I'm not Watsisname (by a long shot!), but I'll try and answer anyway...
Unfortunately, SE does not do terrain or ship shadows yet. But planets, moons, and asteroids do cast shadows (although even potato-shaped asteroids and dwarf moons cast round shadows, no matter the shape of the object). So the best you can do right now is eclipse shadows of a moon on a planet. (I'm sure I have some sample screenshots of such an event somewhere, I'll poke around and see if I can find one or two for you.)
In my pic above, that is a dwarf moon casting a shadow on a rather large ship. Two shadows, actually, as there were two suns here. Also of note is not only are they different colours, but one shadow is rather sharp and the other somewhat fuzzy. I believe the one casting the sharp shadow was a white dwarf.
Edit: Oh! And rings! Rings also cast shadows.