A spectral line from the left side of Saturn's rings, as you see them, is at a wavelength slightly shorter than the same spectral line measured from the right side of Saturn’s rings. Which way (direction) is Saturn rotating, and why?

First, let's discuss the Doppler Effect, which states that all waves, electromagnetic or sound, have a pitch shift depending on whether the source of the wave is moving toward or away from us. If you listen for something moving quickly toward or away from you, like a train or a car, you will hear the pitch change to a lower value as it passes us and back to a higher value as it approaches.

It makes sense that something approaching will be "crunching" the waves together, making them shorter, and something moving away from us will "drag" the waves, making them lower. In other words, a higher pitch in sound is composed of shorter sound waves, and a lower pitch is composed of longer sound waves.

The same applies to light: objects moving toward us will "crunch" the light, causing its waves to get shorter, and objects moving away from us will "drag" the light, causing its waves to get longer.

To remember which electromagnetic waves are longer and which are shorter, consider the fact that almost everything in the universe is expanding away from Earth, a phenomenon known as red-shifting, where red-shifting denotes a direction away from Earth and blue-shifting, a direction towards Earth.

Okay, so let's examine the question regarding Saturn's rings. The rings are rotating from left to right because the light from the left side of the rings is slightly shorter (pointing towards us) than the light from the right side (pointing away).

When looking at Saturn from above its north pole, prograde rotation is observed; the shorter wavelength on the left side (as seen from Earth) means that the approaching side is rotating in the direction of the observer, resulting in a blue shift, and the receding side is rotating in the opposite direction, resulting in a redshift.

Saturn is rotating counterclockwise when viewed from above its north pole. This is because the rotation causes the left side of Saturn's rings to approach Earth slightly faster than the right side, causing a Doppler shift in the spectral lines towards shorter wavelengths on the left side compared to the right side.