The Spacers, as the inhabitants of Earth's long-emancipated colony worlds are known collectively, are far ahead of Earth both technologically and biologically. However, they no longer have anything resembling a police force on any of their worlds: the elimination of want and need caused by their use of robots has made them a virtually crimeless society. Thankfully, run-down, over-populated Earth has lots of crime and thus lots of experience solving crime. As Lije Baley acquitted himself well in the first novel solving the murder of a Spacer on Earth, he's now called upon to run the investigation on Solaria.
Asimov continues to develop the peculiar psychology of Earth residents here -- Baley, like most citizens of Earth, is intensely agoraphobic because Earth's entire civilization exists inside vast, enclosed cities. Earth's surface has been devoted to providing food for the planet's teeming billions. But Baley must work to overcome at least part of this agoraphobia during his investigation. Solaria is so intentionally under-populated that its citizens have developed crippling social phobias when forced to be in the physical presence of other human beings.
Daneel Olivaw, human-form robot from the pre-eminent Spacer world of Aurora, both aids the investigation and acts as a bodyguard against repeated attempts on Baley's life. Olivaw chips in with his emotionless logic and understanding of Spacer psychology, though even he is an outsider on Solaria.
The murder itself has ramifications for Earth and the Spacer worlds on a number of levels. The most wide-reaching consequence attaches to Earth's ability to begin colonizing worlds again with the aid of the Spacers. Baley's own son wants to be one of these new colonists, but the program may also keep both Earth and the Spacer worlds from falling into a social decline. If Baley can solve the case without embarrassing the Spacer powers that be, at least some of Earth's billions may find new homes elsewhere. And a necessary cross-pollination between Spacer and Earther cultures may benefit everyone.
Baley and Olivaw's investigation flows much more smoothly here than in The Caves of Steel, in which the plot required Baley to deduce a killer incorrectly several times before finally getting it right. Here, on an unfamiliar planet, he devotes himself to social fact-finding as well as the murder investigation. The former is necessary for the latter to succeed. This reduces the always entertaining Olivaw's role in the investigation, really the novel's only narrative flaw.
Otherwise, The Naked Sun succeeds as both science fiction and whodunnit. Olivaw functions as the source text for a legion of logical sidekicks that would follow, most prominently Star Trek's Spock and Data, and more precisely in such 'future cop' shows as Almost Human, Future Cop, and even Holmes and Yoyo (!). Recommended.