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Determining the solar siderial rotation period

The sun is a rotating ball of plasma. As the sun is not a solid body, the plasma rotates at different speeds depending on the latitude. The aim of this project is to determine these rotation speeds as function of the latitude. We approach this problem by studying the movement of sunspots in white light. Using digital photography we can determine quite accurately the rotations speeds. For this to work we need to study the movement of sunspots at different latitudes. Most sunspots appear around the equator of the sun, but more nothern or southern spots are likely to appear during the "active" period of the 11-year solar cycle. Currently (2005) the sun is near her most in-active point in this period. Hence, this project will take time.

First data set: at 26.7 degrees latitude, the siderial rotation period is 27.5 days

These two images were acquired on two consecutive days in july 2005. It gives us our first datapoints.

If we blend the two images, we can measeure how much pixels the sunspots moved during 24 hours. Additionally, we can measure the radius of the sun in pixels:


We rotated the image slightly such that some arrows are horizontal. This makes it more evident that not all arrows are parallel
Note that the arrows are not all parallel, which indicates that the axis of rotation is slightly tilted. Fitting an ellips in the following way, allows us to calculate the tilt.
From this image we calculate that the angle is 9 degrees and the sunspot at location A is at 26.7 degrees latitude and the rotation period is 27.5 days (siderial). The calculations are as follows. The sunspot marked at position A moved to position B in 24 hours. The distance is 58 pixels and the radius of the sun is 256 pixels. Hence, during that time, the sun rotated at an angle of alfa, where

sin(alfa) = 58/256 = 0.2265

Hence,

alfa = asin(0.2265) = 13.094 degrees.

A full rotation would be 360 degrees, therefore it will take the sun

360 / 13.094 = 27.5 days,

to make a full siderial rotation. Note that this simple calculation depends heavily on the fact that point A is on the vertical equator, so we were lucky having a sunspot on that exact location. The calculation of tilt and lattitude are similar, except we measure pixels vertically.