This note contains spoilers for the book.

An authorized third book in the series begun with The Mote in God's Eye (#2). This one is written by Pournelle's daughter, who it says here was an Army intelligence officer in the Middle East and then an archaeologist and anthropologist, also around the Middle East. Some online info suggests it includes some feminist critique of the original series.

There's a nice statement from the author on the book's Amazon page.

It's on New Utah mostly, a world just on the edge of being eligible for accession to the Empire in decent status (they could almost have space travel themselves if they cared). There's a lot of LDS future history involved, schisms and such, and the Himmists. There's a natural laser in the rock that almost talks back to the Mote. And there are Swenson's Apes, which are Moties but in a pre-tech civilization. There's an Alderson tram-line connecting them to the Mote every 21 years for a while. And it's not quite clear to me whether the Moties there are the originals, or of they're colonists. They're sociially quite different, and don't have mediators.

It's much more cleanly written (and produced, for that matter) than I would have expected for an early effort at fiction.

I'd probably have gotten more connections if I had read the sequel to Mote more recently or more often. But I liked it as it was, anyway.