Daniel Terdiman/CNET

AUSTIN, Texas -- SpaceX and Tesla founder Elon Musk wowed a capacity SXSW crowd here today with the first public showing of a video of a rocket capable of blasting off and then returning safely and gently to the ground. And he later added he hopes to one day travel (perhaps one-way) to Mars.

The video of the company's Grasshopper rocket, filmed just about a day-and-a-half ago, demonstrates one of SpaceX's key propositions: That it can develop reusable rockets at a fraction of the cost of a traditional NASA mission, and that it can bring them back down with the ease of a helicopter.

According to a statement put out by SpaceX, the Grasshopper -- a vertical takeoff and vertical landing (VTVL) vehicle -- was able to "leap" to about 80.1 meters high, hovering there for about 34 seconds and then landing safely by using its closed loop thrust vector and throttle control, touching down more accurately than ever before. The company also said that the thrust to weight ratio of the vehicle was more than one, which it said was a key landing algorithm for SpaceX's Falcon 9.

This was the Grasshopper's fourth test flight, and in each case, it has gone a bit higher. Musk said that eventually, the tests will transition "all the way through hypersonic and back."

The chief idea behind SpaceX's work, of course, is that future space exploration needs to be much more cost efficient than it has been when run by governments, and that commercial companies like SpaceX can fundamentally change the approach used to launch vehicles into space.

During his talk, moderated by former Wired magazine editor Chris Anderson, Musk also discussed SpaceX's desire to build a new launch facility in Texas that would let the company carry out easterly launches. Currently, the company has facilities at Cape Canaveral in Florida, and at Vandenberg Air Force Base in California.

Musk said he's confident Texas lawmakers will approve the proposal, and that if they do, SpaceX could begin construction next year and start launches in Texas within two or three years.

Tesla and The New York Times

Musk, of course, was recently involved in a battle with The New York Times over the newspaper's review of the Tesla Model S. The reporter who wrote the review said the car's battery had died prematurely, likely due to frigid temperatures during a long trip on the East Coast. But Musk disputed the Times report, suggesting that the reporter had not followed instructions and that logs told a different story than what had been published.

Today at SXSW, Musk expanded on his many recent comments about the episode by saying that he felt the original Times piece was a case of "a low-grade ethics violation," but that the Times reporter was not out to intentionally mislead the public. Still, he said, the report was not written in "good faith."

Though it is known as a car company, Tesla may more accurately be called a battery technology company that happens to build cars. As such, Musk, who is Tesla's chief product officer, as well as its CEO, has a fair bit of knowledge about batteries. In the wake of a series of well-publicized problems plaguing the lithium-ion batteries on board Boeing 787 Dreamliners, Musk offered to help the aviation giant address those issues.

Today, he explained his thoughts -- that the planes' battery cells were too big, but didn't have enough space between them to avoid a "thermal cascade" spreading between them. Ideally, he said, 787s should feature smaller batteries with smaller gaps between the cells. He did note that Boeing had rebuffed his offers to help.

Mars

For a few minutes, Musk talked about his hopes that humanity may someday be able to leave the planet and make it to Mars. For one thing, he said, being able to leave is vital because within 500 million to a billion years, our sun will expand and overheat the Earth, making it uninhabitable.

Musk explained that he would like to take part in a Mars mission -- and even stay there -- assuming that his companies could survive without him. Indeed, he noted that he's long said he wouldn't necessarily expect to return to Earth after such a mission. But he would want to know that the rocket technology was good enough to get him there safely. "I've said I want to die on Mars," he said. "Just not on impact."