Until last week, only four entities had flown a space capsule to the International Space Station: the United States, Russia, Japan and the European Space Agency. Elon Musk is the fifth. Musk is the wealthy Internet entrepreneur we introduced you to last March who has vowed to revolutionize space exploration by bringing down the astronomical costs. Musk's company, called SpaceX, made history on Thursday when it became the first private company to make a roundtrip flight to the space station.

It's been hailed as the beginning of a new era of commercial space travel -- an era that can't get here fast enough for NASA, which retired the space shuttle last summer and now has to pay its old rival Russia to fly American astronauts into space. And Musk's ambition doesn't stop at the space station. He's one of the contenders vying for a NASA contract to build America's next manned spacecraft -- a contest he believes he has the right stuff to win.

When the final shuttle mission ended last July, for the first time in three decades, the United States had no way to launch astronauts into space. It was the end of one era and the beginning of another. Instead of NASA designing the next manned spacecraft, the White House decided that private industry should design, build and fly it -- opening space to commercial development. One of the companies vying for that contract is SpaceX. Elon Musk is the founder and CEO.

Scott Pelley: Is what we are experiencing, at this moment in time, the turning point in man's reach for space? Going from governments to private companies like yours?

Elon Musk: I think we're at the dawn of a new era and it's-- I think it's going to be very exciting. What we're hoping to do with Space X is to push the envelope and provide a reason for people to be excited and inspired to be human.

Musk is 40 years old, a naturalized American citizen, and reportedly worth nearly $2 billion. He isn't your typical corporate CEO. As a teenager, he wrote computer games in his native South Africa before immigrating to the U.S. - and to Silicon Valley where he was one of the most successful Internet entrepreneurs - the cofounder of PayPal.

Despite a chorus of skeptics, Musk built a car company called Tesla that turns out 5,000 high-end, all electric cars a year. Another Musk company sells solar power systems. But his lifelong passion is space. And when eBay bought PayPal in 2002, Musk started looking for ways to launch his new fortune into orbit.

Elon Musk: I went to Russia to look at buying a refurbished ICBM which is a very trippy experience. It was very bizarre. Yeah, when I tell people that-- they have to, like, what?

Musk made three trips to Russia trying to buy an intercontinental ballistic missile called the Dneiper. His plan was bizarre: put a greenhouse on the rocket, land it on Mars and beam back the pictures.

Elon Musk: It would get people really excited and that would recharge human space exploration. That was--

Scott Pelley: You just wanted to get people interested in space again?

Elon Musk: Yes. Yes.

Scott Pelley: Capture the imagination.

Elon Musk: Yes. That was the idea.

Turns out the Dneiper was so expensive his idea never flew. So, Musk decided that the only way to get an affordable rocket was to build it himself. And he started SpaceX.

Elon Musk: The odds of me coming into the rocket business, not knowing anything about rockets, not having ever built anything, I mean, I would have to be insane if I thought the odds are in my favor.

Scott Pelley: Why even begin?

Elon Musk: When something is important enough you do it even if the odds are not in your favor.

Scott Pelley: How much of your personal fortune have you poured into this?

Elon Musk: $100 million.

Scott Pelley: And $100 million into something that you did not believe would work at the beginning?

Elon Musk: Yes.

Musk truly believes - that low-cost space exploration is essential to the survival of mankind.

Elon Musk: I think it's important that humanity become a multi-planet species. I think most people would agree that a future where we are a space-faring civilization is inspiring and exciting compared with one where we are forever confined to Earth until some eventual extinction event. That's really why I started SpaceX.

SpaceX is housed in a sprawling factory near Los Angeles where fuselages for Boeing 747s used to be built. From its beginning -- 10 years ago -- its goal has been revolutionary change in rocket and spacecraft manufacturing.

Scott Pelley: Now tell me what's that big piece right up there?

Elon Musk: That's the second stage of a Falcon Nine rocket.

Instead of multiple companies building parts all across the country, SpaceX builds most of its rockets and spacecraft "in-house" - based on Musk's belief that it's more efficient and lowers costs. Fourteen-hundred engineers and skilled technicians work here --building engines, rockets, space capsules - creating, mostly from scratch, the thousands of components that are the guts of a rocket.

