Rotation of Saturn
Name:______Lab Section: Online Date: ______
Procedure
Please refer to your text for a more complete discussion of the Doppler principle. The following is intended merely as a more descriptive guide for carrying out the steps of the analysis and organizing the computations.
The spectrum printed in Sky and Telescope Laboratory LE-3 has wavelength increasing toward the right, so that the red end of the spectrum is toward the right and the blue end is toward the left. There are a total of six different reference lines (not Doppler shifted) with their corresponding wavelengths labeled across the top of the photograph. Starting with the line at 6128.45 Å and going to the right, denote these reference lines by the letters, A, B, C, D, E, F, (line D at 6217.28 appears twice, once on each page since the spectra overlap). This notation is introduced for your convenience in referring to these lines in your later work. Note the reference lines also appear below the Saturn spectrum. Identify and label the lines A, B, C, D, E, F, at the bottom of the picture as well. Next connect the top and bottom segments of each reference line by means of a thin vertical line which you are to draw on the photograph centered as well as possible on the reference from which the measurements are to be made.
To determine the plate scale, that is, the number of Angstroms in the spectrum that corresponds to a millimeter linear distance on the photograph, measure the distances between the A and D reference lines in millimeters. Using this measured value and the difference in wavelength between the A and D reference lines, calculate the plate scale. Make sure your result has the proper number of significant figures and the correct units. Show your work below.
Having obtained the plate scale calibration, you will be in a position to convert distance measurements (in mm) to actual wavelength differences in the work that follows. You will be working with the absorption lines (dark) in the spectrum of Saturn, that is, the center most band of light containing tilted dark lines. The bright bands that are visible above and below that of the planet itself are due to the rings and will be ignored for the purpose of this laboratory exercise. In this exercise you will determine the rotation rate of the planet only. See, things could be worse!
You are to select 8 of the tilted lines for your measurements spaced about evenly throughout the spectrum. Try to use choose lines that are well defined and not too broad. For each line you select, make two distance measurements in millimeters -- the distance from the top of the line to the closest vertical reference line that lies to the left of the line you selected. The reference lines are labeled A-F. Now repeat this measurement to find the distance from the bottom of the line to the same reference line. Enter these two measurements and the letter of the reference line in the table below. Repeat this procedure for 7 additional lines throughout the spectrum.
For each pair of measurements subtract the top distance from the bottom distance and enter that value in the table’s last column. This difference is the Doppler shift between the light coming from the opposite edges of the planet’s disk. For improved accuracy, average these differences and record the value in the space provided.
Line No. / ReferenceLine Used / Distance Between Top of Lines (mm) / Distance
Between Bottom
of Lines (mm) / Doppler Shift
Difference Between Top and Bottom Lines (mm)
1
2
3
4
5
6
7
8
Average Doppler Shift () ______
Convert the Average Doppler Shift () in millimeters to angstroms ( ) using the plate scale. Show your work below.
1. Calculate the equatorial velocity of Saturn based on your measurements. Show your work.
The rotation period is the length of time required for a point on the equator to be carried around once by the rotation of the planet. This distance it must travel is the equatorial circumference (2pR) and it travels with speed V as determined above. Solving the velocity-distance-time formula, , for the time and substituting for d and v, we obtain the period of rotation:
2. Calculate the rotation period of Saturn. Express your final answer in hours. (The radius of Saturn (R) is 60,400 km.)
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