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Suicide

In: Philosophy and Psychology

Submitted By BaileyCraven
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Jupiter’s Moons Lab
Purpose:
The purpose of this lab was to determine the period and semi-major axis for the orbit of each moon around Jupiter. We then apply Kepler’s Laws to calculate the mass of Jupiter from out observations of each moon.
Procedure:
Choose a moon per lab partner.
Open the Moons of Jupiter program by clicking on START → Programs → Academic
Department → CLEA Exercises → Jupiter Moons.
The Moons of Jupiter program simulates the operation of an automatically controlled telescope with a Charge-Coupled Device (CCD) camera that provides a video image to a computer screen. It is a sophisticated computer program that allows convenient measurements to be made and the telescope's magnification to be adjusted. The computer simulation is realistic in all important ways, and using it will give you a good feel for how modern astronomers actually collect data and control their telescopes. Instead of using a telescope and actually observing the moons for many nights, the Moons of Jupiter computer simulation shows the moons to you as they would appear if you were to look through a telescope at the specified time.
Click on File → Log In. A dialog box appears. Enter the names of each student working at your computer. When all the information had been entered to your satisfaction, click OK to continue. Click on File → Run. The next dialog box to appear is called Start Date & Time. Startup values are needed by the computer to establish your initial observation session, and students at each computer will perform and analyze a different set of observing sessions. The Start Dates for each computer will be one partner’s birthday, including year. Keep the Time = 0, 0, 0.00. The Observation Interval should be set to 12.00 hours. You can adjust this time interval by clicking on File → Preferences → Timing. When all of the information has been entered to your satisfaction, click OK to continue. You control the observing session from this Main Telescope Screen. Notice that Jupiter is displayed in the center of your computer screen. To either side are the small point-like Galilean satellites. Sometimes a moon is behind Jupiter, so it cannot be seen. Even at high magnifications, the moons are very small compared to Jupiter. The current telescope magnification is shown in the upper left corner. The date, the UT (Universal Time – the time in Greenwich, England), and the Julian Day (JD) are all displayed in the lower left. You can display the screen at four scales of magnification by clicking on the 100X, 200X, 300X, and 400X buttons at the bottom of the screen. Try them now. To improve the accuracy of your measurement of a moon, you should always use the largest possible magnification which leaves the moon visible on the screen.
Be careful NOT to click the button marked next just yet! Now, position the mouse cursor over the screen and hold down the button. The measurement system turns on and displays the apparent perpendicular distance X (in JDs) that the cursor is away from the center of Jupiter. Notice that each edge of Jupiter is X = 0.5 JD. In order to measure the perpendicular distance of each moon from Jupiter, move the cursor until the moon is centered in the cross hairs and then hold down the mouse button. When the satellite is carefully centered, release the mouse button and information about the moon will appear at the lower right corner of the screen. This information includes the name of the selected moon, the X and Y pixel location on the screen, and the perpendicular distance X (in units of Jupiter's Diameter) from the Earth-Jupiter line-of-sight for the selected moon, as well as E or W to indicate whether it is east or west of Jupiter. If the moon's name does not appear, you did not center the moon in the cross hairs exactly and you should try again!
To measure a moon, always switch to the highest magnification that still leaves the moon on the screen. It is important to use the highest magnification possible for each moon for best accuracy. The data are for an imaginary moon, Clea. Alternatively, if you recorded the data on the computer, you can analyze them by clicking File → Data → Analyze and Select a moon from the menu. All of that moon’s data are plotted and you can now determine its orbital period and its distance from Jupiter. Use the Plot → Fit Sine Curve → Set Initial Parameters to help you do this. For some moons, you may not get enough observations for a full period, so these points may be of use to you in determining the period, even though the moon has not gone through a complete orbit. On the other hand, if you have enough observations for several cycles, you can find a more accurate period by taking the time it takes for a moon to complete, say, 4 cycles, and then dividing it by 4.
Once you find P, it must then be converted to units of years by dividing by 365.25 days. Remember, it is important to stay in the correct set of units if you are going to use Kepler's Third Law. You can determine the semi-major axis (the radius), a, for each moon by measuring the maxima and minima in your smooth sine curves. When a moon is at the maximum position eastward or westward, it is at the largest apparent distance from the planet. Remember that the orbits of the moons are nearly circular, but since we see the orbits edge on, we can only determine the actual radius of the orbit when the moon is at its maximum position eastward or westward from Jupiter. Repeat Steps 1–4 below for each of the four Jovian moons that you measured:

