ASTRO 102 Homework 2: Understanding Stars and Lunar Phases

ASTRO 102: Stars, Galaxies, and the Universe Winter 2024 Homework 2. Due: Thursday, 02/01 Name: Uniqename: Section Number or GSI name: • We request that you do your homework on paper or a tablet (the sheet you are reading can be printed and you can use it). We recommend that you write out any math by hand (neatly). If you need more space just add a sheet of paper and make it clear what is going on. Alternatively, using a tablet also works quite well. • Scan the pages into a pdf document using your phone (or other method of your choice). Upload to Gradescope, via the Canvas site. Videos on how how to scan into a pdf and upload to Gradescope are available on the Canvas site. • Make sure to mark the pages your answer to specific questions appear on in Gradescope. If you are unsure how to do this, please look at the gradescope video/website or ask your GSI. If you do not tag the pages that questions are answered on, this significantly increases the time it takes to grade the HWs and we will begin deducing points after HW 1. • We suggest you keep your original paper homework or the pdf you submitted to Gradescope for your own records. In the event that there is a computer error associated with Gradescope software your own records or paper copy will help to clarify the problem and secure your credit. • Homework will be graded based on correctness and clarity. Make sure that your work is easy to read and show all the work necessary to complete each quantitative problem, including units and conversions between units at each step. Simply stating the answer is not sufficient for credit, even if the answer is correct. When appropriate, use scientific notation and round your numerical result to a reasonable number of significant figures. • Do not use generative AI (such as ChatGPT or UM GPT) to produce your solutions. 2-1 Harper Johnston harpjohn Robert Frazier

2-2 Homework 2. Due: Thursday, 02/01 Problem 1 Review of motions in the solar system and lunar phase. 20 points total Problem 1.1 (10 points) : It is 6pm and you see the Moon just rising above the horizon. What phase is the Moon? Draw a diagram to illustrate the relative position of the Sun, Earth, and Moon, and show which part of the Moon is illuminated.

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Homework 2. Due: Thursday, 02/01 2-3 Problem 1.2 (10 points) : What phase is the Moon on the day of a solar eclipse? How about a lunar eclipse? Draw a diagram justifying your answer.

2-4 Homework 2. Due: Thursday, 02/01 Problem 2 Take one page of notes on Chapter 3 of the textbook/lecture. (hint: the Big Picture and Summary of Key Concepts sections at the end of the chapter may be useful.) 10 points

Homework 2. Due: Thursday, 02/01 2-5 Problem 3 Answer 5 Quick Quiz Questions from Chapter 3. Write out the question and your answer selection. Justify your answer in no more than 2 sentences. Make sure to give the number of the ques- tion you are answering. 10 points

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2-6 Homework 2. Due: Thursday, 02/01 Problem 4 Quantitative problems from Chpt 3 (50 points total) Problem 4.1 (10 points) : Suppose a new planet with a semimajor axis of 9 AU was discovered in orbit around the Sun. What is the period of this planet? Problem 4.2 (20 points) : A comet in orbit around the Sun with an orbital eccentricity e = 0.5 and a semimajor axis of a = 25 AU. Calculate the comets distance from the Sun at closest approach (perihelion) and greatest distance (aphelion). Draw a diagram of the orbit with the perihelion, aphelion, and location of the Sun labelled. If you are having difficulty with this consult Mathematical Insight 3.1 in your book.

Homework 2. Due: Thursday, 02/01 2-7 Problem 4.3 (20 points) : Method of Eratosthenes. You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside and observe that the altitude of your sun is 80°. What is the circumference of Nearth? (Hint: Apply the technique used by Eratosthenes to measure Earth’s circumference. Drawing a diagram may help.) & o X circumfrence N = 1 , 500 m & x CN = 1 , 500 km x · O 6 circumfrence of Nearth = 6 , 750 km

2-8 Homework 2. Due: Thursday, 02/01 Problem 5 The intertwining of astronomy, empire, and war Read this article on the relationship between astronomy, empire, and war over the last several hundred years. https://www.nature.com/articles/d41586-018-06612-w (10 points total) Problem 5.1 5 points : Summarize the relationship between astronomy, empire, and war in a short paragraph. Problem 5.2 5 points : Modern world powers continue to invest large sums in astronomy even when it is not of any military use. Apart from pure interest in astronomy for its own sake, can you think of any other reasons why these nations continue to do so?

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2. Which of the following was not a major advantage of Copernicus’s Sun-centered model over the Ptolemaic model? Answer: A. It made significantly better predictions of planetary positions in our sky. Justification: While Copernicus was correct in his idea that the Earth orbits the Sun, he was incorrect in assuming that the orbital paths of the planets were all perfect circles. Because these orbits were still perfectly circular rather than elliptical, the model still produced inaccurate predictions. 4. Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler’s second law, Answer: B. Earth travels faster in its orbit around the Sun in January than in July. Justification: Kepler’s second law states that a planet moves faster in the part of its orbit nearer the sun, and slower when it is furthest away from the sun. Therefore, the Earth will travel faster in its orbit in January than in July because it will be closer to the Sun. 5. According to Kepler’s third law, Answer: B. Jupiter orbits the Sun at a faster speed than Saturn. Justification: Kepler’s third law states that the more distant a planet is from the Sun, the slower its average speed will be as it orbits. Because Jupiter is closer to the Sun than Saturn, Saturn will orbit the Sun at a slower speed than Jupiter. 6. Tycho Brahe’s contribution to astronomy included Answer: C. Collecting data that enabled Kepler to discover the laws of planetary motion.

Justification: Tycho Brahe was obsessed with discovering and solving discrepancies between the Ptolemaic and Heliocentric astronomical models, which inspired him to collect careful data on the positions of the stars. While Brahe did not arrive at a conclusion, his measurements helped his student, Johannes Kepler, to discover the laws of planetary motion. 7. Galileo’s contribution to astronomy included Answer: C. Making observations and conducting experiments that dispelled scientific objections to the Sun-centered model. Justification: Galileo’s observations of craters on the moon dispelled the idea that all of the heavenly bodies are perfect (therefore they must orbit in perfect circles). His observation of the moons of Jupiter–which clearly orbit Jupiter rather than the Earth–dispels the idea that the Earth must be at the center of the universe.

Problem 5.1– Summarize the relationship between astronomy, empire, and war in a short paragraph. The relationship between astronomy, empire, and war has been a mutually beneficial one for hundreds of years. This relationship began in early modern Europe, when a hunger for power, discovery, and expansion furthered the development of astrophysics. Nations began to use their knowledge of the cosmos and astronomical instruments to navigate on the seas. “Voyages of discovery”, aided by astronomy, led to violence and profiteering as well as knowledge. But, the relationship also works inversely. Because astronomical equipment is so expensive, scientists had to rely on interest and sponsorships from the government. The use of astronomy as a weapon of war has continued into the present, with examples like V-2 rockets in WWII, or Earth-imaging satellites in the Cold War. The reality is: the drive of military competition is a crucial motivator of astronomical discovery. Problem 5.2– Modern world powers continue to invest large sums in astronomy even when it is not of any military use. Apart from pure interest in astronomy for its own sake, can you think of any other reasons why these nations continue to do so? Modern world powers may decide to continue investing large amounts of money in astronomy because of the many unanswered questions left to solve. Because we have seemingly infinite possibilities, simply waiting to be discovered with the right tools and mindset, countries continue to fund astronomy as a way to ensure they still have a horse in the race. If all nations but one

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stopped looking for new astronomical discoveries, then unknown valuables would default to that nation. If a country has astronomers who are actively searching for the next big thing, that country still has the opportunity to lay claim to it.

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