Day Lab - Step 3: Determine the Rotational Period of the Sun

Now we have all the information needed except for the Sun's rotation around its own axis. Following Galileo's example, we can use sunspots as tracers of the Sun's rotation

Source

Unfortunately, whenever my lab group checked, there were no large, obvious sunspots to track. Instead, we used previously recorded video data (much like the gif above) to track sunspots over time. I tracked three sunspots from 2001:

The top sunspot traveled:

• 51 degrees in 3:12:48 days = 305280 seconds
• 53 degrees in 3:17:36 days = 322560 seconds
• The average is 52 degrees in \(3.14 \times 10^5\) seconds (pi!), giving a period of: \[ \frac{P}{360^{\circ}} =  \frac{seconds \: traveled }{degrees \: traveled} \] \[ P =  \frac{3.14 \times 10^5 \times 360^{\circ}}{52^{\circ}} = 2.17 \times 10^6 s\]

The middle sunspot traveled:

• 50 degrees in 3:12:48 days = 305280 seconds
• 40 degrees in 2:17:36 days = 236160 seconds
• The average is 45 degrees in \(2.71 \times 10^5 \) seconds, giving a period of: \[ \frac{P}{360^{\circ}} =  \frac{seconds \: traveled }{degrees \: traveled} \] \[ P =  \frac{2.71 \times 10^5 \times 360^{\circ}}{45^{\circ}} = 2.17 \times 10^6 s\]

The bottom sunspot traveled:

• 83 degrees in 6:19:12 days = 587520 seconds
• 30 degrees in 2:11:12 days = 213120 seconds
• The average is 56.5 degrees in \(4.00 \times 10^5 \) seconds, giving a period of: \[ \frac{P}{360^{\circ}} =  \frac{seconds \: traveled}{degrees \: traveled} \] \[ P =  \frac{4.00 \times 10^5 \times 360^{\circ}}{56.5^{\circ}} = 2.52 \times 10^6 s\]

The average is \(2.29 \times 10^6 s \) or 26.5 days. Interestingly, the first two spots were very consistent and decently close to the actual rotational period of the Sun (24.47 days) and the bottom sunspot was significantly farther than the other two data points. Alas, we cannot throw out data just because we know it is off and get a more accurate answer. However, we can pay attention to this discrepancy as a potential source of error.

Due to a lab group of uneven numbers, I worked on this section alone.