# Sunspots: Calculating the Rotation Period of the Sun

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### Abstract

This project concerns activity happening millions of miles away, on the sun. Sunspots are cooler, dark regions of the sun where the magnetic fields are disturbed. They are signs to an active sun. They can disrupt commutations on Earth when there is a solar maximum, or many sunspots and activity on the sun. A solar maximum is apart of the 11 year sunspot cycle. At the beginning of the cycle there are few sunspots, solar minimum, then gradually more appear, solar maximum, then it returns back to a solar minimum.

I have an interest in the sun, so I chose to perform this project. The problem is to discover the rotation rate of the sun and if there is a daily change in the number of sunspots. The other problems were to find the duration of sunspots, and if there are changes in the sizes of spots. It was hypothesized that there would be a smaller amount of large sunspots when compared to lesser ones and that they will last up until 30 days. It was also predicted that the rotation period of the sun determined by sunspots would be about 27 days. I believe that all sunspots will gradually increase in number and appear more frequently near the equator of the sun.

To answer the problems, accurate maps of the sun were received by logging on the Internet and visiting NASA's web site. The angle in which a sunspot had moved over a period of time was found next. To find the total number of sunspots, the sunspots were grouped into sizes by comparing a mark on an index card to the spot on the maps. The groups were >3mm, 2-3mm, 1mm, and <1mm. The sunspots in each group were totaled to find the variation in the number of spots. I also mapped the sun on my own using a reflecting telescope and a piece of white paper.

It was found that it takes the sun about 26 days to make a complete rotation, which is close to the actual rotation period, and my prediction of 27 days. It was also found that there are more less than 1mm marks than any other size. Next came 1mm, 2-3mm and, the least most occurring size of a sunspot is greater than 3mm. The number of sunspots varied from 18 spots to 52 spots. The predictions that were made were correct! Scientists can use my data to more thoroughly understand the sun and sunspots. I now look at the sun in a different 'light'.

### Background Information

#### What is a Sunspot?

A sunspot is a cooler, dark region of the sun that is magnetically disturbed. Magnetic fields produce pressure, and this pressure can cause gas inside a sunspot to become equal with the gas outside of a spot, but now at a lower temperature. The darkest part is the umbra, (the center portion) and is about 4500 Kelvin. Surrounding the umbra is the penumbra, a hotter portion of a sunspot. The penumbra is typically 5500 Kelvin, and appears lighter than the umbra because of the change in temperature. An average sized sunspot is as large as the Earth.

The sun produces many different types of light in the core. Scientists with new tools have captured the sun's emission and therefore scientists are able to compare the results and it gives them a new way to examine the sun. The energy produced by converting hydrogen into helium is carried outward into the convection zone, which is the outer 20-30% of the sun. The sun is so massive that it takes about 50,000,000 years for energy produced in the core to make it to the surface. Magnetism is the key to understanding the Sun. Magnetism, or the magnetic field, is produced on the Sun by the flow of electrically charged electrons. Magnetic fields are the root of all activity on the sun.

#### The Sunspot Cycle

Sunspots follow an approximate cycle between 9.5 and 11 year, on average 10.5. Heinrich Schwabe was the first to note this cycle in 1843. The part of the cycle with high sunspot action is called a solar maximum. When there is little action it is called a solar minimum. Scientists have found that at the end of each cycle the magnetic poles of the sun switch. After the next 11 years the poles return to their original positions. The sunspot cycle results from the recycling of magnetic fields by the flow of energy in the interior.

#### History

In 1611 Italian astronomer Galileo, discovered dark blotches on the sun. Chinese astronomer also reported sunspots as early as 200 BC, but they did not think of the sun as an evolving body. Galileo's discovery marked the beginning of a new approach to the studying of the sun. The sun was then viewed as an evolving body, and its properties then could be understood scientifically.

#### Effects on Earth

Sunspots, as well as solar flares, have effects on Earth. From 1645 to 1715 there was a mini ice age in Europe. During this time almost no sunspots were detected. Some tree rings show that their growth is affected in the 11 year cycle of sunspots, but this is now under investigation by scientists. Sunspots tell us that are sun is active. An active sun can cause geomagnetic storms that disrupt commutations, endanger satellites, and disrupt power systems on Earth. An active sun can give airplane passengers a dose of radiation equivalent to a medical x-ray. It also heats the Earth's atmosphere so that spacecrafts are exposed to more atmosphere drag.

#### Size and Number

Sunspots change in size and shape, and usually last about 30 days, but some can last much longer or shorter. In the beginning, a group of sunspots develop and become visible. Then, the sunspots spread apart and grow in the next 5 to 10 days. Next, the group begins to disappear over the next couple of weeks.

#### Duration and Rotation Period

Scientists have found that the sun takes 27 days to complete one rotation. The average sunspot lasts for several days, but some have lasted for weeks. Since the Sun is a ball of gas it and not solid it does not rotate like the solid planets and moons do. In fact, the Sun's equatorial regions rotate faster, taking about 24 days, than the polar regions, which rotate once in more than 30 days. The source of this different rotation is under current research in solar astronomy.

### Problem and Hypothesis

Problem

1. What is the rotation rate of the sun determined by sunspots? (See Table)
2. Is there a daily change in the number of sunspots?
3. What is the duration of sunspots?

Hypothesis

1. I predict that the rotation period of the sun will be about 27 days.
2. I hypothesize that all sunspots will gradually increase in number and appear more frequently near the equator of the sun.
3. I predict that there is a smaller amount of large sunspots when compared to small ones and that they will last up until 30 days.

Method #1: Use reflecting telescope

1. Take telescope outside and put on a stool.
2. Line sun up with center of telescope.
3. Take a piece of white paper and draw a circle on it. Place on clipboard.
4. Focus image and line it up inside circle.
5. Have a friend hold the clipboard and with a pencil make a mark where you see a sunspot. Remember, the image is backward.

http://sohowww.nascom.nasa.gov/data/synoptic/sunspots/

### 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.

### Discussion

#### 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.

### Conclusion

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.