Sunspots: Calculating the Rotation Period of the Sun (page 3)

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Author: Jennifer, Grade 7

Procedures: Math

  1. Find the center of map1 by folding it into quarters. Unfold and mark the center lightly with a pencil.
  2. Measure the distance from a selected spot to the center. (d1)
  3. Setup the proportion (1.35/13 = x/d1) to find the diameter of the sunspot circle. Divide by 2 to find the radius. (r)
  4. Use this equation to find b1. b1=square root of [(r*r)-(d1*d1)] See Table
  5. Use arctangent to find the angle on the first day. Arctan. Of (b1/d1)
  6. Repeat steps 1-5 on map2
  7. Subtract arctan1 from arctan2 to find the angle moved from map1 to map2. Note: If negative, find and use absolute value.


Rotation and Duration

The rotation period of sunspots is about 26 days. An ordinary ruler was used, and therefore affected the data. The ruler could only measure to the nearest millimeter. The longer periods of time were closer to the actual time because the margin of error with the ruler was smaller. The size of a spot had no effect on my data. The average sunspot lasted between 13.5 and 27 days.

Size and Number

Spots that were >3mm, 1-2mm, 2-3mm, and <1mm were looked for. The average number of spots on the sun was about 19.5. There was a lot of variation on a day-to-day basis and causing the total number of sunspots to not stay at a roundabout number. Frequently there are smaller spots than any other size. The next most occurring size of a spot was 1-2, then 2-3. The least occurring size of a spot was >3mm. This data is only looking at half of the sun, and varied.


To discover the rotation period of the sun, if there is a daily change in the number of spots, and the duration of sunspots, a sunspot map was printed and a spreadsheet was setup. A map was looked at to compare the sizes of a spots, to total them and when they appear and disappear. With help, a reflecting telescope was used to make my on maps, but it was decided not to use them because of they are not as accurate as NASA's.

It was found that the rotation period of the sun is 26 days. The most accurate readings were when the difference in time was long. This is because the percentage of human error is smaller during a large period of time. Another reason that it came up short was because an ordinary ruler was used which can only measure to the nearest millimeter. It was also found that the sunspots less than 1mm in size, an actual of about 9.63 kilometers, always significantly outnumbered the other sizes. Next came 1-2mm, than 2-3mm and last greater than 3mm. There was no consistent pattern or correlation and it varied on a day-to-day basis still remaining within the guidelines above. The total number of sunspots varied widely, from 25.821 to 2.179, a standard deviation of about 11.821.

The findings of this project could/would help scientists better understand sunspots and the sun. They are still learning about the sun and its effects on earth. With a better understanding, they can more accurately predict the solar cycle, which can make us better prepared for some effects, like colder weather, and disruptions in satellites.

If this project were to be repeated things should be done differently. I would first get the actual times of readings off of the NASA's site on more of my maps to receive more data. It would also help to follow though an entire solar cycle of 11 years.

It is concluded that, according to my present data, the sun rotates every 26 days, the total number of sunspots varies, and sunspots last between 13.5 and 27 days.

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