In a strip mall just off Houston’s NASA Parkway is a restaurant called Frenchie’s Italian Cuisine. You wouldn’t know it from the unassuming beige storefront, but inside, Frenchie’s looks like a museum. The walls are covered in framed pictures of smiling astronauts, in their blue jumpsuits and puffy spacesuits, holding up bubble helmets and model spaceships. Frenchie’s has been a popular spot with NASA employees at Johnson Space Center, a few minutes away, since it opened in 1979. Over the years, astronauts have dropped in before a flight to chat with Frankie Camera, the owner, and returned with autographed mementos.

Camera, now in his 70s, still runs Frenchie’s, but American spaceflight is changing fast. In the next decade, the restaurant’s walls could display the stories of a new kind of astronaut. Soon rich businessmen with $55 million to spare could become astronauts. So could the founder of a company that processes credit-card payments, and a physician’s assistant who works with cancer patients. Jeff Bezos could count as an astronaut too.

That thought might sound more like an SNL skit than a real future, but here we are. Americans who want to fly to space can skip the long and difficult process of becoming a NASA astronaut. Now all that’s necessary is some combination of money and luck. Three wealthy people are flying via Elon Musk’s SpaceX for a trip to the International Space Station. Another rich entrepreneur purchased a SpaceX flight around Earth for himself and three others, two of which he picked from a raffle and a Shark Tank–style competition. Meanwhile, Jeff Bezos’s Blue Origin plans to start flying customers to the edge of space this summer, and the first passenger will be chosen through a live, open auction, like a thirsty eBay bidding war.

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All of this has renewed debate about who counts as an astronaut and who doesn’t. Most people would agree that the professional astronauts who work for NASA are astronauts. But what about NASA Administrator Bill Nelson, who flew to space in 1986 as a member of Congress and has since referred to himself as an astronaut? And what about Bezos, who says he wants to try out his own Blue Origin spacecraft someday? Do you have to reach orbit to become an astronaut, or is simply crossing the boundary between Earth’s atmosphere and space enough to earn the title?

In the American consciousness, astronauts are seen as almost superhuman, with “the right stuff,” a secret-sauce set of qualities that distinguishes them from everyone else. The wealthy astronauts-to-be have promised they aren’t just going to look out the window; they will donate money from raffles and auctions and help do research on the ISS. But if astronauts become synonymous with billionaires, our lofty view of them is bound to come back down to Earth.

The definition of astronaut has always been a little complicated. In 1958, when NASA was brand-new, the agency wasn’t sure what to call the people it would soon send to space. Officials gathered for brainstorms, a process that involved consulting dictionaries and thesauri and scribbling ideas on a blackboard. “Somebody said ‘spaceman’ and someone else said ‘superman’ and still another said ‘space pilot,’” wrote Allen Gamble, a NASA psychologist, in an essay in 1971. The group liked Mercury, for the mythological messenger of the gods, but it turned out that NASA headquarters had already claimed it as the name of the country’s first spaceflight effort. They considered aeronaut, the term for hot-air ballooners and other high-flyers, before settling on astronaut, which first appeared in science-fiction literature.

NASA’s early astronauts were military test pilots. After a few moon landings, the agency started flying scientists alongside them. In the 1980s, with the Apollo days over and the era of the space shuttle just beginning, NASA introduced two new kinds of astronauts: mission specialists, astronauts who performed experiments and spacewalks but who weren’t trained to steer the ship, and payload specialists, who were chosen from academia or industry to conduct specific research in space and received far less training than the other classes. At first, some astronauts bristled at these new categories. “There was a reluctance to see them as full-fledged astronauts,” Alan Ladwig, a former NASA program manager and the author of See You In Orbit? Our Dream of Spaceflight, told me. But they went along with it and smiled for the cameras, reserving their opinions about the politicians who wanted to try it out, and fretting privately about the teacher who was picked as the first “ordinary citizen” to go.

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The U.S. space shuttles stopped flying a decade ago, grounded by cost and safety concerns, and NASA astronauts can now reach orbit on SpaceX vehicles. Though NASA helped bankroll the SpaceX program, the agency buys seats as other customers would. SpaceX’s private passengers will undergo considerable training, including head-spinning centrifuge tests, and can even take camping trips together to build camaraderie and teamwork. The flyers going all the way to the ISS will receive additional training from NASA on how to conduct research on the space station. Blue Origin’s passengers will spend three days prepping for their jaunt into space. Virgin Galactic, the space company owned by the billionaire Richard Branson, plans to offer three days of training for its own flights to the edge of space. But when these people return to Earth, will they be newly minted astronauts?

Over the years, some professional astronauts have felt that private citizens have jumped the line to space, skipping the rigorous training of traditional spacefarers. Michael López-Alegría, a NASA astronaut who has flown four times, told me that he wasn’t initially keen about flying alongside the “space tourist” Anousheh Ansari, an Iranian American entrepreneur who paid an undisclosed amount to the Russian space agency for her ride to the ISS in 2006. But he changed his mind after working with her. “If you go to space, you’re an astronaut,” said López-Alegría, who works for Axiom, the private company that arranges spaceflights for SpaceX. He will accompany SpaceX passengers on their trip to the ISS next year.

The tricky thing, though, is that not everyone agrees on where space actually begins. On the ISS? You’re in space. But what about trips closer to home? NASA and other U.S. agencies say the space boundary is about 50 miles from Earth’s surface, but the International Astronautical Federation says the line is 62 miles up. Several Virgin Galactic employees, who surpassed 50 miles during test flights, have already been formally recognized by the Federal Aviation Administration as “commercial astronauts.” The Blue Origin vehicle scheduled to launch this summer is designed to take passengers beyond the 62-mile threshold.

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An expansion of the astronaut club could give the impression that space travel will soon become accessible for many more people, and that it is almost ordinary. It is not. When I visited Frenchie’s a couple of years ago, Camera, the owner, gave me an iced tea and a tour. He spoke animatedly about the parties he’d hosted with the astronauts, remembering the time one of them took him on a too-fast ride in his Corvette, and pointing out which one was a good singer. But his voice softened when we reached the group photos of the Challenger and Columbia crews, who lost their lives. Spaceflight was dangerous then, and it’s still dangerous now.

In a sense, America is on the precipice of a reality that NASA first considered more than 60 years ago, around the time officials had brainstormed formal names for its future spacefarers. Ladwig writes in his book that in 1958, the agency had prepared to circulate a job ad for “research-astronaut candidates” that listed some professions that might make prospective candidates a good fit for the work: pilot, certainly, but also submariner, arctic explorer, parachute jumper, mountain climber, and scuba diver. President Dwight Eisenhower didn’t like the idea and told NASA to just pick people from the military. The mountain climbers and scuba divers of this century have a shot, if they have the new “right stuff.” I asked Ladwig whether anyone who touches spaces, even for a few minutes, should count as an astronaut. “My own view,” he said, “is if somebody is going to pay $250,000, $500,000, $5 million to go into space, they can call themselves whatever they want.”