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In rocketry, what goes up usually comes down in pieces.

The cost of getting to orbit is exorbitant, because the rocket, with its multimillion-dollar engines, ends up as trash in the ocean after one launching.

Elon Musk, the chief executive of the Space Exploration Technologies Corp., better known as SpaceX, likens the waste to throwing away a 747 jet after a single transcontinental flight.

“Reusability is the critical breakthrough needed in rocketry to take things to the next level,” Musk said in October during a talk at the Massachusetts Institute of Technology.

On Tuesday, his company hopes to upend the economics of space travel.

At 6:20 a.m. Eastern time, one of SpaceX’s Falcon 9 rockets is scheduled to lift off from the Cape Canaveral Air Force Station in Florida on what is otherwise a routine unmanned cargo run to the International Space Station.

But this time, the company will attempt to land the first stage of the rocket intact on a barge floating in the Atlantic Ocean. After the booster falls away and the second stage continues pushing the payload to orbit, its engines will reignite to turn it around and guide it to a spot about 200 miles east of Jacksonville, Fla.

SpaceX has attempted similar maneuvers on three earlier Falcon 9 flights, and on the second and third attempts, the rocket slowed to a hover before splashing into the water.

“We’ve been able to soft-land the rocket booster in the ocean twice so far,” Musk said. “Unfortunately, it sort of sat there for several seconds, then tipped over and exploded. It’s quite difficult to reuse at that point.”

The first rocket stage, Musk noted, is as tall as a 14-story building. “When a 14-story building falls over, it’s quite a belly flop,” he said. “What we need to do is to be able to land on a floating platform.”

So SpaceX built a floating platform, 300 feet long and 170 feet wide, for the rocket stage to land on.

A new addition to the rocket is a set of “grid fins” that will fold out after separation to help steer the rocket toward the platform. No people will be aboard the barge during the landing attempt.

If SpaceX’s gamble succeeds, the company plans to reuse the rocket stage on a later flight.

Musk put the chances of success at 50 percent or less. But, he added, over the dozen or so flights scheduled for this year, “I think it’s quite likely, 80 to 90 percent likely, that one of those flights will be able to land and refly.”

Eventually, SpaceX would like to land the first stage back at the launch site.

A longer-term goal is to recover and reuse the second stage as well, and Musk has predicted that a fully reusable rocket could cut launch costs to a hundredth of what they are now.

This NASA cargo mission, SpaceX’s fifth, is carrying more than 5,000 pounds of supplies and equipment, including an IMAX movie camera, a laboratory habitat for studying fruit flies, and an instrument to measure the distribution of clouds as well as particles of dust, smoke and air pollution. After four weeks docked to the space station, the SpaceX cargo capsule will carry experiments, trash and other items back to Earth.

This flight is also attracting scrutiny, because Orbital Sciences Corp., the other company that NASA has hired to ferry cargo to the space station, suffered a catastrophic failure in October when its Antares rocket fell back to the ground moments after liftoff.

Among the items destroyed in the explosion were 18 student experiments, part of a program run by the National Center for Earth and Space Science Education.

Some of the students had traveled to the Orbital’s launching site in eastern Virginia and left crestfallen.

But Jeff Goldstein, the director of the center, and Nanoracks, the company that made arrangements for the experiments on the space station, were already working to juggle the manifests on future cargo flights.

Three weeks later, 17 of the 18 student teams had recreated their experiments and shipped them to Houston for NASA to add them to the SpaceX payload, then scheduled for launching on Dec. 19.

“It was nuts,” Goldstein said. “NASA moved heaven and earth for this.”

The 18th team, Goldstein said, decided to modify its experiment, requiring a new safety review.

The launching was subsequently postponed after a test firing of the Falcon 9’s nine engines was cut short. After a later successful test firing, the launch date was set for Tuesday.