By the look of things you should be able to apply this script to your moon and simply point to the planetary object you want it to orbit. However given the fact that your planet is moving, it looks like your moons will probably be playing catch up to the planets orbiting the sun. You should be able to fix this with a simple hierarchy change.
- Sun Container Object (Parent) - Sun Model (Child) - Planet Container Object 1 - Planet Model 1 - Moon Container Object 1 - Moon Model - Moon Container Object 2 (if your planet has two or more moons) - Moon Model ... - Planet Container Object 2 - Planet Model 2 ...
The important thing to notice is that by parenting your moon objects to your planet objects they will gain the benefit of the planets orbit for free. Then they just have to adjust themselves for their localized planetary orbit. Also be sure to make your models children of empty container objects, this way you can have them rotate without messing up the orbits of the their child celestial objects.