Jupiter and its Satellites worksheet

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Clemson University *

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123

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Physics

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Dec 6, 2023

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Jupiter and its Satellites 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: Nicky Section: _______ Observing Jupiter Table 1 Data Jupiter Earth’s Moon % illumination 99.7% 95.6% Magnitude -2.7 % 11.9 % Rising time 2:27pm 2:53 pm Setting time 5:29 am 5:24 am Moons of Jupiter Table 2 Name Diameter (km) Orbital Period (days) Io 3643 km 1.77 days Europa 3122 km 1.57 days Ganymede 5262 km 7.16 days Callisto 4821 km 16.69 days 1) Were the brightest four moons ever visible all at once to him? If so when? Yes, January 7. 2) Do you think the Moon may have made Galileo's observations of Jupiter more difficult? Why or why not? No the moon never blocks Jupiter, so it would not interfere with Galileo’s observation 3) What other planet was close to Jupiter on the night of January 7, 1610? Uranus was close to Jupiter that night

4) Center on it. Which direction would Galileo have looked to see it (relative to Jupiter)? He would have to look on the right side of Jupiter to see Uranus. 5) Center on Mars, then Venus and determine if Galileo could have observed them on January 7th. Explain your answer. Mars: Yes, but not at the same time as Jupiter, because Jupiter is below the horizon Venus: Same as mars, it is visible just not at the same time as Jupiter 6) Observe Jupiter and its moons until 05:00 hours, 5 am. If Galileo had observed all night, would he have detected the movement of any of the moons? The movement we are looking for here is their distance from Jupiter. Name them and describe their movement. He would have seen the movement of all the moons. Io and Europa were the closest to Jupiter during their orbit. Ganymede and Callisto were farther from Jupiter. Return to the instructions to help understand the next steps Mass of Jupiter (use the google sheet to help with calculations) Table 3 Moon Period (Days) Period (Years) Io 1.77 days 0.005 years Europa 1.57 days 0.004 years Ganymede 7.16 days 0.020 years Callisto 16.69 days 0.046 years 7) Distance from Earth to Jupiter (found in info pop up of Jupiter): 4.27 A.U. 8) Maximum separation of Jupiter and Ganymede °5 ʹ44.5 ʺ (as read from measurement tool) = 0.09566 ° (in decimal degrees only) 9) Convert this to radians by dividing by 57.3 degrees/radian: 0.001667636223 radians. 10) Ganymede’s orbital semi major axis, a = θ (radians) × distance (A.U.) = 0.00713054231 A.U.

Table 4 Moon Time of greatest separation (hour:min) Visual Distance (Decimal degrees) Orbital distance / semi major axis (AU) Io °1’58.8” 0.033° 0.002462524503 AU Europa °3’36.6” 0.06016666667 0.00448975427 AU Ganymede °5’34.5” 0.09566° 0.007130542331 AU Callisto °9’09.6” 0.1526666667° 0.01139228507 AU Now you can calculate Jupiter’s mass from each moon using Kepler’s Third Law. M = a 3 / P 2 You can copy the table created in google sheets here instead of manually typing each number into this table. Table 5 Moon a (A.U.) P (years) a 3 P 2 Mass of Jupiter (M sun ) Io 0.0024625245 03 0.0048493150 68 0.00000001 49 328149 0.00002351 58 5663 0.0006350104584 Europa 0.0044897542 7 AU 0.0097808219 18 years 0.00000009 05 0398799 0.00009566 44 7739 0.0009460563676 Ganymede 0.007130542 331 0.0196164383 6 years 0.00000036 25 498146 0.00038480 46 539 0.0009421658778 Callisto 0.0113922850 7 A.U 0.0457260274 years 0.00000147 85 38138 0.00209086 95 82 0.0007071402976 11) Average of four masses: 0.0008075932503 Msun

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12) Which moon's value is farthest from the average? Io 13) Suggest a reason why they do not all give the same answer. They dont give the same answer because the method of measuring the mass of jupiter is not 100% accurate. 14) Do a google search to find the mass of Jupiter in terms of the mass of the sun and compare it to your result. How far off from your calculation is this? Explain how you could improve your technique to get a more accurate result. The mass of jupiter in terms of the mass of the sun is 0.000954588, which is greater than the mass i got, 0.0008075932503 Msun. My calculation is 0.00014699474 less than what google said.

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