Using After Effects and the free VC Orb plugin, I have the rings cast a shadow on the gas giant. 
In this video, I'm revisiting my earlier tutorial showing how to add rings to a planet when using Video Copilot's Orb plugin. I show how to make the rings using Polar Coordinates, then use an Alpha Invert Matte along with a simple expression to cut the rings out. I then add fake shadows using adjustment layers to have the planet cast a shadow on the rings and the rings cast shadows on the planet. 
Finally, I show how to recreate the planet and rings in Cinema4D Lite (included in the Adobe After Effects CC licence)

Dan Ebbert's LookAts
X Rotation:
delta = toWorld(anchorPoint) - thisComp.layer("Sun").toWorld([0,0,0]);
Y Rotation:
delta = toWorld(anchorPoint) - thisComp.layer("Sun").toWorld([0,0,0]);
Variation for the shadow on the planet:
Angle = comp("Saturn").layer("Shadow Pointer").transform.xRotation;
if (Angle < 0) {
X = linear(Angle, 90, 180, 50, 100);
Y = linear(Angle, 90, 180, -25, -50);

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