Here was used a black cylinder. So we can go to imitate the shadow not only on the rings but also the shadow on satellites and moons. And you're right. I used a simple approximation for moons - circular orbits with an arbitrary initial positions.
saturnradius1 =
QuantityMagnitude[Entity["Planet", "Saturn"]["PolarRadius"],
"Kilometers"];
saturnobliquity = .2; Shadow = Graphics3D[{Black,
Cylinder[{{0, 0, 0}, {30*ringouterradius*Cos[saturnobliquity],
0, -30*ringouterradius*Sin[saturnobliquity]}},
saturnradius1]}];
