"Space feels tantalizingly close now", Branson tweeted after Thursday's test flight.
The rocket went into a steep climb as the engine burned for 30 seconds and went supersonic, reaching Mach 1.87.
With the engine shut down, Unity coasted upward to an apogee of 84,271 feet (25,686 meters).
The company has not yet announced a date for the start of passenger flights but is selling tickets for a ride aboard SpaceShipTwo at $250,000 USA a seat.
Early Thursday morning, the company's SpaceShipTwo VSS Unity suborbital vehicle was launched mid-flight by White Knight Two, a larger plane. The company has not revealed how many more test flights are planned, or when tourist flights are likely to begin.More news: Chrissy Teigen Drops Her Biscuits at Cardi B's Suggestion of a Threesome
The firm praised pilots Mike Masucci and Nicola Pecile for the "great milestone test flight". Used to re-orient and slow the spacecraft for its descent back to a runway landing, the twin tail booms are supposed to be unlocked and rotated later in the SpaceShipTwo flight sequence. Both were employees of Scaled Composites, a Northrop Grumman subsidiary based in Mojave that built the vehicle.
The VSS Unity utilised the SpaceShipTwo spaceflight system which consists of WhiteKnightTwo, a custom-built, carrier aircraft, and SpaceShipTwo, the world's first passenger carrying spaceship to be built by a private company and be operated in commercial service. The space plane had previously performed seven unpowered glide flights and four "captive carry" tests, in which it remained attached to the mothership, which is known as VMS Eve.
After the rocket burn, Stucky and Mackay configured the tail booms into their feather position for descent, then lowered the feathering mechanism as the spacecraft dropped below 50,000 feet. For now, the company's engineers will be reviewing the valuable flight, motor, and performance data gleaned from the test flight.
A reusable space plane created to carry two pilots and up to six passengers (or research payloads) into suborbital space, the SS2 is Virgin Galactic's means for "transforming access to space", for paying customers and researchers, according to the company's vision statement. The company can now proceed with new phases, including full-duration rocket burns and powered flight. 'Another great test flight, another step closer to being NMReady'.