CAPE CANAVERAL, Fla. — A decade after Internet entrepreneur Elon Musk founded Space Exploration Technologies Corp. to cut the costs of reaching orbit, SpaceX flew its first paid mission to the international space station, reopening a U.S. supply line shut down when NASA retired its space shuttle fleet last year.

The SpaceX Dragon cargo capsule reached the $100 billion orbital outpost Oct. 10 following launch Oct. 7 from Cape Canaveral Air Force Station, Fla., aboard the Hawthorne, Calif.-based firm’s fourth Falcon 9 rocket. Like the practice mission in May, Dragon’s rendezvous and berthing at the station went smoothly.

“Looks like we’ve tamed the Dragon,” station commander Sunita Williams radioed to Mission Control at NASA’s Johnson Space Center in Houston after crewmate Akihiko Hoshide snared the capsule’s grapple fixture with the station’s 17.6-meter robotic crane.

The two spacecraft were flying 402 kilometers over the Pacific Ocean west of Baja California, Mexico. Williams later berthed the capsule to a docking port on the station’s Harmony module, where it was expected to remain for the next 2.5 weeks.

“It’s great to have the Dragon spacecraft on board the space station,” NASA’s space operations chief Bill Gerstenmaier said after the docking. “The control center team here and the team out at Hawthorne at SpaceX just did a phenomenal job of making a pretty complex ballet in space look pretty easy.”

NASA had built into its contract with SpaceX some insurance that Dragon would reach its intended orbit with propellant to spare. After one of the Falcon’s nine Merlin engines shut down early during ascent, that commitment kept an Orbcomm prototype communications satellite, flying as a secondary payload aboard the rocket, from reaching its intended orbit.

“For the protection of the space station mission, NASA had required that a restart of the upper-stage only occur if there was a very high probability (over 99%) of fully completing the second burn. While there was sufficient fuel on board to do so, the liquid oxygen on board was only enough to achieve a roughly 95% likelihood of completing the second burn, so Falcon 9 did not attempt a restart,” SpaceX spokeswoman Katherine Nelson wrote in an email to Space News.

SpaceX and NASA formed a joint postflight investigation board to investigate the anomaly, SpaceX announced Oct. 12.

SpaceX’s next launch, also for NASA, is scheduled for Jan. 18. The company is working under a 12-flight, $1.6 billion Cargo Resupply Services contract awarded in 2008 for the delivery of 20 metric tons of cargo to the space station through 2016. Orbital Sciences, the Dulles, Va.-based company preparing to debut its Cygnus cargo tug in early 2013, holds an eight-flight, $1.9 billion Cargo Resupply Services contract that also runs through 2016.

“With the way it looks, over the 12 flights we’ll be taking up and back about 60 metric tons,” SpaceX President Gwynne Shotwell told reporters after launch.

On its first haul, Dragon carried a relatively light load: 400 kilograms of food, clothing, science experiments and equipment for the space station including a low-temperature Glacier freezer for experiment samples.

While this mission took full advantage of Dragon’s 10-cubic-meter volume constraints, future missions are expected to make greater use of the spacecraft’s roughly 3,000-kilogram up-mass capacity.

Unlike the station’s Russian, European and Japanese freighters, Dragon is designed for round-trip flights, giving the station partners their first opportunity to bring back science experiments and unneeded equipment since the shuttles stopped flying last summer.

“[Dragon] has a great return capability,” said NASA’s lead space station scientist Julie Robinson. “It essentially replaces that capacity that we lost when the shuttle retired so that now we’ll be able to bring home a wide variety of biological samples, physical sciences samples and we’ll be able to bring home research equipment that we need to refurbish and then relaunch.”

A freezer will be coming back with Dragon, filled with medical and biological samples that have been stacking up on the station for more than year.

“We have three minus 85-degree freezers on board space station,” Gerstenmaier said. “We’ve not returned anything from those freezers since the shuttles quit flying last year, so they’re stocked full of really precious blood samples from the crew. There’s also biological samples in there, there’s also some plant samples.

“We’re going to take approximately one-third of the samples that have been stored in those freezers on orbit and return them here to Earth,” he said.

Dragon, which will be coming back with about 770 kilograms of cargo, is due to splash down Oct. 28 in the Pacific Ocean off the coast of California.

The station cargo flights for NASA comprise about 25 percent of SpaceX’s current launch manifest.