Download PRELAB CLEA : 4. The Revolution of the Moons of Jupiter

Name________________________ Section______________________ Date_________________________ PRELAB CLEA : 4. The Revolution of the Moons of Jupiter Objective: Determine the mass of Jupiter by observing the motion of its four moons: Io, Europa, Ganymede, and Callisto. You will need to know basic parameters of a sine curve. •
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Amplitude: ½ * ( Maximum value – Minimum value ) (2pt) *Question: In the example, what would the amplitude be? Period: The time from one maximum (minimum) to the next maximum (minimum). (2pt) *Question: In the example, what would the period be? 
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T-­zero: The time of the beginning of the sine curve, which begins by sloping upwards from y=0. (2pt) *Question: In this example, what is the T-­‐zero? •
In this lab, the period of the sine curve corresponds to the orbital period of the moon around Jupiter. The amplitude corresponds to the radius of the moon’s orbit. •
You will also need to have some knowledge of Kepler’s Third Law of Planetary Motion. The law states that: The square of the orbital period of a planet is directly proportional to the cube of the semi-­major axis of its orbit. In equation form this corresponds to: •
For two objects, both orbiting the same central object, their ratios can be set equal as such: a31
a32
= 2
P12
P2
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(2pt) *Question: If Moon 1 has a semi-­‐major axis of 7 Jupiter Diameters and a period of 3.5 days, and Moon 2 has a semi-­‐major axis of 20 Jupiter Diameters, what is Moon 2’s period or revolution in days? •
This can be used to determine the mass of the central object the moon is orbiting. In the case of the planets, we could determine the mass of the sun. a3
M= 2
P
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In the context of this lab, P is the orbital period of the moon and a is the amplitude of the orbit. The period in this equation MUST be in YEARS. The amplitude MUST be in ASTRONOMICAL UNITS (AU). The resulting mass value in SOLAR MASS UNITS. •
(2pt) *Question: If Moon 1 has an orbital period of 1.4 years and a distance of 0.25 AU, what is the mass of the object it orbits in solar mass units? •
Jupiter is the largest planet in our solar system and is made of gas unlike the rocky Earth. It has 63 known satellites including its 4 largest moons: Io, Europe, Ganymede, and Callisto. Name________________________ Section______________________ Date_________________________ CLEA : 4. The Revolution of the Moons of Jupiter Objective: Determine the mass of Jupiter by observing the motion of its four moons (l to r) Io, Europa, Ganymede, and Callisto. Image courtesy NASA/JPL-Caltech.
Background: • For this lab you will need a calculator. • You will need to know basic parameters of a sine curve.  Amplitude: ½ * Maximum value – Minimum value. In the example below, the amplitude would be ½* 3-­‐(-­‐3) = 3 Jupiter Diameters.  Period: The time from one maximum (minimum) to the next maximum (minimum). In the example below, the period would be 17.5 – 3.5 = 14 days.  T-­zero: The time of the beginning of the sine curve. In this example, the beginning of the sine curve occurs at 7 days. •
In this lab, the period of the sine curve corresponds to the orbital period of the moon around Jupiter. The amplitude corresponds to the radius of the moon’s orbit. •
You will also need to have some knowledge of Kepler’s Third Law of Planetary Motion. The law states that: The square of the orbital period of a planet is directly proportional to the cube of the semi-­major axis of its orbit. In equation form this corresponds to: •
For two objects, both orbiting the same central object, their ratios can be set equal as such: a31
a32
= 2
P12
P2
•
This can be used to determine the mass of the central object the moon is orbiting. In the case of the planets, we could determine the mass of the sun. a3
M= 2
P
•
In the context of this lab, P is the orbital period of the moon and a is the amplitude of the orbit. The period in this equation MUST be in YEARS. The amplitude MUST be in ASTRONOMICAL UNITS (AU). The resulting mass value in SOLAR MASS UNITS. •
Jupiter is the largest planet in our solar system and is made of gas unlike the rocky Earth. It has 63 known satellites including its 4 largest moons: Io, Europe, Ganymede, and Callisto. Procedure: •
Open the CLEA lab titled “The Revolutions of the Moons of Jupiter” by double clicking on the Icon labeled Revolutions of Jupiter. •
Click on File -­‐> Login. Enter the first names of each group member and click OK and then YES. •
Click File -­‐> Run and verify the date and time you would like to begin observations of Jupiter’s moons. •
Click File -­‐> Timing. Change the observation step to 12 hours. •
Click File -­‐> Features and check the box next to the following and then click OK. 
