Keplers Laws Worksheet

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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: Chloe Carpenter Section: __ 9___ I. Read the introductory information on the instructions page for a reminder of the terms used in this lab. II. Kepler's First Law 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): This orbit is found between Jupiter’s orbit and Mars’ orbit. It’s eccentricity is much closer to 0 than 1, therefor it has more of a circular shape. It does not cross any planetary orbits. Because it has a low eccentricity, it does not have a dramatic change in distance from the sun, but it does have some change, as it is still slightly ellipse-shaped. 2) 125P/Spacewatch: This orbit is between Jupiter’s orbit and Mars’ orbit. It’s eccentricity is between 0 and 1, so it has an oval shape, with a noticeable change in distance from the sun. It does not interfere with any planetary orbits, however it does come very close to the orbit of Mars. 3) 96P/Machholz 1: This orbit lies within the orbit of Jupiter, and crosses the planetary orbits of Mars, Earth, Venus, and Mercury. It has an eccentricity extremely close to 1, therefore this orbit has a very strong elliptical shape. At one end, this orbit comes close Comet name Semi Major Axis (AU) Periapse/ Perihelion distance (AU) Eccentricity Aphelion Distance (AU) [see instructions on how to calculate] P/2010 H2 (Vales) 3.831869 AU 3.076098 AU 0.197233 4.58764 AU 125P/Spacewatch 3.129373 AU 1.526693 AU 0.512141 4.732053 AU 96P/Machholz 1 3.011873 AU 0.123794 AU 0.958898 5.899952 AU

to the Sun (closer than any of the planetary orbits), and on the opposite ends, extends almost to the orbit of Jupiter, showing a drastic change between distance. 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? - P/2010 H2 has the most similar orbit shape to the planets. This tells us that the eccentricity of the planet’s orbits falls very close to zero. 5) Which comet will have the largest changes in temperature? Explain - 96P/Machholz will have the greatest change in temperature, considering how extremely close this comet gets to the sun, and then a switch to a drastic distance from the sun. Return to the instruction document to set up Starry Night before answering the next set of questions. III. Kepler's Second Law 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 close to the sun, and we know this because it took much less time to go from half way to perihelion than it took to go away from the sun. 7) When does the comet move the fastest in its orbit? Give dates and use terminology. - It moves fastest at perihelion, when it is closest to the sun. For example, on July 10th, 2021, it moved quicker to the next point than compared to March 1st, 2018, when it took a longer time to move to the next point. 8) When does the comet move the slowest in its orbit? Give dates and use terminology - The comet moves slowest at aphelion. For example, on March 1st, 2018, it took a much longer time to move from that point to the next than compared to the comet moving from perihelion, on July 10th, 2021, to the next point. Location Date Distance from sun (AU) Aphelion (1) March 1st 2018 6.02 Half way to Sun November 1st, 2020 3.01 Perihelion July 10th, 2021 0.99 Half way away from sun March 26th, 2022 3.01 Aphelion (2) August 17th, 2023 6.02

9) Use the info panel to find the eccentricity of this comet. Eccentricity of 15p/Finlay: 0.716687 10) Describe if this eccentricity is large or small and how it affects the perihelion, aphelion and changing speed of the comet. - This eccentricity is large, as it is close to 1. This affects perihelion and aphelion, as the shape is dependent on the eccentricity, and perihelion and aphelion depend on the closest and furthest points on the shape. With a higher eccentricity, the shape is more elliptical, cause a quick curve around the edge which is closest to the sun. 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, 2024 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 0.241 years 0.387099 AU Earth 1.001 years 1.000003 AU Jupiter 11.86 years 5.202887 AU Saturn 29.44 years 9.536676 AU Uranus 84.10 years 19.189165 AU

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12) Insert graph here with trendline added. 13) Describe the graph using the trendline in your description. - The trend line shows that there is a straight linear relationship, going through all of the points, between the period squared and the semi-major axis cubed. 14) Looking at your table in the google sheet is P^2=a^3 exactly? Why or why not? - Not exactly. They slightly differ because of uncertainties and the use of rounded numbers and not exact numbers. 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? - 39.685 AU

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