# Surface Differential Rotation by measuring the position of sunspots

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• TheSpectacularSpecs
In summary, the conversation was about a university lab project involving the measurement of sunspots' positions and the calculation of the Sun's rotation using images from NASA's SDO. The individual has successfully obtained the angular velocity of several sunspots at varying heights but is now looking for a way to find the angular velocity at a specific latitude, particularly the equator. They have come across an equation on Wikipedia for surface rotations at different latitudes, but they have not been able to find a reliable source for it. The individual confirms that the equation is relatively true, with the equatorial rotation denoted as A and the latitudinal gradient of rotation as B. This information was found in a cited article from the Monthly Notices of the Royal Astr
TheSpectacularSpecs
TL;DR Summary
I am measuring positions of sunspots and use them to calculate the rotation of the Sun. Wikipedia has an equation that is very simple for surface rotations at different latitudes, but I have not been able to find the equation properly sourced.
I am doing a University lab project where I measure positions of sunspots (using images from NASA's SDO) and use them to calculate the rotation of the Sun. Currently, all is going well: I have the angular velocity of several sunspots at varying heights. However, I want to be able to find the angular velocity at a specific latitude, especially the equator. Wikipedia has an equation that is very simple for surface rotations at different latitudes, but I have not been able to find the equation anywhere else, and Wikipedia does not have sources for that particular equation. Wikipedia, although significantly better than it used to be, is not an acceptable source to reference in my project. Does anyone know if this equation is true and where I can find a referenceable source with it?
Equation: https://ibb.co/7Ys3WHG (or on https://en.wikipedia.org/wiki/Differential_rotation under the Surface differential rotation heading)

For anyone wondering, I have confirmed this equation is at least relatively true, with:
ω(Φ) = A + Bsin2Φ
where A is the equatorial rotation and B is the latitudinal gradient of the rotation. This is all the information that I need, and was found in the article cited below.
K. J. Li, X. J. Shi, J. L. Xie, P. X. Gao, H. F. Liang, L. S. Zhan, W. Feng, Solar-cycle-related variation of solar differential rotation, Monthly Notices of the Royal Astronomical Society, Volume 433, Issue 1, 21 July 2013, Pages 521–527, https://doi.org/10.1093/mnras/stt744

berkeman and Drakkith

## 1. What is surface differential rotation?

Surface differential rotation refers to the phenomenon where different parts of the Sun's surface rotate at different speeds. This is due to the fact that the Sun is not a solid body, but rather a gaseous sphere made up of different layers that rotate at different rates.

## 2. How is the position of sunspots used to measure surface differential rotation?

Sunspots are dark, cooler areas on the Sun's surface that are caused by magnetic activity. By tracking the movement of sunspots across the Sun's surface, scientists can measure the rotation rate of different latitudes and determine the presence of surface differential rotation.

## 3. What tools and techniques are used to measure the position of sunspots?

A variety of tools and techniques can be used to measure the position of sunspots, including telescopes, cameras, and specialized software programs. Some scientists also use spectroscopy to measure the Doppler shift of light emitted by sunspots, which can provide information about their movements.

## 4. What is the significance of studying surface differential rotation?

Studying surface differential rotation is important for understanding the dynamics of the Sun and its magnetic field. It can also help us better predict and understand phenomena such as solar flares and coronal mass ejections, which can have significant impacts on Earth's space weather.

## 5. How does surface differential rotation change over time?

Surface differential rotation is not constant and can change over time. It is affected by a variety of factors, including the Sun's magnetic field, convection currents, and the tilt of its axis. Scientists continue to study and monitor these changes to better understand the Sun's behavior and its effects on our planet.

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