The light levels at Saturn are far, far to small to allow plants to grow
Light diminshes with the square of the distance - the inverse square law. Saturn is almost 10 times as far from the sun as Earth is. The amount of light it receives from the sun is only about 1% that of what we get on Earth. That isn't anywhere near enough for plants to grow.
The movie would have made more sense if the ship had been around Mars; even there, the light is only 36% of what we get on Earth, but that would probably be enough.
I want the doctor to take your picture so I can look at you from inside as well.