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Use ID colors Show Top View Show eclipsed moon •
Click on one of the moons and make sure that it is circled in the Top View. •
Click record. Continue by clicking on each of the other moons, again making sure it is circled in the Top View. Each time you click on a moon you MUST hit record to store its position. •
When you have finished, record all positions in the data sheet provided. •
Click OK on the pop-­‐up box to save the data. •
Click Next to move onto the next observation. •
If the day is cloudy, then just record so in the data sheet provided. •
When a moon is behind Jupiter, use the Top View to make sure the moon gets selected and to help you see where on Jupiter to click. If after several tries, you cannot click on the eclipsed moon, leave the space blank and record eclipsed in your chart. •
Continue to record the positions of Jupiter’s moons for 15 days (30 measurements). •
Now, we would like to analyze the movement of these moons across our line of sight. Click File -­‐> Data -­‐> Analyze •
In this new window, click Data -­‐> Select Moon . Begin with Callisto, then Ganymede, then Europe, and finally Io. •
Once you’ve selected a moon (preferably Callisto!) click Plot -­‐> Fit Sine Curve -­‐> Set Initial Parameters. Enter your estimates for T-­‐zero in Julian date, Period in days, and Amplitude in Jupiter diameters. The cursor position in the lower left can help with your initial guess by giving you the position when you click on the graph. •
Once you’ve made initial guesses, use the scroll bars to adjust the T-­‐zero, Period, and Amplitude until the RMS residual (how well does the sine curve fit the data) is less than 5E-­‐01 or 0.5. •
Record on the provided sheet the T-­zero, Period, Amplitude, and RMS residual. Print the final result. •
Complete this process for each moon. For Io, you may want to only consider 10 days of data by clicking Data -­‐> Plot -­‐> Set Data Span. Also, it may help to see the points connected. You can do this by clicking Data -­‐> Plot -­‐> Plot Type. Name________________________ Section______________________ Date_________________________ Record Sheet – The Revolution of the Moons of Jupiter Table of Observations (5pt) # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Date Time Io Europa Ganymede Callisto 29 30 Record values of sine curve fit. (3pt) Amplitude Moon Period (days) (Jup. Diam.) T-­zero (days) RMS residual Io Europa Ganymede Callisto Now, convert period to years, and amplitude to AU. (Note: 1050 Jupiter Diam. = 1 AU) (2pt) Amplitude Amplitude Moon Period (days) Period (years) (Jup. Diam.) (AU) Io Europa Ganymede Callisto Now, recall that to find the mass of Jupiter we must use this equation: (2pt) a3
M= 2
P
Jupiter Mass Moon Period (years) Amplitude (AU) (Solar Masses) Io Europa Ganymede Callisto 1. 2. What is the average mass of Jupiter? ______________________ (2pt) Express the mass of Jupiter in Earth masses. (2pt) (1 Earth mass = 3 x 10-­‐6 Solar Masses) 3. If a moon were located at a further distance from Jupiter, would its period be larger? Or smaller? Explain why. (2pt) 4. Moon A is 1 J.D. from Jupiter and goes around in 1 day. Moon B is 4 J.D. from
Jupiter. What is the period of Moon B? (2pt)
a. 8 days
b. 12 days
c. 4 days
d. cannot be determined