homework ess 01

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Apr 3, 2024

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ESS001 Geosphere, Lab 1 Module 1: Geosphere Lab 1: An Introduction to Earth System Science, Online learning, and Hubble's Law Learning Outcomes:  Be able to give a definition of "Earth Systems Science"  Become familiar with Canvas and the online site for this course  Practice graphing data and fitting the equation of a line to derive the Hubble constant  Note: All work should be typed and uploaded onto the class website under this week's assignment by the deadline. Everything that you turn in from this point on must be answered in complete sentences and be put into your own words. ANSWERS ARE COLORED IN RED Part I. What is Earth Systems Science? So you've enrolled in this course, but do you know what you are going to study? Many people don't have a clear idea of what "Earth Systems" means, and what exactly it encompasses – isn't it just environmental science? Think for a few minutes on your own, and then write down a one-sentence definition of "Earth Systems". In Earth Systems we explore ways that show us how life, water, air, and other different Earth structures shape the state of our planet. Now think about what the most important problems or questions related to Earth Systems. What do you think is the most important Earth Systems problem? Write it down one sentence. I believe the most imprortant Earth systems problem is climate change, and global warming showing to have environmental impacts. Turn In: Definition (1 point) and most important Earth System problem (1 point). Part II. How am I supposed to learn it online? On your laptop, log in Catcourses. You should see ESS 1 under Courses. If you have not done so already, go to the "Course Essentials" page and read through the information. Become familiar with where to find course material, assignments, quizzes, and grades, and how to send messages. III. Working with data: Hubble's Law Background Scientific understanding is built on observations and information – often generalized as "data". Data comes in many different forms, and making graphs is a powerful and essential way to understand and interpret data. There are a number of ways to graph data, and an important skill to learn in this course is how to make and interpret different kinds of graphs. In Last revised on 08/27/2018 by SM 1

ESS001 Geosphere, Lab 1 this short exercise, you will make a simple x-y plot, examine the relationship between the variables, and fit a line to the data. You will then interpret your graph in terms of what is now known as Hubble's Law, and discuss how it relates to the Big Bang theory for the origin of the Universe. This topic is the first lesson in the online course materials. In the 1920's, astronomer Edwin P. Hubble measured the velocities of galaxies (i.e., how fast they are moving) and the distance to the galaxy from Earth using telescope images. When he made a graph of his data, he noticed that there was a linear trend associated with these two measurements. A. Using Excel, make an x-y graph of the data below with x = Distance and y = Velocity. (Your instructor will show you if you don't know how to do this.) Distance is given in megaparsecs (mpc): 1 megaparsec = 3.26 million light years (3.26 x10 6 light years) Velocity is given in kilometers per second (km/s) Speed of light = 300,000 km/s Galaxy Distance (mpc) Velocity (km/s) NGC-5357 0.45 200 NGC-3627 0.9 650 NGC-5236 0.9 500 NGC-4151 1.7 960 NGC-4472 2.0 850 NGC-4486 2.0 800 NGC-4649 2.0 1090 B. In Excel, use the "trendline" function to fit a straight line through the data, and determine the slope and y-intercept of the line. Plot the line and the equation on your graph. 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0 200 400 600 800 1000 1200 f(x) = 412.09 x + 135.67 R² = 0.81 Distance (mpc) Velocity (km/s)  How is the slope defined in the equation of a straight line? What is the value of the slope from your graph? What are the units of the slope from the graph? The slope defined in the equation of a straight line is the steepness of a line on a graph, a.k.a rise over the run. Our value is 412.09 in km/s, meaning its distance squared divided by the time.  How is the intercept defined in the equation of a straight line? What is the value Last revised on 08/27/2018 by SM 2

ESS001 Geosphere, Lab 1 of the intercept from your graph? What are the units of the intercept value from the graph? The intercept is the value of Y when X is equal to 0, and our value is again km/s.  What does "R2" mean in the fit? R2 tells us how well our line fits our data, and since the value is closer to 1, it means our line matches our data pretty well. Turn in: The answers to the previous questions (3.5 points) along with your plot with labeled axes, line of best-fit, equation, and R 2 value displayed on it (2.5 points). C. What is the range of distances in your graph from Earth to the galaxies you plotted? Convert this range from megaparsecs (mpc) to light years. Our largest value (2) minus our smallest value (0.45) makes our range 1.55 mpc, and this is equal to approximately 5,055,480 light years Turn in: The range of distances in both megaparsecs and light years (2 points). Last revised on 08/27/2018 by SM 3

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ESS001 Geosphere, Lab 1 D. When Hubble made this type of a graph, he realized that the linear relationship between the y and x variables was very profound: Velocity (v) = slope (m) * Distance (d) The equation above is now known as Hubble's Law, and the value of the slope (m) is named after Hubble – the Hubble constant. If the slope of the line is always constant (i.e. linear), think about what this equation means. Turn in: Write three to four sentences interpreting Hubble's Law – the constant relationship between a galaxy's increasing velocity and its distance from the Earth (5 points). Summarize in your own words what this equation means, and how Hubble's law supports the Big Bang theory (5 points). See the online material in Lesson 1 and reading links for more information. Hubble’s Law tells us that the relationship between a galaxy’s increasing velocity and its distance from Earth can be represented as, the farther a galaxy is away from us, the faster it is moving. This law supports the Big Bang Theory as it tells us that our universe has been expanding ever since it’s formation, and it is put into the equation of v=Ho x d. To explain it, v is the velocity of a galaxy, Ho is Hubble’s constant, and d is the galaxy’s distance from Earth. Last revised on 08/27/2018 by SM 4