A real (smooth) sphere? I’m a first-time Blender user, and just got started with 2.8.

I want to make an animation where a sphere is zoomed from billiard-ball size to planet sized; a factor of over a hundred million.

That’s fine when spheres are mathematical geometry, as with POV-Ray.  But in Blender, everything is a mesh.  I’m tried looking into nurbs and blobs but I don’t understand it well enough — The blob (Metaball in Blender) allows specifying the number of polygons at render time anyway, but I can't apply a UV texture map.

How can I make a sphere that adapts its tessellation to the needed scale?
You can activate POV-Ray addon in user preferences.  A povSphere then becomes available among other primitives for Blender to add to the scene. It will behave like you're used to in POV and never show any tesselation at render time