A test flight of Virgin Galactic's SpaceShipTwo is scheduled to launch from the Mojave Air and Space Port, north of Los Angeles.
Virgin Galactic officials said Thursday's spaceflight represents an incredible opportunity, not just for the company, but for the future in general.
Given the tragedy that struck in 2014 when the previous Virgin ship, the VSS Enterprise, crashed as a result of pilot error, the company warns that "there is no guarantee that everything will work perfectly first time".
"SpaceShipTwo, welcome to space", Virgin Galactic tweeted.
Virgin Galactic considers that altitude to be the threshold of space because it's defined that way by the Air Force and other US agencies, although others have long considered the boundary to be higher.
While critics point to Branson's unfulfilled space promises over the past decade, the maverick businessman told a TV interviewer in October that Virgin's first commercial space trip with him onboard would happen "in months and not years".
"Reusable vehicles built and operated by private companies are about to transform our business and personal lives in ways which are as yet hard to imagine".
It had reached space altitudes around 50 minutes after take-off, which the company's Twitter account acknowledged with a tweet which read: "SpaceShipTwo, welcome to space".More news: Russian nuclear-capable bomber aircraft fly to Venezuela, angering US
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Thursday's test flight carried two pilots, four NASA research payloads, and a mannequin named Annie as a stand-in passenger.
Virgin Galactic's SpaceShip Two is preparing for its next testing stage, and the likely event of it reaching space for the first time.
The company considers an altitude of 50 miles to be the boundary of space.
SpaceX and Northrop Grumman operate cargo ships that launch from the United States, toting supplies and food to the space station, but not people. Branson's goal: Open up space travel to more and more people.
Virgin Galactic has continued its incremental test programme and a third flight in July cracked Mach 2 as pilots kept the rocket burning for 42 seconds, powering through the stratosphere to an apogee of 170,800 feet.
More than 600 clients have already paid US$250,000 for a ticket.
"Commercial space has great potential for American economic and innovative leadership", Elwell said.
Musk, the billionaire CEO of electric carmaker Tesla, said the Big Falcon Rocket could conduct its first orbital flights in two to three years as part of his grand plan to shuttle passengers to the moon and eventually fly humans and cargo to Mars.