How do I measure the synodic rotation period using sunspots?

[fatima_a]

Ok so I have a project and I have to measure the sidereal synodic rotation period of the sun using sun spots. I have included a diagram of what to do. but I will explain it too. you take 5 images with a common sunspot and track it's movement on those 5 days (on the diagram, the sunspot is labeled s1 - s5, where s = sunspot and # = the day it was observed)

you draw a line connecting the sunspots and it should be parallel to a line across the center of the sun. then you draw a semicircle across the line connecting the sunspots and transfer the sunspots onto the semicircle, this is the actual position of the sunspots on the sun.

I have done all this, but here is where I am confused, it says you have to measure the angle between each pair, not all the pairs, but only for at least 8 pairs. how would i get 8 pairs from 5 sunspots? does that mean angle b/w s1 and s2 = 1 pair and angle b/w s1 and s5 = 2nd pair etc...and I need to do this for 8 pairs?

I do have the time and date of when the sunspots were observed, which I didn't show on the diagram or here, but how would I use the information of the angle and the time to compute the synodic period of rotation? is there a formula i have to use which incorporates angles and time? because so far I have came across 3 formulas:

1) the regular 1/s = 1/sidereal - 1/earth's sidereal...I can't use this because I don't know the sidereal period, that's what I have to find at the end.

2) synodic rotation period = circumference of sun/speed of sunspot travel...I don't think I am suppose to use this because it doesn't ask me to calculate the speed or use the circumference anywhere

3) synodic period = 360/slope...is this the one to be used? I am not sure about this.

The link to the diagram is given below, any help would be appreciated

http://i.imgur.com/d6OhX36.png

thanks

 

[Nino MMP]

!Yes, the third formula is the one to be used. To get 8 pairs from 5 sunspots, you can take the angle between any two consecutive sunspots: s1-s2, s2-s3, s3-s4, s4-s5. Then you calculate the angle between the first and last sunspot: s1-s5. This will give you a total of 8 pairs of angles. Once you have the angles, you can use the third formula to calculate the synodic period of rotation. The slope is the average rate of change of the angle over time, so for each pair of sunspots, you calculate the angle between them, then divide that by the time difference between when they were observed. You then add up all those slopes and divide it by the total number of pairs (which should be 8). That will give you the average rate of change of the angle over time, or the slope. You then plug that into the third formula to calculate the synodic period of rotation.