Saturn is rotating on itself. Due to Doppler effect, absorption bands from the planet (or from the Sun that enlight Saturn) are tilted.
Question 1: what is the rotation speed at equator?
Tip: light coming from the Sun is affected twice by Dippler effect: first when light arrived onto the planet, and second when it comes out.
Question 1: quelle est la vitesse de rotation à l'équateur?
Astuce: la lumière arrivant du Soleil est réfléchie; le phenomène Doppler est donc doublé.
Question 2: Saturn is rotating in 10.656h; what is its diameter?
Get there the original FITS file of this image. Addition of three 5min exposures with C11 f/10.
Above image has been taken with a Lhires III (2400), dispersion D=0.11A/pixel. It has been taken around 6550A.
We first measure the delta in X at border of the planet (not the rings!) on top and at the bottom. We find dx=7pixels.
We divide dx by two (otherwise you measure the sum of the radial velocities on both sides); we also divide result by two to correct of the double Doppler effect: once when the Sun light come on the planet, twice when it goes out... We use the Doppler formula: "v/c = dLambda / Lambda".
Radial velocity is then V = 1/2 * c * D * (dx/2) / L = 1/2 * 300000 * 0.11 * 3.5 / 6550 = 8.8km/s
Simply, rotating speed is T = pi * d / V = 10.656*3600 = 38362s
So: d = T * V / pi = 38362 * 8.8 / 3.14 * 8.8 = 107511km
In books, one can find the diameter of 120536km!