Investigating Solar Rotation

This a two-day inquiry-based learning activity for seventh and eighth grade students. Over these two days, students develop and implement their own strategies for measuring the rotational period of the sun. They begin by viewing an image of the sun directly from a screen attached to a telescope (NEVER look at the sun through an unfiltered telescope!!). The teacher then motivates a discussion in which the students suggest general strategies for measuring a rotational period. Breaking into small groups, students work to devise and implement methods to apply these general strategies. To wrap up, the students will come back together as a class and present various group's methods and results and then discuss the differences among their findings and examine what the differences mean.

Throughout, this activity is largely student driven, with students brainstorming strategies, figuring out how to implement those strategies, and analyzing the differences among their results. To aid the teacher in keeping things on track to interesting phenomena, we have noted several key concepts in italics below. Not all of these points will be broached by the kids' investigations, so it's not expected that every point should be explained to the kids--only the ones that can help unwrap the problems the kids encounter need be mentioned.

The importance of the relationship between this activity and national teaching standards cannot be over-stated. In fact, the goals of this activity consist of standards we hope will be realized for the students. For a discussion of the relevant standards and the goals and rationale underlying this activity, please follow this link.

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• telescope fitted with sunspot screen (optional)
• A series of solar images
• tracing paper or overhead sheets with markers
• rulers
• string

I. Motivation.

If you have a chance prior to the activity, it's a good idea to set up the telescopes and sunscreens outside to show the kids real-life sunspots. Seeing these sunspot images directly from the sun will hopefully make the images taken from the web seem more real (that is, less like computer magic).

About ten minutes for a motivating discussion:

What does the class know about he Sun? Hold up a pair of solar images from consecutive days, and read the dates off (for example, October 2nd, 2000 and October 3rd, 2000.) What has happened from October 2nd to October 3rd? Invariably, someone will say that the spots have moved to the right, or even that the sun has turned to the right. So now we know something new about the sun - it rotates! Let's explore this new fact: let's determine the rotational period of the Sun, how long it takes for the sun to rotate all the way around one time.

To get us pointed in the right direction, how could we measure the rotational period of the Earth if we were looking at the Earth from a distant spaceship? Can anyone think of reasons why picking a feature on a body and waiting for it to go all the way around might not always be practical? (it might take too long if the object has a very long rotational period, or clouds might get in the way). While there are no clouds to cover the sunspots, each spot is only temporary (they can last from 2 or 3 to 100 or more days) and may simply disappear before a full rotation is completed. The solution: As is often the case in science, we modify our plan to work with the data we can get.

II. Problem Solving: Devising Strategies.

About fifteen-twenty minutes for brainstorming:

To make sure everyone has a sense that we don't necessarily need data that spans an entire rotational period, try posing a question: Draw a circle and two dots on the board, about like the picture to the right, and tell the kids to suppose the dots represent the position of a sunspot on two consecutive days. Now ask, "What if I told you it will take 1000 days for the sun to make one complete rotation? Would you believe me? Why not?"

This is a good point to introduce the images from the web and break into small groups. As the students can now see, our data only spans a fraction of a rotation. Ask the students to discuss (in their groups) possible strategies for determining the full rotational period from this data. It is probably best to announce that materials such as rulers and tracing paper are available in case the students need them, rather than simply handing things out. When the students begin analyzing the data (for example, by tracing the sun's image on the tracing paper and then picking a sunspot and tracing the spot's image for each day onto the paper), they might notice any of several points. You may want to guide a group through some of these if the kids are having trouble sorting something out:

1. The measured circumference of the sun can be determined at any latitude by measuring the diameter of the sun at that latitude and multiplying by Pi.
2. If the daily travel of a spot is to be divided into the measured circumference of the sun (Pi times measured diameter), then using the distance between two consecutive days will tend to reduce a certain geometric error (as opposed to measuring the travel of a spot over nine days and then dividing by nine.)
3. If a spot goes from the center of the sun to the edge, then the sun has completed one fourth of a rotation.
4. The sun rotates on a slightly tilted axis (only about 7.25 degrees, as opposed to the Earth's 23.5 degree tilt.)
5. Since the sun is spherical, the spot's images from day to day tend to be closer together when the spot is near the edge of the sun's image than when the spot is near the center.
6. Measuring the total travel of a spot over the nine days and then dividing by nine to determine the average distance traveled in one day might tend to reduce measurement error (as opposed to just measuring the distance between two consecutive days' images).

