Sunspots are temporary, visibly darker spots on the photosphere of the Sun. They occur in places with concentrated magnetic fields, causing convection, and thus resulting in reduced surface temperature. Sunspots have temperatures of about 3,000 to 4,500 K while surrounding areas have temperatures of 5,780 K. This large difference in temperature allows the sunspots to be distinctly visible as darker spots. In the image below, clearly see the sunspots.
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| Image Credit: http://science.nasa.gov/media/medialibrary/2008/09/30/30sep_blankyear_resources/midi512_blank_2001.gif |
Since the sunspots are near the surface of the Sun, they move with the Sun's rotation, and can be used to find the rotational period of the Sun.
Equipment:
Unfortunately, due to a series of cloudy days, we were unable to directly observe the sunspots from the heliostat, so instead we used previous data images from the Solar and Heliospheric Observatory (SOHO). On the Observatory's website, there is an application with a slider bar that can slide through the images of the Sun over time. With the application open on the computer screen, we placed a grid with the lines of latitude and longitude that was printed on transparency paper over the image of the Sun on the screen. The image of the Sun was scaled to fit the grid. The screen with the image of the Sun and the grid placed over it would look something like the following:
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| Image Credit: http://sohowww.nascom.nasa.gov/classroom/docs/Spotexerweb.pdf |
Procedure:
On the slider bar application, I chose a sunspot towards the left of the screen and recorded its latitude and longitude using the grid. Then, following this same sunspot, I used the slider bar to track its motion, recording its position at two times as it moved across the Sun. On the grid that we used, each line represented 10 degrees of angular displacement. I repeated this process for six different sunspots. The image below gives an example of what this progression of sunspots looks like.
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| The sunspots move across the sun in a relatively short period of time. Image Credit: http://sohowww.nascom.nasa.gov/classroom/docs/Spotexerweb.pdf |
Results and Analysis:
The following table shows the data collected for each sunspot.
To solve for the rotational period, we can create a ratio of the angular distance traveled to the time taken to travel this distance:
\(\dfrac{360^\circ}{P_\odot}=\dfrac{\Delta \theta}{\Delta t}\)
Where \(P_\odot\) is the rotational period of the Sun, \(\Delta\theta\) is the change in longitude, and \(\Delta t\) is the time to travel this longitude. Solving for the rotational period, we get:
\(P_\odot =\dfrac{360^\circ t}{\Delta\theta}\)
Now, using each data point, we can calculate the rotational period of the Sun:
So we have an average rotational period of 27.6 days.
Error Analysis and Discussion:
From Wikipedia, the rotational period is about 24.47 days, so we are off by 3.13 days, which is a percent error of 11%. Possible factors that contributed to this error include inexact measurements of the location of sunspots on the grid. Also, the latitude affects the rotational period. The rotational period at the poles is larger than the rotational period at the equator.
Calculating the standard error of the rotational periods using the methods described in the first blog post of this series, we get a sample standard deviation of \(s=2.4\), and a standard error of:
\(SE_{\overline{x}}=\dfrac{2.4}{\sqrt{6}}\)
\(SE_{\overline{x}}=0.98\) days
I would like to thank Charles Law and the TFs, Allyson and Andrew for their help in the lab.
Citations:
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