Is Blender a sensible environment for making a first-person orrery? I want to show simple views of various solar system phenomena from the perspective of an observer on a crudely simulated Earth (basically a ball with some relief bumps as pseudo-mountains to provide some guide to rotations of the view, etc). The phenomena of interest are things like the tracks of the sun and moon at various latitudes/times of year, eclipses, and planetary motion. Somewhat unusually for a Blender question the graphical quality isn't important, instead I hope to get a high degree of automation. Taking the example of a sun track from dawn to dusk, I hope it's possible to place a camera on a bumpy globe, set the camera to point to the sun, and then simply rotate the globe (mountain bumps and camera included) - this seems a lot easier than using the API to slide the mountains and camera around the surface of a smooth globe. At the same time the other planets would be moving in their orbital paths (ideally ellipses, though for simple didactic work circles are probably good enough)

From my reading and (ignorant) playing with Blender I'm unsure whether this approach of forming a complex object (with attached camera) and then moving it is well within normal use or whether that's going to be an uphill struggle to use Blender in some other product's native domain (e.g. CAD/CAM). Part of my difficulty is that as a rank amateur I lack even the usual vocabulary so may be overlooking some clear guidance in the FAQ (etc).
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of interactive or game-like real time first person demo Blender Game engine may be useful, even though it's considered outdated and stalled in development.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