Deadline: April 21.

The Teaching Observatory is located just south of the Reitz Union. Public open houses are held every clear Friday night from 8:30pm to 10:00pm. Attend the open house. Describe the objects you observed through the telescopes by answering the questions on the Observing Form. You should obtain a token from the telescope operator to attach to this form. This project can be done anytime throughout the semester. However, the completed form will be due by April 21, at the very latest.



The goal of this project is to measure the rotation of the Sun using sunspots as tracers of the spin motion. The Sun rotates differentially, i.e., faster at the equator and more slowly at the poles. To investigate this phenomenon, the positions of two sunspots at different latitude on the Sun's surface will be recorded daily over a period of at least 15 days. From these observations, you will be able to measure the Sun's rotation following the steps given below:

1.- Get the daily SOHO image of the Sun from the SOHO web page (Click here) . You will need at least 15 consecutive daily images to do this project. If you miss one day, you can always retrieve the image from the SOHO archive. Just click on "Archive" from the main SOHO web page, and then click on "Search for Near Real Time Images". You can select the desired start and end dates and retrieve all the images you need for this project. The images are called "MDI Continuum".

2.- For each image of the Sun, draw the rotation axis (North-South diameter) and the equator (East-West diameter). Measure the East-West diameter (d) in mm.

3.- Choose two sunspots located left of the rotation axis and at different distances from the equator. The sunspots can be located above or below the equator. The closer the sunspots are to the left edge of the solar disc the better.

4.- Draw a line parallel to the equator from the position of each sunspot. The intersection of these lines with the rotation axis for each sunspot will be the origin of coordinates to measure the motions of each sunspot across the solar disc. As the days go by, each sunspot will move along the horizontal coordinate from left to right till it disappears behind the right edge of the solar disc.

5.- Measure the distance (s) from each sunspot to their origin in mm. Distances to the left of the rotation axis will have negative sign. Distances to the right of the rotation axis will have positive sign.

6.- Draw a graph of s/d versus t, where "t" is the time of each SOHO observation in units of days (see example below). For instance, t=5 corresponds to 5 days after the first observation.

7.- Identify the time when each sunspot disappears behind the right edge of the solar disc (tf). The time it takes the sunspot to move across half the solar disc (tq), or one quarter of the Sun's surface, is the difference between tf and the time when s=0. The Sun's rotation period (p) is then: p = 4 * tq * 86400 (this will yield "p" in seconds).

8.- Calculate the latitude (l) of each sunspot using the following formula: cos L = sqrt(1 - 4 * (h/d)2). The latitude is then calculated using cos-1 with your calculator in degree mode.
L = latitude (in deg)
h = distance from the sunspot to the equator (in mm)
d = diameter of the solar disc (in mm)

9.- Calculate the radius (r) of the circunference described by each sunspot on the Sun's surface using the following formula: r = Rsun * cos L (this will yield "r" in km).
Rsun= Solar radius in km (see Chapter 9)

10.- Calculate the rotational velocity (v) at the latitude of each sunspot using the following formula: v = 2 * pi * r / p (this will yield "v" in km/s).

Once you have done all the calculations, the results should be presented in three pages as illustrated in the example below. The first page should have the fifteen SOHO images taken at different days. Each image should be dated. The two sunspots used in your study should be clearly identified in each image, as well as the Sun's rotation axis and equator. The second page should show the s/d versus t plot for the first sunspot and give the measurements and calculations made to estimate the Sun's rotation, including "tq" "h/d", "L", "r", and "v" (do not forget the units). Please, show the results in the front and include all your calculations in the back. The third page should show the same information for the second sunspot.