Elon Musk: So what that means is raw metal comes in and then we build the engines, the frame, the electronics and we integrate all of that together and that's all done more or less under one roof.

Scott Pelley: At SpaceX, metal comes in one end of this factory, spaceships come out the other?

Elon Musk: Yes.

Final assembly takes place at the Cape Canaveral launch pad.

[Elon Musk: If the margin is there and we don't have margin to the fourth power, then it's fine.]

Musk has college degrees in business and physics, but SpaceX is his first venture in aerospace. He bills himself as chief designer and chief technology officer.

Scott Pelley: How did you get the expertise to be the chief technology officer of a rocket ship company?

Elon Musk: Well, I do have a physics background. That's helpful as a foundation. And then I read a lot of books and talked to a lot of, a lot of smart people.

Scott Pelley: You're self-taught?

Elon Musk: Yeah. Well, I-- self-taught, yes, meaning I didn't, I don't have an aerospace degree.

Scott Pelley: So, how did you go about acquiring the knowledge?

Elon Musk: I read a lot of books, talked to a lot of people, and have a great team.

His "team" is a mixture: there are newcomers -- mostly 30-something engineers, some of them straight out of college -- and then there are the skilled technicians and aero space veterans. Former NASA astronaut Garrett Reisman spent three months aboard the space station and flew on one of the final shuttle missions. He was brought in to help oversee the company's manned space work.

Scott Pelley: You know, I'm curious. You have so much background in engineering, such a long and enviable career at NASA. You could have easily gotten a job at Boeing or at Lockheed, but you came here and I wonder why.

Garrett Reisman: If you had a chance to go back in time and work with Howard Hughes when he was creating TWA, if you had a chance to be there at that moment when it was the dawn of a brand new era, would-- wouldn't you want to do that? I mean, that's why I'm here.

And that's why most of the engineers we met are here. Building spaceships is the chance of a lifetime.

Scott Pelley: If you reach the point of having a successful manned flight, what will you have proven?

Kevin Brogan: We're not doing it to prove anything. You know, we know it can be done. I think, we're just trying to do it a little bit differently, a little bit faster, and to push the fence a little bit farther out.

Steve Davis: And--

Scott Pelley: And--

Steve Davis: And then we can all go-- I mean, I want to go into space. I assume most people here do as well. So, there's that as well.

Scott Pelley: How many want to ride? OK. Everybody wants to go--

Steve Davis: Caroline wants--

Caroline Conley: I-- I'm-- I'm not so sure.

Four years after starting, SpaceX rolled out its first rocket: an unmanned booster called the Falcon 1.

[Voice: Falcon has cleared the tower.]

But the first three test flights failed to reach orbit.

[Voice: We are hearing from the launch control center that there has been an anomaly on the vehicle.]

Scott Pelley: When you had that third failure in a row, did you think, "I need to pack this in"?

Elon Musk: Never.

Scott Pelley: Why not?

Elon Musk: I don't ever give up. I mean, I'd have to be dead or completely incapacitated.

It turned out that the third failure was caused by a two-second glitch in the timing. Eight weeks later, Musk bet the company on another flight.

[Voice: We have lift-off.]

And this time around, everything worked.

[Voice: Perfect]

Elon Musk: If that fourth launch hadn't worked, that would have been it. We would have not had the resources to mount a fifth.

Scott Pelley: You couldn't have gone on at that point?

ELON MUSK:

Yes. Death would have been, I think inevitable because we did not have the resources to mount a fifth launch."

Scott Pelley: This is a tricky business.

Elon Musk: Tricky. Yeah, the-- with-- yeah. I wish it wasn't so hard.

[Voice: M-VAC ignition confirmed. 3.2 kilometers per second]

In 2010, SpaceX tested a larger more powerful, nine-engine rocket called the Falcon 9 and an unmanned cargo capsule known as Dragon. It was the first privately developed rocket designed to carry cargo and eventually astronauts to the space station.