The last fifteen to twenty minutes for reporting out:

Once the groups have had enough time for a few of them to come up with feasible strategies for measuring the rotational period, reconvene the class and tell them about the homework assignment: each kid will write a brief description of a method for determining the period; include any drawings and prose they feel they would need to convince a skeptical friend that the method is reasonable (due the next day). They should feel free to use any of the ideas presented in the remainder of the class period. This worksheet describes the assignment and helps the students organize their thoughts.

At this point, the groups who have come up with methods explain their strategies to the rest of the class. Here are a few examples of what they might come up with.

III. Putting Theory into Practice.

Fifteen minutes for groups to decide on a strategy and implement it:

At this point, everyone in the class should have a clear understanding of at least one method for determining the rotational period. So the task for the next fifteen minutes is for the students (in their small groups) to agree on a method and carry it out.

If they have extra time, they may want to check their results by trying out a different method. Or, if their method involved rounding off to the nearest day (and if the rounding error was significant), you might ask them to see if they get a different period if they carry out the calculations using data rounded to the nearest hour.

IV. Putting it all Together.

Twenty to twenty-five minutes to discuss the results:

Once the groups have come up with measurements, it's time to reconvene as a class and discuss the results. In this segment, each group will report to the rest of the class, describing the method they used, which spot(s) they examined, and their findings for the rotational period. It is important to emphasize that there are advantages and disadvantages of different methods, and that it is not appropriate to think of any one method as "best."

If there are discrepancies among the measurements for a given spot, then have the groups explain their methods and see if the students can come up with reasons for the differences based on differences in the methods. Such reasons may include geometric considerations, proneness of a particular method to human error, etc..

Do the measurements for each given spot tend to agree from group to group, but average measurements from one spot to the next tend not to agree? Do the students see any reasons for this? If the rotational periods appear to be increasing as spots are chosen farther away from the equator, then point (2) below should be mentioned (with congratulations for observing a subtle physical phenomenon!). Here is more detail on this phenomenon.

Below are some general considerations for this part of the discussion:

1. Measurement error is compounded when smaller distances are measured. For example, if an object 10.0 cm long is measured to be 10.1 cm, then you are only off by one percent, but if an object 1.0 cm is measured to be 1.1 cm, then you are off by ten percent, even though you are still off by the same amount, 0.1 cm!
2. Sunspots near the equator may give rise to a shorter measured rotational period than those farther away from the equator. This may not be due to error. Owing to the fluid nature of the sun's body, the rotational period actually increases as you move away from the equator toward the poles. It may be best to leave this point alone unless the students' measured rotational periods seem to demonstrate this fact.
3. If a spot is near the edge of the sun's image, not much of its movement is in a direction we can see, so we measure it as moving less in a day than it really does move. Hence, we should expect our measurement to imply that the spot takes longer to get all the way around than it really would take. That is, if we observe spots near the edge, we may tend to get longer rotational periods. For more on how this works, review the geometric observations page.
4. When we measure the movement of a spot on our paper, we are measuring travel on a straight line (since our paper is flat and our ruler is straight), but the sun is spherical so when it turns, a spot on its surface really moves in an arc. So instead of measuring an arc's length, we measure the length of a certain line segment which is even shorter than the line segment connecting the arc's endpoints. Naturally, this line is shorter than the arc (after all, we all know what the shortest path between two points is!), so we measure the spot as having traveled less than it actually did. Again, this results in a longer measured rotational period and the geometric observations page serves as a reminder of how this works.

Here is a homework assignment you can give after the second day.

To help focus the question of whether this activity has met its goals in the classroom, Scopes for Schools has created a guide for assessment, which includes both homework and in-class components.

Assessment is a vital tool for Scopes for Schools as we seek to improve and evaluate our activities and our program as a whole. After you have had a chance to assess this activity , Scopes for Schools would greatly appreciate a chance to learn from both your specific experience with the activity and your general experience as an educator.

We invite any feedback you care to give, and would especially like to hear about:

• How well the activity met it's goals, as demonstrated by the assessment;
• What we can do in terms of altering the activity itself or the assessment techniques to better meet our goals;
• Any suggestions you have ("shoulds" or "should nots") for future teachers who use this activity.

This questionaire fleshes out these questions in a way that we have found particularly helpful.