Hi, Glad you are participating in Solar Week!

1. How can we tell that the different layers of the Sun rotate at different speeds? Can these values be calculated?

We can determine how fast the interior of the sun is rotating using a techniques called "helioseismology" . You can read more about it on these web pages:

http://solar-center.stanford.edu/heliopage.html

http://soi.stanford.edu/results/heliowhat.html

To describe it quickly, helioseismology is the study of the Sun's vibrations (like "seismology" is the study of Earth's vibrations). Rotation of the layers inside the Sun affect waves bouncing around inside the Sun, and that can be measured. The actual calculations are quite complex.

3. How can we identify the chemical composition of the Sun through satellite imaging?

I am answering these out of order because both of these questions relate to spectroscopy. Solar physicists spend a lot of time studying the spectra of the Sun. Here is an example of an ultraviolet spectrum from the SOHO mission: http://folk.uio.no/paalb/atlas_full.jpg

A spectral plot like this shows how much light is produced at different wavelengths of light (different colors in visible light). You will notice there are a lots of lines - it is not a smooth curve.

Each of those lines is produced by a particular kind of atom. Each type of atom had an "atomic finger print" of spectral lines which we can recognize. In fact, each ion has an identifiable collection of spectral lines (for instance the spectral lines of iron ionized 5 times are at different wavelengths than the lines of iron ionized 6 times). We can identify the lines in the spectra and use their relative strengths to get an idea of the relative amounts of different elements.

2. How can we measure the Sun’s density using satellite imaging?

The strength of some of those lines also depends on density, so we can figure out densities in the Sun's atmosphere with spectroscopy too.

Figuring out the average density of the Sun, though, is a matter of basic physics - we can measure the size of the Sun, and determine its mass using the laws of gravitation (which you may have learned about already, as you are in high school). Then average density=mass/volume.

I hope that is at least reasonably understandable. there are a lot of details that go into the actual measurements.

Terry