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Lab 5: the Galilean Moons and Kepler's Third Astronomy Lab I Lab 5 Fall 2018 Lab 5: The Galilean Moons and Kepler's Third Law October 17th, 2018 On January 7th, 1610, Galileo Galilei made a remarkable discovery. He turned his crude telescope to look at Jupiter, which was high in the Eastern sky shortly after sundown, and he discovered three points of light in close proximity to the planet, points of light that were not visible to the naked eye. At first he just thought they were ordinary background stars, but when he looked again the following night they weren't where he expected them to be (with the same configuration but further East). Instead they had a different configuration from the previous evening and they remained near the planet. Upon repeated observations he saw that the points of light appeared to dance around the planet, and about a week after his first observation he identified a fourth point of light. It was apparent to him then that these were not background stars at all, but that they had to be associated with the planet itself. Now at this time Copernicus' model of the Solar System, with the Sun at the center and the planets orbiting around it, was not yet accepted as fact. The Catholic Church deemed the theory heretical. But Galileo's discovery provided powerful support for the Copernican heliocentric model. The points of light around Jupiter clearly did not orbit the Earth, in violation of the geocentric cosmology. But they also clearly did not orbit the Sun directly the way the planets do. Rather, they orbited Jupiter, as if Jupiter were its own small solar system. At the time, Galileo was seeking to gain patronage from his wealthy former student, Cosimo de Medici, the Grand Duke of Tuscany. He was also seeking influential allies in Italy at a time when the Catholic Church was not looking favorably upon his work. He therefore named his newfound objects the "Medician Planets." Nowadays, the moons Galileo discovered are called Io, Europa, Callisto, and Ganymede. Collectively they are known as the Galilean moons in honor of Galileo. Today we are going to replicate Galileo's observations using the program Stellarium. We will measure how the positions of the moons change from night to night, derive the orbital periods and semi-major axes, and as an added treat, measure the mass of Jupiter using Kepler's Third Law! Throughout this we will also discuss the scientific significance and novelty of Galileo's work. Pre-lab expectations: In your lab notebook, describe in several sentences what you expect to do in today's lab and what you expect to learn throughout the next three hours. 1 Using Stellarium to \observe" Jupiter • Open the program Stellarium on your computer. The sky as it currently appears will show up on your screen. • First, you will need to make sure that the angular measurement tool is enabled. Look at the menu at the bottom of the screen and check if you see the angular measurement icon, which looks like this: . If you do, great! You can skip this step. If not, take youre mouse to the left side of the screen and you'll see a series of options pop up. Click on the icon with a wrench called “Configuration Window," navigate to the last tab labeled \Plugins," and choose \Angle Measure" from the drop-down menu. At the bottom of the screen, make sure the checkbox next to \Load at startup" is selected. Then close the window, quit stellarium, and start it up again. Now the angular measurement icon ( ) should appear in you menu on the bottom. • If you pan around your screen, you'll see tonight's night sky. But we don't want to observe Jupiter today (although we could do this), nor do we want to observe it from New York City (or from whichever default location your computer loaded). Instead, we will call up the sky as it appeared the night Galileo first observed Jupiter with his telescope. 1 Astronomy Lab I Lab 5 Fall 2018 • Take your mouse to the left side of the screen and you'll see a series of options pop up. Click on the icon on the top that looks like a compass rose and says \Location Window." In the window that appears, find the search bar on the top left and input the city where Galileo conducting these observations: Padua, Italy (if Padua doesn't come up, try searching for Padova, Italy). • Close the location menu. Go back to the pop up menu on the left hand side of the screen, and now click on the second icon that looks like a clock that says \Date/Time Window." In the window that appears, set your date to 1610/1/7. The sky will now appear as it did on that historic evening. If it is still light outside advance the clock by an hour or two. • Drag your mouse on the screen to move about the sky (you can also use the arrow keys on the keyboard). First try and locate the Moon. Once you have found that, look for Jupiter nearby. It should be labeled, but if it isn't, simply hit `p' and the name should appear. If a line is passing through Jupiter, that indicates Jupiter's orbit. Hit `o' to turn that off if it's showing up. • Now click on Jupiter to select it. A slowly rotating red cross will illuminate around Jupiter and a number of details about the planet will show up in the upper left corner of your screen. • To make our observations you'll want to zoom in on the planet. You can hold the ctrl or command key and use the up/down arrows to zoom in and out. Put Jupiter in the center of your screen and zoom in on the planet. Once you zoom in enough, you should notice the moons, but also that as you zoom in Jupiter is moving across your screen. That's the rotation of the Earth! Obviously this will make observations difficult, as it would have for Galileo. Let's get rid of that and simulate what it's like making this observation with a modern telescope with tracking capabilities. With Jupiter selected, hit the spacebar to track the object. Notice how now you view is moving with Jupiter, maintaining Jupiter in the center of the screen. 2 Measuring the position of Jupiter's moons It's time to start taking measurements. Use the attached table to record your measurements of Jupiter (you only need to fill out one table per group, and then make a photocopy so each of you has one). The table has four columns, one corresponding to each of Jupiter's moons, and 20 rows { Galileo observed the positions of Jupiter's moons every night for over two full months, but we will only reproduce the first 20 days of these observations. The following instructions will aid you in performing these observations. Make sure to read through all of these instruction once before beginning your observations. 1. If you have clicked on Jupiter, you should see a list of details about the planet in the upper left corner of your screen. Locate the the distance to Jupiter, and record the value in meters in the relevant place on the attached worksheet. 2. For each moon, use the angular measurement tool to measure from the center of the Moon to the center of Jupiter. The angular distance between the two should show up in blue in the vicinity of the distance bar. Note that the measurement is written in terms of degrees, arcminutes and arcseconds (arcminutes have a single 0 mark while arcseconds have 00). 3. Before recording each measurement, let's convert them so that instead of expressing them in arcminutes and arcseconds we are only using arcminutes. What to do with those pesky arcseconds? Simply divide them by 60 to get decimals. So if my measurement was 305200, I can convert that into 3.870. Make sure you can reproduce this calculation before proceeding! Once you have, begin recording these converted values in the attached table, and also make note of whether the moon appears to the 2 Astronomy Lab I Lab 5 Fall 2018 right or left of the planet, as we will want this information later on. Do this for each of the four moons. If you are unable to see one of the moons, try zooming in or zooming out, but its also possible that the moon may be hidden behind the planet on this particular day, in which case the angular separation is roughly 0. 4. When you have recorded the angular separation of each Moon for January 7th, it's time to move on to the next day. Hit the '=' key to skip ahead 24 hours. You can use '-' to go back 24 hours. If Jupiter doesn't remain centered in your screen, just click on it again and press the 'spacebar' key to re-center it. Make ne measurements of all four angular distances and repeat this process until youve filled up your table (i.e., you should make it all the way to January 26th). Make sure you aren't skipping ahead too many days! Youll want to keep an eye on the date/time at the bottom of your screen to make sure your measurements are lining up with the appropriate day in your log. 5. You may find it helpful for one person to perform the measurement on Stellarium, while the the other converts the values to arcminutes and records it in the table.
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