Astronomy 111 Observing Project 1: data analysis

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1 Astronomy 111 Observing Project 1: data analysis Fall 2022 Purpose: observationally to demonstrate Kepler s third law, and therefore Newton s law of gravitation, and to measure the mass of Jupiter, using the motions of the four Galilean moons of Jupiter. 1. Find the data (team) Your data are in D:\2022 ASTR 111 folders on MEES-CTRL, the server-class workstation in 203H B&L. Here are the relevant directories and their contents: prepend ASTR 111 to the date sting in each case : Jupiter, Kepler-785 b : WTS-2 b, egress only : Jupiter, Neptune : WTS-2 b : Kepler-548 b, Jupiter, Neptune : WTS-2 b, ingress only : Jupiter, Uranus, Neptune, Mars, NGC : Jupiter, Uranus, Neptune : Jupiter, Uranus, WD b I have taken the liberty of calibrating all the images, and aligning all the images taken as part of an exoplanet-transit light curve. You won t have to learn about calibration of the images with CCDStack this time. IDL and Excel are used for processing the data in Project 1. Both are available on MEES-CTRL if you log in as Mees. 2. Extract distances, diameters and fluxes from the images (team) Join your teammates in 203H B&L and prepare to spend a few hours getting your results. Start IDL by doubleclicking its desktop icon or single-clicking its toolbar icon: which opens the IDL DE window (Figure 1), a programming environment that may remind you of python;s Jupyter Notebooks. Within IDL you will run a program called jupiter_moons.pro. There s a copy of it in each data directory, and in the parent directory D:\2022 ASTR 111 folders. Navigate to a data directory that has a copy, using the IDL DE Browse button. Then open jupiter_moons.pro. jupiter_moons.pro measures the diameter of Jupiter, and the distance from Jupiter s center to each moon. It needs as input a list of image-file names in each data directory, for which it expects the name moons_files.txt. For each data directory you will use, generate a list as follows: 2022, University of Rochester 1 All rights reserved

2 Browse Figure 1: IDL DE console, with some useful buttons labelled. a. open a Windows command session: type cmd in the search window at lower left of the screen, next to the Start button and hit Enter. b. navigate to the data directory using cd <directory name here> at the command prompt. c. once in a data directory, list the image-file names using the dir /b command, redirecting the output to moons_files.txt. For example, to list in a text file all the images with extension.fit containing Jupiter and H-alpha (in that order) in their names, use dir /b *Jupiter*H-alpha*.FIT > moons_files.txt d. followed by Enter. Edit moons_files.txt if you want, to make sure it has only the images you will use. Once you have moons_files.txt in place and jupiter_moons.pro open, push the IDL DE Run button. This generates a text file called moons_positions.txt, in the same data directory. Part of such a file is shown in Figure 2. Run jupiter_moons.pro in each data directory you will use, generating a moons_positions.txt file each time. When you are done, move all your moons_files.txt and moons_positions.txt files to another directory for use by you and your team. Don t leave copies behind to confuse the next team. 2022, University of Rochester 2 All rights reserved

3 Figure 2: part of a moons_positions.txt output file, with column headers prepended. The time corresponding to each measurement is given as Modified Julian Day (MJD), for which the units are Earth days. Jupiter s radius is given in pixels. Jupiter-moon distances are given in Jupiter radii. For Jupiter the total and median flux per pixel near the planet s are given. For each moon, flux and its uncertainty are given. Fluxes for the moons are how we tell the moons apart: they always have the same rank order of brightness. 3. Compile the results; identify the moons (team) For this step, the team can divide the output files among its members, so as to work in parallel. a. Open the text files in Excel for ease of sorting, copying and pasting, and merging everyone s results into one Excel workbook. Parse the text-file contents into spreadsheet columns using Excel s Data > Text to Columns feature or its Text Import Wizard. Save the result as an Excel spreadsheet (*.xlsx). b. On at least some of the images each observing night, all four Galilean moons appear. Find one of those times in each of your moons_positions.txt outputs. From the fluxes of the moons, identify which moon is which. Note the identification in one of your spreadsheet columns. c. Then for each other observing time, identify the moons. Their fluxes and positions should be reasonably close to those of the same moons at the same time of the same night. d. Merge these spreadsheets into one. Sort this spreadsheet by object, then by time, as shown in Figure 3. e. It would be helpful to generate a new observation time column that starts at zero, in turn defined as the time of our first Jupiter observation of the semester. (I think that was MJD = ) Subtract this value from all times listed in the spreadsheet to make the new column. f. Save this spreadsheet, and give a copy to each of your teammates. The rest of the observing project is a solo effort. For this, make sure each team member has a copy of jupiter_3.xlsx, found in D:\2022 ASTR 111 folders on MEES-CTRL. 2022, University of Rochester 3 All rights reserved

