This particular flight was not, by design, intended to make it all the way around the Earth. At 8:25 a.m. Central time, Starship — the biggest and most powerful rocket ever to fly — lifted off from the coast of South Texas. The ascent was smooth, with the upper Starship stage reaching orbital velocities. About 45 minutes after launch, it started re-entering the atmosphere, heading toward a belly-flop splashdown in the Indian Ocean.

Live video, conveyed in near real-time via SpaceX’s Starlink satellites, showed red-hot gases heating the underside of the vehicle. Then, 49 minutes after launch, communications with Starship ended, and SpaceX later said the vehicle had not survived the re-entry, presumably disintegrating and falling into the ocean.

Even so, Bill Nelson, the administrator of NASA, congratulated SpaceX on what he called a “successful test flight” of the system his agency is counting on for some of its Artemis lunar missions.

SpaceX aims to make both the vehicle’s lower rocket booster and the upper spacecraft stage capable of flying over and over again — a stark contrast to the single-launch throwaway rockets that have been used for most of the space age.

That reusability gives SpaceX the potential to drive down the cost of lofting satellites and telescopes, as well as people and the things they need to live in space.

Completing most of the short jaunt was a reassuring validation that the rocket’s design appears to be sound. Not only is Starship crucial for NASA’s lunar plans, it is the key to Mr. Musk’s pipe dream of sending people to live on Mars.

For Mr. Musk, the success also harks back to his earlier reputation as a technological visionary who led breakthrough advances at Tesla and SpaceX, a contrast with his troubled purchase of Twitter and the polarizing social media quagmire that has followed since he transformed the platform and renamed it X. Even as SpaceX launched its next-generation rocket, the social media company was dueling with Don Lemon, a former CNN anchor who was sharing clips from a combative interview with Mr. Musk.

SpaceX still needs to pull off a series of formidable rocketry firsts before Starship is ready to head to the moon and beyond. Earlier this week, Mr. Musk said he hoped for at least six more Starship flights this year, during which some of those experiments may occur.

But if it achieves them all, the company could again revolutionize the space transportation business and leave competitors far behind.

Phil Larson, a White House space adviser during the Obama administration who also previously worked on communication efforts at SpaceX, said Starship’s size and reusability had “massive potential to change the game in transportation to orbit. And it could enable whole new classes of missions.”

NASA is counting on Starship to serve as the lunar lander for Artemis III, a mission that will take astronauts to the surface of the moon for the first time in more than 50 years. That journey is currently scheduled for late 2026 but seems likely to slide to 2027 or later.

The third flight was a marked improvement from the first two launch attempts.

Last April, Starship made it off the launchpad, but a cascade of engine failures and fires in the booster led to the rocket’s destruction 24 miles above the Gulf of Mexico.

In November, the second Starship launch traveled much farther. All 33 engines in the Super Heavy booster worked properly during ascent, and after a successful separation, the upper Starship stage nearly made it to orbital velocities. However, both stages ended up exploding.

Nonetheless, Mr. Musk hailed both test flights as successes, as they provided data that helped engineers improve the design.

Thursday’s launch — which coincided with the 22nd anniversary of the founding of SpaceX — occurred 85 minutes into a 110-minute launch window. The 33 engines in the booster ignited at the launch site outside Brownsville, Texas, and lifted the rocket, which was as tall as a 40-story building, into the morning sky.

Most of the flight proceeded smoothly, and a number of test objectives were achieved during the flight, like opening and closing the spacecraft’s payload doors, which will be needed to deliver cargo in the future.

SpaceX did not attempt to recover the booster this time, but did have it perform engine burns that will be needed to return to the launch site. However, the final landing burn for the booster, conducted over the Gulf of Mexico, did not fully succeed — an area that SpaceX will attempt to fix for future flights.

SpaceX said the Super Heavy disintegrated at an altitude of about 1,500 feet.

SpaceX engineers will also have to figure out why Starship did not survive re-entry and make fixes to the design of the vehicle.

Even with the partial success of Thursday’s flight, Starship is far from ready to go to Mars, or even the moon. Because of Mr. Musk’s ambitions for Mars, Starship is much larger and much more complicated than what NASA needs for its Artemis moon landings. For Artemis III, two astronauts are to spend about a week in the South Pole region of the moon.

“He had the low price,” Daniel Dumbacher, the executive director of the American Institute of Aeronautics and Astronautics and a former high-level official at NASA, said of Mr. Musk, “and NASA chose to take the risk associated with that configuration hoping that it would work out. And we’ll see if that turns out to be true.”

To leave Earth’s orbit, Starship must have its propellant tanks refilled with liquid methane and liquid oxygen. That will require a complex choreography of additional Starship launches to take the propellants to orbit.

“This is a complicated, complicated problem, and there’s a lot that has to get sorted out, and a lot that has to work right,” Mr. Dumbacher said.

Thursday’s flight included an early test of that technology, moving liquid oxygen from one tank to another within Starship.

Mr. Dumbacher does not expect Starship to be ready by September 2026, the launch date NASA currently has for Artemis III, although he would not predict how much of a delay there might be. “I’m not going to give you a guess because there is way too much work, way too many problems to solve,” he said.