# Sunspotter telescope measure sunspots and measure rotation of sun

I love the sunspotter. I've helped High School students use them. My favorite experiment is to determine the rotation of the sun by looking at sunspots a few days apart. This is both harder and easier than one would think. I worked out all the dificult details so you can use this website for all the details and materials you need.

### First of all you will want templates. Click here to download a word document with the template shown at right. Print out enough templates for every student and cut them up (two templates per page) so they fit inside the sunspotter.

Alternatively you can make your own word document by instead downloading the image on the right but you need to print it to the correct scale exactly. The correct scale is 300 pixels per inch. If you are off by a few millimeters it will be fine but you need to get it very very close. Of if you have a competing product to the sunspotter you can use the image at the right to scale the circle to be the correct size.

## First Day of Measurements

Have the students write down their name and date and time. Go outside and put the paper in the sunspotter. It's very tricky to use the sunspotter. The first time allow at least 40 minutes for a group of 2-4 students to create one drawing of the sunspots. By the 3rd day they can do it in 5 minutes. Have one student in charge of constantly moving the sunspotter to put the sun in the circle and another student ready with a pencil to make a mark. It's best to make a single mark first, then check it and mentally visualize how much to adjust the first mark. Then mark where the darkest sunspot is and erase the original mark and check a third time. Only when you are pleased with one sunspot can you then draw the whole cluster of spots (while the sun drifts away from your drawing - can't help it). After drawing the sunspots you need to measure west by letting the sun drift. What? you say?

## Measure Sun Drift

In the image at left I measured the "west direction" by measuring sun drift. This is the mark circled in red. First I drew the 3 sunspots that were visible that day. Next to the 3 sunspots you can see a faint plus sign. This is at the center of the circle. So I placed one of the 3 sunspots (the easiest to see) on that plus sign and then waited a few minutes. The 3 sunspots drifted towards the red circle. It takes 2 minutes for the sun to move it's diamter (due to rotation of the earth) so I had to wait a little over a minute. As the chosen (darkest) sunspot approached the degree markings I got my pencil ready and marked the degree direction closest to the sunspot. This shows me the angle that the sunspots (and the sun) apparently drifted. On this day it was down and to the right. In the morning it will tend to be up and to the right (in the northern hemisphere) around noon straight to the right and in the afternoon (like this example) down and to the right. But you need this position very accurately as you will see in a few days when you make your second observation.

Then I took the paper out of the sunspotter, went inside and at a desk I marked the "Earth N" point which is north and is 90 degrees left of the red circled west point. If the earth had no tilt relative to it's orbit and if the sun had no tilt to relative to the earth's orbit then we would be done and that would be the north pole of the sun. But because of these 2 tilts we now need to find the correct adjustment.

You can use this excel spreadsheet to calculate the adjustment or you can use this javascript tool:

Month (1 through 12): Day of month (1 through 31): Day of year (0 through 366): --
Adjustment from earth tilt of 23.5 degrees: -- Adjustment from sun tilt of 7.5 degrees: --
Total Adjustment: --      B0 (sun tilt away/towards us): --
So in my example above you put in 3 for the month and 27 for the day and you get 26 degrees (yellow area). If the value is positive you travel around the circle to the right to find the sun north (negative values go to the left). Unfortunately in this example I used 23 degrees because I didn't know about the sun tilt. So I showed the sun north point 3 degrees off. This error is actually visible below. Anway, repeat the measurements for the next day or a few days later and then plot both on a full grid. You need to choose a grid based on the B0 value (green area). For my example date (march 27) you get -7 degrees. But I stupidly chose the +7 grid. Obviously it isn't *that* critical but if I chose the correct grid I may have gotten better results. Here are grid files (aka stonyhurst grids) for some B0 values. The grid for -3 is upside-down for the grid for B0 of +3 so there are only 7 grids:

## Stonyhurst B0 Grids

### b0 is 0 (not available - email me if you want this. Don't want to bother if not a single person ever asks for it) b0 is 1 or -1 (not available - email me if you want this. Don't want to bother if not a signle person ever asks for it) b0 is 2 or -2 (not available - email me if you want this. Don't want to bother if not a signle person ever asks for it)b0 is 3 or -3b0 is 4 or -4b0 is 5 or -5b0 is 6 or 7 or -6 or -7

I was very careful to make sure these grids are the *exact* same size as the sun image on the sunspotter.

I got the originals for these grids here so you can make your own for other sized telescopes or to use with software (rotate upside down to get negative B0): 0 degrees 1 degrees 2 degrees 3 degrees 4 degrees 5 degrees 6 degrees 7 degrees

## Final Combining of Data onto Grid

Finally you need to transfer your data from at least 2 days to your Stonyhurst grid. Take one of your pieces of data and your grid on 2 separate pieces of paper. Put them both on a window (during the day) with the grid on top. Line up the sun image circles and rotate the grid until North for the Stonyhurst grid is lined up perfectly with the north from your "Sun North" point that I explained earlier. This is harder than one would think and takes a whole minute which is like a year to an eighth grader. Tell them to take their time.

Shown to the right are my two dates drawn onto a single Stonyhurst grid. The blue circled 3 dots are from the first date and then you can see the 3 sunspots moved to the right after 2 days (this is real data from march 25,27 2011). Each longitudinal line is 15 degrees so eyeing it carefully I decided it moved 25 degrees in 2 days (actually 1.95 days because it was about an hour earlier the second day).

### Final calculation:

Complete Rotation of Sun in days = (days between measurements(1.95)) X (365 degrees) / (degrees between measurements (25))
About 28 days. The actual rotation at the equator is closer to 25 days. The error is due to the difficulty of marking the sunspot accurately (and using the wrong damn grid). If you do 3 or 4 days between measurements or if you do this repeatedly and average all your data you should be able to get greater accuracy. Of course using the correct grid would have helped also! I think I would have gotten closer to 30 degrees using the B0=-7 grid which gives 24 days!

### Going Further

A few independent research projects might include trying to verify the difference in sunspot speeds as you get farther from the equator of the sun. This is a bizarre property of the sun. It rotates faster at the equator. The earth of course is solid and so doesn't do this. Near the pole it is closer to 34 days which I would think is measureable. If not with the Sunspotter at least using soho data which has daily pictures archived over many years and the ability to measure sunspots is much much more accurate than the sunspotter.

Another independent research project might be to try to make many measurements on consecutive days and photograph or scan your measurements and turn it into a video (more difficult than one would think!).

 If you used anything from this website, please let me know! I would like you to email me so I know that I didn't waste my time creating this page. Really! If I get too many emails I'll just get rid of this line of text from this page. Or if you want me to add the remaining stonyhurst grids let me know. They only take about 10 minutes each. Also please share with me your experiences with sunspotter or similar. e-mail: