Other eye-popping details, not all of them previously reported, are flecked atop this book like sea salt. His five children don’t merely have nannies but have had a nanny manager. He worries that Google is building a fleet of robots that may accidentally destroy mankind. He rents castles and sumo wrestlers for his parties. At one of them, a knife thrower aimed at a balloon between the blindfolded Mr. Musk’s legs.

The best thing Mr. Vance does in this book, though, is tell Mr. Musk’s story simply and well. It’s the story of an intelligent man, for sure. But more so it is the story of a determined one. Mr. Musk’s work ethic has always been intense. One observer says about him early on, “We all worked 20 hour days, and he worked 23 hours.”

Mr. Musk was born in 1971 and grew up in Pretoria. His father was an engineer; his mother, whose family had roots in the United States and Canada, was a model and dietitian. There are indications his father was brutal, and that Mr. Musk is a tortured soul trying to make up for a wrecked childhood. But no one will speak specifically about any such events.

He attended college in Canada before graduating from the University of Pennsylvania and moving to the West Coast. His first start-up, a company that provided maps and business directories, was bought by Compaq Computer and made Mr. Musk $22 million. His interest in online banking led to his part in the creation of PayPal. When it was sold to eBay, he walked away with roughly $250 million, the author says, enough to bankroll his interests in space and green technology.

Mr. Musk got started in space exploration by first learning all he could about it, sometimes reading Soviet-era rocket manuals. There were many failures, and several near-bankruptcies, along the way to making SpaceX what it is today, notably one of only two private companies to have docked with the International Space Station.

Mr. Vance tells the stories of both SpaceX and Tesla with intricacy and insight, often stuffing the technological details, for those who are interested, into long footnotes. We come less close to Mr. Musk himself. Though the author interviewed him for several dozen hours, he remains a remote and somewhat chilly figure, a perfectionist not unlike Mr. Jobs, often given to confrontation and fits of rage.

What does come through is a sense of legitimate wonder at what humans can accomplish when they aim high, and aim weird. The animosity and jealousy some feel toward Mr. Musk’s achievements put me in mind of a great line from the HBO show “Silicon Valley,” in which the tech chief executive Gavin Belson comments, “I don’t know about you people, but I don’t want to live in a world where someone else makes the world a better place better than we do.”