Virgin Galactic sister firm called The Spaceship Company already was working on the second in a planned fleet of five vehicles when the accident occurred on Oct. 31, 2014.
For Unity and subsequent ships, Virgin will be handling manufacturing, testing and operations.
"Our first flight test was an emotional and fulfilling moment," Virgin Galactic said in a statement on Friday.
Many more test flights and much analysis are planned before passengers start flying.
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The six-passenger, two-pilot spaceships are carried into the air by a jet and released at an altitude of about 50,000 feet.
The spaceship's rocket engine then ignites to to catapult the vehicle beyond the atmosphere to an altitude of about 62 miles so passengers will be able to see the limb of Earth set against the blackness of space and experience a few minutes of microgravity. Gravity then pulls the ship back into the atmosphere so it can glide back to the runway and land like a conventional airplane.
For Thursday's test run, called a captive carry flight, Virgin pilots Mark Stucky and Dave Mackay flew aboard Unity. The WhiteKnightTwo carrier aircraft Eve was flown by pilots Mike Masucci and Todd Ericson and test engineer Wes Persall.
Photos: SpaceShipTwo Takes Flight