The rules: This homework set should be done on your own. You may consult with the AI or the professor, but not your colleagues.
Introduction
You will be using a modified version of a Project CLEA laboratory exercise to simulate observations of the four Galilean moons of Jupiter in order to determine the mass of Jupiter. The computer program creates a realistic simulation of an imaging camera attached to a moderate size research telescope. You will use this instrument to collect data for 3 weeks (21 days); note that all observations can be obtained during the same computer based observing session since the computer will simulate observations for any particular date. The distance between Jupiter and each moon should be measured and recorded for each observing date.
When you start the observations, you will notice that the moons appear to be lined up (approximately) in the equatorial plane of Jupiter (unless, of course, you see clouds!). As time goes by, the moons will move around Jupiter. While the moons move in roughly circular orbits, you can only see the perpendicular distance of the moon to the line of sight between Jupiter and Earth. The perpendicular distance of the moon should be a sinusoidal curve if you plot it versus time. By taking enough measurements of the position of a moon, you can fit a sine curve to the data and determine the radius of the orbit (the amplitude of the sine curve) and the period of the orbit (the period of the sine curve). Once you know the radius and period of the orbit of that moon (and convert into the appropriate units), you can determine the mass of Jupiter by using Kepler's Third law. Here, you will determine Jupiter's mass by measuring the orbital parameters of each of the four Galilean satellites.
What to hand in: For a total of 50 pts, you should hand in a formal report of your observations and analysis. Your report should include at minimum (1) a description of the motivation for the observations and a brief summary of how the data were collected; (2) a data table with the dates of your observations and the distances for each moon (in Jupiter diameters, as given by the computer program); (3) a plot (or plots) showing the orbital motion of each moon; and (4) your calculations for the mass of Jupiter as derived for each moon, and a final mass of Jupiter (with error bars) as derived for this experiment. The data table should clearly indicate in the column header what units have been used. The plots are best shown as distance from Jupiter vs time, where time is the number of hours since the start of the observing sequence (i.e., first day is 0, second day is 24, 3rd day is 48, etc). Your report should follow standard scientific journal format and include: Abstract, Introduction, Data Acquisition, Analysis, Conclusions, Acknowledgements, and References.
Telescope Control
The program is located on the IU computer clusters (e.g., the public (windows) computers located in Lindley Hall or the Main Library). Log into the computer using your IU account and look under All Programs --> Departmentally Sponsored --> Ast --> Revolution of Jupiter's Moons to start the program.
After the program starts, you must first select Log In from the menu before taking data. You may enter your name in the blanks, but it is not necessary to do so (we are not using the automatic log capabilities of the program). Click OK to continue.
Select Run to begin the program. The next dialog box to appear is Start Date and Time. Use the defaults (the current date). Click OK to continue.
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. In order to improve the accuracy of your measurement of a moon, you should use the largest possible magnification which leaves the moon on the screen.
In order to measure the perpendicular distance of each moon from Jupiter, move the pointer until the tip of the arrow is centered on each moon and click the mouse. Information about the moon will appear at the lower right corner of the screen. This includes the name of the selected moon, the x and y pixel location on the screen, and the perpendicular distance (in units of Jupiter's diameter) from the Earth-Jupiter line of sight for the selected moon as well as an E or W to signify whether it is east or west of Jupiter. If the moon's name does not appear, you did not center the arrow exactly on the moon; try again. Note: sometimes a moon is behind Jupiter so it cannot be seen.
Record your data either with a pencil and paper or using a spreadsheet/analysis program of your choice. Note: you should use + for west and - for east (by convention).
When you have recorded the date and the perpendicular distance for every moon, you may make the next set of observations by clicking on the Next button. Continue until you have observations for 21 days.
When you have finished taking readings, you may quit the program by selecting Quit.
Data Analysis
Using a spreadsheet/analysis program of your choice, plot position versus time for each of the moons. You are likely to have an irregular spacing of observations, due to poor weather or other problems on some nights. You will need to determine the sine curve that fits your data best in order to determine the orbital properties of each moon. Here are a few hints: the orbits of the moons are regular; that is, they do not speed up or slow down from one period to the next. Also, the radius of each orbit does not change from one period to the next. Therefore, the sine curve that you draw should also be regular. It should go through all of the points and not have a varying maximum height nor a varying width from peak to peak.
The time period between two maxima is the period. Since the exact time of maxima can be hard to determine with irregularly spaced data, you may wish to measure the time period between crossings at 0 J.D., which is equal to half of the period (the time it takes to get from the front of Jupiter to the back of Jupiter). Furthermore, 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, for example, 4 cycles, and then divide that time by 4.
When a moon is at the maximum position eastward or westward, it is 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 radius when the moon is at its maximum position eastward or westward.
Use Kepler's third law to calculate the mass of Jupiter. You may wish to convert the period into years and the orbital radius into AU (by dividing by the number of Jupiter diameters in an AU, 1050.). Your final answers should be either in units of solar masses or kilograms. Determine the average mass of Jupiter (with error bars), based on your calculations above.