4 Figure 3: sorting a merged spreadsheet by object (column H) and then by time (column B), to produce a list for each moon separately in increasing order of observation time. 4. Measurement of orbital radius and period for the Jovian moons (solo) Save a copy of jupiter_3.xlsx for each of the four moons. a. Then, copy and paste the results for each moon, from your spreadsheet of moon positions as functions of time, into the Enter data sheet of each workbook: times in the Time of observation column, distance in the Distance to moon column. b. For each entry provide also an estimate of the uncertainty in distance in units of Jupiter radii, in the Uncertainty in distance column. You can change this value as you go along and have a better sense of what the uncertainty is (step f, below). 2022, University of Rochester 4 All rights reserved

5 c. Then, one moon at a time, switch to the Fit sine curve sheet, and enter trial values of the amplitude, period and phase offset into the gray shaded cells. d. Adjust these values til the sine wave goes through all the points, at which stage the green shaded cell labelled Reduced χ 2 will be a minimum. e. While adjusting and minimizing, you may find if useful to change the scale on the sine curve s Time axis, to zoom in on groups of closely-spaced points, and to zoom back to see the entire data set. f. Ideally the minimum value for Reduced χ 2 should be close to 1. If the Uncertainty in distance is overestimated, the minimum will be much smaller than 1; if underestimated, the minimum will be much larger than 1. g. When you re satisfied with a good fit, save your result and go on to the spreadsheet for the next moon. When you have done this for all four moons, you have measurements of orbital radius and period for each. Their values are respectively in the gray Amplitude and Period cells. 5. Testing Kepler s third law, and Newton s law of gravity (solo) In Excel, make a spreadsheet with your orbital radius and period for each moon in corresponding rows of different columns. From these, make columns of orbital radius cubed and period squared. Select these new columns and tell Excel to make a scatter plot (Insert > Chart > Scatter) without lines connecting the points. Then select the plot and ask Excel to add a trend line (Chart Design > Add Chart Element > Trendline > Linear). Ask Excel to display the trend line s equation and r 2 value on the plot. If all has gone well, the trend line will fit the points very well and r 2 will be very close to Measuring Jupiter s mass (solo) Each moon is a test particle in orbit around Jupiter. Use your results to determine Jupiter s mass. (Hint: Jupiter was near opposition throughout our observations. So what is its distance, approximately?) Compare your result to that on our website s Solar-system planetary data pages. If your result differs significantly, explain the difference. 7. Writing your report (solo) The expectations for your report are listed in the Project report page of the course website. Include all your results, described in words and illustrated with images and graphs. And explain the meaning of your results, in the light of the purpose of the experiment (page 1). In particular, make sure you answer these questions in your narrative: a. Given the radii and geometric albedos of the Galilean moons listed in the lecture notes or the NSSDC Jovian Satellite Fact Sheet, what is their rank order of flux? How securely are the moons identified in your results? b. Roughly what are the uncertainties in the orbital periods and radii you determine for the Galilean moons? c. What is the greatest source of uncertainty in the experiment? d. Why did I ask you to plot Jupiter-moon distances in units of Jupiter radii? e. How closely does the measured relation between the Galilean-moon periods and orbital radii -- expressed as a graph of data points and overlain curves -- resemble Kepler's third law? Over what range could you vary the exponents of period or orbital radius, and still fit the data? f. What mass do you measure for Jupiter? 2022, University of Rochester 5 All rights reserved

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