Name:____________________________ Lab Section: Online Date: _____________
Difference Between Lines
|
Line |
Wavelength |
Lines |
Wavelength |
Distance |
|
F |
6304.79Å |
F and E |
38.29 Å |
|
|
E |
6266.50Å |
E and D |
|
|
|
D |
6217.28Å |
D and C |
|
|
|
C |
6163.59Å |
C and B |
|
|
|
B |
6143.06Å |
B and A |
|
|
|
A |
6128.45Å |
Sums: |
Å |
mm |
You will use the plate scale below to convert measurements in millimeters on the photograph into Ångstroms.
You will be working with the absorption lines
(dark) in the spectrum of Saturn, that is, the centermost band of light containing
slanted, dark lines. The bright bands above and below that of the planet
itself are due to the rings and will be ignored for the purpose of this
laboratory exercise, which is to determine the rotation rate of the planet
only. [See, things could be worse!] Select several of these slanted lines for
your measurements, choosing lines that are well-defined and not too
broad. Label the lines you choose as 1, 2, 3... on the photograph.
Distribute your chosen lines evenly throughout the spectrum.
For each line you have selected, you will make two measurements -- the distance of each end from the most convenient vertical reference line. Take the difference of these two distances (in millimeters) to get the amount of shift between the light coming from the opposite edges of the planet’s disk. You can then use the plate scale to convert the differences in mm to differences in wavelengths (Dl or average Doppler shift). Again you can reduce the errors by choosing several lines and averaging the results.
|
Line No. |
Reference Line |
Distance From Ref. To Top of Line (mm) |
Distance From Ref. To Bottom of Line (mm) |
Difference Between Columns 3 and 4 (mm) |
|
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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Sum of Difference = ____________ mm Number of Lines = 8
We may now use the Doppler equation to find the equatorial velocity of the planet Saturn. The standard Doppler equation is
Here we have a slight modification to make, due to the fact that we are taking light Doppler shifted from each limb of the planet (contributing a factor of two) and the light is reflected from the atmosphere of Saturn to reach us on the Earth (an additional factor of two). The correct form for the equatorial velocity is then
(1)
Taking the speed of light (c) as 300,000 kilometers/sec., your answer will also be in units of km/sec. The value lo = 6200 Ǻ will serve with negligible error over the region in question.
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 (2R) 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)
1. Calculate the equatorial velocity (equation 1) and the rotation period (equation 2) of Saturn based on your measurements. Show all of your work and clearly indicate your results. Use consistent units in your calculations and express your final answer in hours. For the radius of Saturn (R), use 60,400 km. Please be neat and orderly.
V = ________ km/sec P = ___________ hrs.