In its first test flight, the Dragon capsule performed flawlessly, orbiting the earth twice before splashdown in the Pacific -- the first time a private company had launched and recovered its own spacecraft.

Scott Pelley: And this is a historic spacecraft.

Elon Musk: It is, yeah.

We came across the Dragon capsule while Musk was showing us around.

Scott Pelley: You know, what I noticed about your cargo ship is that it has windows.

Elon Musk: The windows are there in case there's an astronaut onboard who wants to look up.

Scott Pelley: But people don't put windows in cargo ships.

Elon Musk: That's right. Exactly.

Scott Pelley: So what that tells me is that this was never intended to be only a cargo ship.

Elon Musk: No it-- no, the Dragon was always designed to carry astronauts.

Musk says that a manned version of the Dragon capsule will be safer than the space shuttle and a lot cheaper. Engineers are already designing escape rockets, life support equipment and computer guidance systems. They were studying seating for seven when we were there.

Scott Pelley: Do you believe that your rocket will be the next American rocket to take an astronaut into space?

Elon Musk: I believe that is the most likely outcome, yes.

That sort of confidence has not exactly endeared him to the space establishment or to his competitors.

Scott Pelley: There are people who've been in the rocketry business for decades who say about you that you don't know what you don't know.

Elon Musk: Well, if-- I suppose that's true of anyone. How can anyone know what they don't know?

Scott Pelley: But when critics say, "You can't do this," your answer to them is?

Elon Musk: We've done it.

He's done it -- in partnership with NASA -- which has given SpaceX technical advice and a contract worth up to $1.6 billion, mostly for 12 cargo flights to the space station. But SpaceX's lack of experience bothers some NASA legends like Apollo astronauts Neil Armstrong and Gene Cernan. They've testified to Congress that the Obama administration's drive to commercialize space could compromise safety and eventually cost the taxpayers.

[Gene Cernan: Now is the time to over rule this administration's pledge to mediocrity.]

Scott Pelley: You know, there are American heroes who don't like this idea?

Elon Musk: I--

Scott Pelley: Neil Armstrong--

Elon Musk: Yeah--

Scott Pelley: --Gene Cernan have both testified against commercial space flight and the way that you're developing it, and I wonder what you think of that.

Elon Musk: I was very sad to see that because those guys are-- yeah. You know, those guys are heroes of mine, so it's really tough. You know, I wish they would come and visit, and see the hard work that we're doing here. And I think that would change their mind.

Scott Pelley: They inspired you to do this, didn't they?

Elon Musk: Yes.

Scott Pelley: And to see them casting stones in your direction?

Elon Musk: Difficult.

Scott Pelley: Did you expect them to cheer you on?

Elon Musk: Certainly hoping they would.

Scott Pelley: What are you trying to prove to them?

Elon Musk: What I'm trying to do is to make a significant difference in space flight, and help make space flight accessible to almost anyone. And I would hope for as much support in that direction as we, as we can receive.

President Obama made his support clear when he visited SpaceX's launch site just before Falcon 9's first test flight. The rocket's third and most ambitious flight blasted off from Cape Canaveral 10 days ago, carrying a space capsule called "Dragon" loaded with cargo for a complicated rendezvous with the space station, moving 17,000-mph, 240 miles above the Earth. NASA controllers put the capsule through a series of maneuvers to guarantee that flight software was working and the capsule posed no threat to the multibillion dollar station before docking was finally allowed.

[Launch control: Looks like we got a dragon by the tail.]

The Dragon capsule was released last Thursday and splashed down safely in the Pacific off Baja California. If all goes well, SpaceX will begin routine cargo deliveries to the space station later this year. But the big prize is winning the NASA contract to build America's next manned spacecraft. And Elon Musk is facing stiff competition.

Elon Musk: I'm probably not the guy that most people would bet on. Usually--

Scott Pelley: Who wins?

Elon Musk: It's like a little kid fighting a bunch of sumo wrestlers. Usually, the sumo wrestlers win. We're a little scrappy company. Every now and again, the little scrappy company wins. And I think this'll be one of those times.