Space Exploration Technologies Corp.’s supply ship flew about 2.5 kilometers (1.6 miles) under the International Space Station and is on track to dock tomorrow, a government official said. “It’s been very, very successful up to this point,” Holly Ridings, flight director at the National Aeronautics and Space Administration, said today during a news briefing at Johnson Space Center in Houston, Texas. The company, known as SpaceX and founded by billionaire Elon Musk, will make history if it parks its unmanned vehicle at the station, becoming the first nongovernment entity to accomplish the feat. After the docking, scheduled for about 11:30 a.m. New York time tomorrow, astronauts would open the hatch and unload test cargo of more than 1,000 pounds of food, clothing and lab equipment. SpaceX launched its Falcon 9 rocket, carrying the Dragon capsule, at 3:44 a.m. on May 22 from Cape Canaveral, Florida, in its second attempt to send the vehicle to the space station. It called off a May 19 liftoff with a half second left in the countdown because of a faulty engine valve. “The significance of this day cannot be overstated,” NASA Administrator Charles Bolden said in a media briefing at Cape Canaveral following the launch. “We’re handing off to the private sector our transportation to the International Space Station so that NASA can focus on what we do best: Exploring even deeper into our solar system with missions to an asteroid and Mars on the horizon,” he said. Berthing involves “extreme precision,” Hawthorne, California-based SpaceX said in a press release last week. Both the ship and station will be traveling at about 17,500 miles per hour and orbiting Earth once every 90 minutes.