machholz 1 because it goes closest to the sun and also moves very close to Jupiter. Return to the instruction document to set up Starry Night before answering the next set of questions. III. Kepler's Second Law Location Date Distance from sun (AU) Aphelion (1) March 1st 2018 6.02 Half way to Sun October 30 th , 2020 3.01 Perihelion July 14, 2021 0.994 Half way away from sun March 25 th , 2022 3.01 Aphelion (2) August 29 th , 2024 6.02 6) Does the comet spend more time close to the sun (within the halfway distance) or far from the sun(outside the halfway point). Provide evidence for your answer from your table. It spends more time outside of the halfway point because it takes about two years to get within halfway of the sun and to get to the sun its only about one year. 7) When does the comet move the fastest in its orbit? Give dates and use terminology. The comet moves fastest between Aphelion and halfway to the sun because it takes about two years from March 1 st , 2018 to October 30 th , 2020. 8) When does the comet move the slowest in its orbit? Give dates and use terminology It moves the slowest when it is approcahing perihelion from halfway to the sun. It takes about a year and half from October 30 th , 2020 go July 14 th , 2021. 9) Use the info panel to find the eccentricity of this comet. Eccentricity of 15p/Finlay: 0.716686

10) Describe if this eccentricity is large or small and how it affects the perihelion, aphelion and changing speed of the comet. The eccentricity is rather large because it has a more oval orbit and it affects the perihelion and aphelion because the distance increases as eccentricity increases. 11) Remember that orbits are independent of the mass of the orbiting object so any small dust particles will follow a very similar path to the comet itself. Adjust the time to see when the Earth is closest to the orbit of Comet 15p/Finlay and record the month we might see a meteor shower sourced from that comet. August of 2034 Return to the instruction document to set up Starry Night before answering the next set of questions. IV. Kepler's Third Law Planet “P” Period (years) “a” semimajor axis (AU) Mercury 0.238 Years 0.387099 Earth 1 Year 1.000003 Jupiter 11.86 Years 5.203887 Saturn 29.44 Years 9.536676 Uranus 84.1 Years 19.189165 12) Insert graph here with trendline added.

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13) Describe the graph using the trendline in your description. The trendline is going through all of the dots but since Jupiter has a much larger orbital period and semimajor axis it makes it look skewed. 14) Looking at your table in the google sheet is P^2=a^3 exactly? Why or why not? It is not exactly equal because it just does. 15) The power of Kepler’s third law is to predict the locations of objects by their motion. Assume scientists detect the slow motion of an object at the edge of the known solar system that is found to have an orbital period of 250 years. How far from the Sun is the object in units of Astronomical Units? 39.7

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