Step 1. Enter the data for each of the four moons into an Excel spreadsheet. The first column should contain the observing interval (i.e. 1, 1.5, 2, 2.5); the second column should contain the distance. Create a graph by highlighting both columns and choosing the XY(Scatter) option. Along the horizontal scale, should be the day numbers, starting on the left with the number of the first day for which you have data. Calibrate the horizontal scale of each graph to make your data as stretched out as possible. (The graph for Io, in particular, will benefit from this stretching). The vertical scale should be divided by a zero (0) line, with positive and negative numbers on each side of it.
Each day's measurement of a moon's apparent separation from Jupiter should give you one dot on the graph for that moon. Since each observing day has two sessions, be sure that each point on the graph on the horizontal axis represents only one session. Remember NOT to plot any points for Cloudy Days since you don't know where any of the moons are on those days. Also remember that the computer does not recognize ±0.5 when it creates the plots, so do not enter this information either. You will have to make a best guess as to the moon’s location based on the other observations.
Step 2. For each moon, print out the plot and draw a smooth sine curve through the points. Mark all maxima and minima on the curve by crosses. They need not fall on one of the grid lines. The curve should be symmetric about the horizontal line corresponding to zero apparent separation. The maxima and minima should have the SAME values, except for their sign.
Step 3. Read off the period, P, and the semi-major axis, a, from your figure, in the manner shown in the earlier example for Moon Clea on page 7 (Figure 3). These units will be days for P and JD for a.
Step 4. To obtain P in years, divide your result in days by 365.25 since there are 365.25 days in a year. To obtain a in AU, divide your result in JD by 1050, since there are 1050 Jupiter diameters (JD) in one AU. Include your converted values on each of the graphs you’ve created for each moon. You now have all the information you need from each of the four moons to use Kepler's Third Law to determine the mass of Jupiter, mJ, as: m J = Pa 32 where: P has units of years, a has units of AU, and mJ has units of solar masses.
Materials:
* Computer * CLEA program The Revolution of the Moons of Jupiter * Calculator
Results:

Moon Name | RMS Residual | T-Zero (Julian Day) | Period (seconds) | Amp (Jupiter Diameter) | Ganymede (Jabari) | | | | | Callisto (Bailey) | 2.0927266E-01 | 2456359.32 | 1454978 | 13.1850 | Io
(Mohan) | | | | |

Evaluation of Data:

4π/GM = T^2/a^3

Io:
((4π ( 421,800,000 m^3)/(6.67x10^-11))/ 152649.792^2= 1.90*1025kg
Callisto:
((4π (1,882,700,000m^3)/(6.67x10^-11))/ 1454978^2= 196 × 1023 kg
Ganymede:
((4π (1,070,400 m^3)/(6.67x10^-11))/ 621080.352^2= 3.4562× 1023 kg
Conclusions:
Bailey:
Callisto has T-Zero of 2456359.32 Julian days, a period of 1454978 seconds and an amplitude of 13.1850 Jupiter diameters. By using 4π2/GM = T2/a3, I calculated a mass of 196 × 1023 kg. The actual mass of Callisto is 137 × 1023 kg. My error percentage was about 69.7. Somehow the math may have been off. I could have miscalculated on of the data figures such as period or amplitude.
Mohan:
Jabari:

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