How are you looking to present said orrery, are you planing on taking a few simple screenshots or full realistic renderings?
Will you be presenting some static images, or are you thinking of animations or video? Or perhaps even an interactive/real time game-like demo?
Either way all you want to achieve seems pretty reasonable and relatively withing reach. Blender has good animation and modeling capabilities that suffice for what you want to do.
Since you say you lack the vocabulary and terminology here are some quick keywords and that may be useful for your research and to get you on the right track.
You may need to look into animation and mostly constraints stuff, also Curve path Animations and Follow track. Look for tutorials youtube, there should be plenty to get you started
If you are looking to make some sort of interactive or game-like real time first person demo Blender Game engine may have be useful, even though it's considered outdated and stalled in development.
A more flexible and modern approach may be WebGL based solutions like blend4web