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Oct 30, 2023

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R Ny Name:N\C,\C\ N\\NPV\\\ (7,(0 Moons of Jupiter LAB EXERCISE ‘ PART I: DETERMINING THE ScALE OF OUR MEASUREMENTS For this lab, you will be observing three moons as they orbit the planet Jupiter using the Stellarium program. Once you open the program; follow these directions to get set up: o Stop time from advancing o Turn off the Ground + Turn off the Atmosphere Switch to Equatorial Mount Once you are set up, continue with the following directions: o Using the Search tool, find Jupiter. IF AT ANY TIME YOU LOSE JUPITER ON THE SCREEN, SIMPLY SEARCH FOR IT AGAIN. o Zoom in until you can see the moons you will be observing (Europa, Ganymede, and Callisto), but not too many other distracting objects. gefore we make angular measurements of t.he dlst'ances of the moons from Jupiter, we need to know how to convert those measurements into a linear distance, To do so, we need an object where we know the size of the object, and can also measure ts angular size. Fortunately, we can do that with Jupiter. With Jupiter selected for observation, Stel!arium provides a vyealth of information. Look down the list of information provided until you find the apparent diameter of Jupiter. Record this value below: Angular size of Jupiter (1 1D.): -Hﬂ\?)\ arcsecond ("). This is the scale of our measurements. This will allow you to convert all of your measurements into Jovian diameters. 68 Scanned with CamScanner

e . A _.-wve1 the research question “What, if any, relationship exists between a moon’s orbital period and its distance from Jupiter?” Based on the background information ... 1. How can we determine the distance of a moon from Jupiter (its orbital radius)? VY NORNANY AWM DAEMONS GE ¥ye oo W VONOLS \QLa\g, 6 S 2. How can we determine a moon’s period of orbit? Mgy o S Qovue, drkevivivy) L e b \Any YRGS Zoom in close enough to Jupiter to the point where you are able to see the four Galilean _moons: lo, Europa, Ganymede, and Callisto. Open the Date/Time Window and advance the time In one-hour increments. 3. Which one appears to orbit Jupiter in the least amount of time? 10 4. Which one appears to take the longest to complete one orbit around Jupiter? 5. Continuing to advance the time in one-hour increments, estimate how long it takes for each of the four moons to complete one orbit. T 6’]‘ biee Europa—gko s Ganymede — \/l Q M Callisto —L\\’L Zw s 69 Scanned with CamScanner

#ame: N\C,\L\ Y\{\\j\( ‘OV\\’\ '),k‘, Moons of Jupiter PART IV: ANALYZING THE ORBITAL DATA Once you have finished measuring the distances for the moons, you are now ready to create a plot of the data. * Highlight the Date column along with one of the Moon columns (from the ones on the right with the data converted into Jovian Diameters). Create a plot of the Moon’s Apparent Distance (y-axis) as a function of the Date (x-axis) * Repeat for the other two moons AS BEST AS YOU CAN, determine the period of orbit for each moon, as well as the maximum amplitude (see background information for details) for each moon, and record them below. -_— Your Values for a & P Moon Period (days) Orbital Radius (Jovian Diameters) Europa g "S' 4.0 Ganymede i4! L Callisto (7. \Z.45 Scanned with CamScanner Using the values that you calculated, create a plot of orbital period as a function of orbital radius. Add a trendline to the data and have Excel include the formula for the trendline (If you don’t know how, consult the Appendix.) 6. Write the equation below, substituting “P” for the orbital period and “a” for the orbital radius. (NOTE: Feel free to round the exponent to the nearest tenth) CWNORe) Y\/\‘Z)S"—"’ \_“”'S < ’2% zq73 L Y &'%l\? anr AN PNt ‘Hfi ' “H».vv\:ﬂé..s 94 6. Is your formula consistent with Kepler’s third law? Explain why or why not? Yoy Pl Qo Swowss Ml Q swaney o l \D 99Uk O I YRANS 71

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Name:N.\Q"C\ W\\N\{N\\'\ 'L&" . Moons of Jupiter Notice that these values are in units of days and Jovian diameters. We wish to convert them into more appropriate units of years (for the period) and astronomical units (for the orbital radius)~ There are 1050 Jovian Diameters in 1 Astronomical Unit. 7. How many days are there in a year? ’b\’pé REALITY CHECK: g. When converting from days to years, will your number be larger or smaller than it was pefore? %\N\Q\\Q\r 9. When converting from Jovian Diameters to Astronomical Units, will your number be larger or smaller than it was before? DOV Google the orbital period and radius for each of the moons and compare to your answers. 10. Calculate the percent error for each of your values. v Ragivs Poriod oA = BB g e O Scanned with CamScanner

Name:N\.Cz-\ \(V\VTY) Y\ \ﬂ ,Z' b ‘Moons of Jupiter PART V: FURTHER INVESTIGATIONS In today’s lab you observed the angular separation between Jupiter and a few of its moons over time and used this data as evidence to confirm Kepler’s Third Law of planetary motion, at least in the case of moons orbiting Jupiter. Following procedures similar to the ones you conducted in the lab you performed today, what other related research questions could you pursue? Come up with at least TWO questions related to today’s lab that could be answered by gathering and analyzing data similar to what you did in lab. Haw Cown W £\ Hu QlvCSecondS COY e O YLD \WAGenS . Co Yoo emna #he Gngu\aY gize 06 SaNS Yings WHAT DO I TURN IN? In addition to the Lab Exercise pages which contain your answers, please upload the following: e A copy of your data table/Excel file e Yourlabreport 73 Scanned with CamScanner

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