ACTIVITIES WITH SUNSPOTS
By
Jim Roberts
OBJECTIVE: In this activity the motion of the sun will be studied using the movement of sunspots on “the surface” of the sun.
INTRODUCTION
One of the first records of sunspots is that made by Galileo Gallilei around 1610. He recorded the patterns of sunspots for 21 days and noted that they moved and that the sun was not a perfect object. This discovery had strong scientific and philosophical implications for the time. Thus, we should know something about sun spots and their activity.
This activity is designed to show two things:
- The sun rotates on its axis
- The sun in not made of solid materials.
A sketch of the sun’s motion as it rotates about the polar axis. Note that the sunspots near the equator rotate along a path of a great circle equal to that longitude’s distance around the sun. Those sunspots that are near the pole, either north or south, will rotate along a path much shorter in their distance of travel in one revolution . We can work these paths out using spherical geometry. Any sunspot will move along a path expressed by a formula:
Distance = Rsun X Cosine(Θ)Sine(Ф),
Where Θ is measured from the equator, North or South, and Ф is measured about the polar axis.
A table is provided to allow you to find the values needed for calculations, after you have made some measurements.
The table below can be used to find the angle of rotration of the sunspot on the sun. The arithmetic has been simplified to a minimum need. To convert the table to your measurement you will need to scale the distance on the sun’s picture and then use the fact that the radius of the sun has been set at 1 unit. All of the images of the sun have been set for the same size to make it simple to compare the motion of the sun spots. You will need to measure each one separately to make sure there is no variance in size. Table 1 below is shows the cosine data for a rotation about the polar axis of the sun. A rotation of the sunspot through 90º carries it to the zenith of the latitude at which it is located. For an angle of more than 90º the sunspot will pass through the zenith and down the other side of the sun.
ANGLE OF ROTATION ABOUT VERTICAL AXIS THROUGH THE SUN / DISTANCE FROM VERTICAL AXIS(X)
0 / 1.00000
5 / 0.99619
10 / 0.98480
15 / 0.96590
20 / 0.93964
25 / 0.90623
30 / 0.86592
35 / 0.81901
40 / 0.76586
45 / 0.70688
50 / 0.64252
55 / 0.57326
60 / 0.49963
65 / 0.42220
70 / 0.34156
75 / 0.25831
80 / 0.17309
85 / 0.08656
90 / 0.00000
The angle of turning is obtained by measuring the distance over from the vertical axis of the picture of the sun. Measure the distance to a sun spot from the axis of the picture of the sun as shown in the next figure. Measure the distance across the sun along a line drawn perpendicular to the axis of the sun and through the sunspot of interest. Scale this distance X to the radius of the sun where the sunspot is located. The figure below shows the geometry required to find the angle of location of the sunspot.
Measurements of X and r give the values of 4.5 units and 5.5 units with a ratio of 4.5/5.5 = 0.82. This corresponds to an angle of rotation of the sunspot up from the plane of the page and across by an angle of 35º about the vertical axis. This angle is the beginning point of our data. Repeat these measurements for figures 2-8. When all of these measurements are completed, determine the value of the angle of rotation for each sun spot by using Table 1. The pictures were taken for a time interval of one day so, each of the angles determined should be about the same. Average the values of the angle that you get and divide this number into 360º. This will tell you the number of days that it will take for the sunspot (sun) to rotate at that latitude. This number will vary from 24 days to about 30 days as the sunspots are located near the equator or near the polar regions.
A sketch of the measurements X and r to find the angle of rotation of the sun about its polar axis. The value of r will change as the latitude at which the sun spot is locates changes.
Figure 1. A color picture of the sun with several groups of sunspots. The sunspot activity of the sun varies in number over an eleven-year cycle.
X / r / DAYS / ANGLE / COSINE6.3 / 6.88 / 1 / 30 / 0.876827
6.18 / 7.5 / 2 / 29 / 0.860125
4.8 / 7.3 / 3 / 47 / 0.668058
3.9 / 7.4 / 4 / 57 / 0.542797
2.15 / 7.4 / 5 / 72.5 / 0.299235
0 / 7.2 / 6 / 90 / 0
1.5 / 6.9 / 7 / 102 / 0.208768
2.8 / 6.9 / 8 / 110 / 0.389701
SUMMARY OF DATA FOR EIGHT DAYS
Figure 2. A picture of a sunspot on the sun for September 2, 2004.
Figure 3. A picture of a sunspot on the sun for September 3, 2004. Note two new sunspot patterns appearing to the lower right.
Figure 4. A picture of a sunspot on the sun for September 4, 2004.
Figure 5. A picture of a sunspot on the sun for September 5, 2004. Note two new sunspots to the left of #0667.
Figure 6. A picture of a sunspot on the sun for September 6, 2004.
Figure 7. A picture of a sunspot on the sun for September 7, 2004. Note the appearance of two sunspot regions 0071.
Figure 8. A picture of a sunspot on the sun for September 8, 2004. Note that o669 appear to be farther apart than when we first saw them. This is due to the fact that they are moving up toward us from the left limb of the sun and across the sun toward the equator. This motion on the surface of a sphere is interesting.
When you have measured all of the distances across the sun and converted the distances into angles, you will need to plot the angular distances versus the days to see what the angular rate is per day. This will give you the rate of rotation of this section of the sun. Your plot should look like that on page 4 of this exercise. A sheet of graph paper is attached for you to make the plots.
X / r / DAYS / ANGLE / COSINE1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10
ELAPSED DAYS
Fill in the data table and then plot the data in the grid above. You should plot the angle of turning on the vertical axis and the elapsed days along the horizontal axis.
Why worry about what the sun is doing, anyway? For daily updates and for information on present and past sun spots, see the web site below.
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