Musk said the landing appeared close to perfect and the company 'could not have asked for a better mission or a better day'
SpaceX employees broke into cheers and chants, some of them jumping up and down, following the smooth touchdown nine minutes after liftoff. Previous landing attempts ended in fiery blasts, but those aimed for an ocean platform.
Musk said he ran outside and heard the sonic boom of the returning booster just as it landed; he assumed it had exploded. He learned the happy truth when he went back into Launch Control and saw video of the standing rocket.
'I can't quite believe it,' he said. 'It's quite shocking.'
Several attempts to land the Falcon 9's first stage on a floating ocean platform have failed - with the rocket either colliding with the autonomous drone ship or tipping over.
But SpaceX has insisted that each attempt has helped engineers come closer to perfecting the technique.
The launch was due to take place yesterday, but the Musk tweeted ahead of the proposed launch time that a lift off tonight would increase the chances of a good landing by 10 per cent.
He wrote: 'Just reviewed mission [parameters with] SpaceX team. Monte Carlo runs show [tomorrow] night has a 10 per cent higher chance of a good landing.'
It is the first time the rocket has flown in the past six months following an explosion in June when carrying supplies to the ISS.
The firm had planned to launch its rocket on Saturday, but Musk similarly tweeted before the launch time to say the team had been faced with 'engineering challenges'.
The first stage of the SpaceX Falcon 9 rocket returns to land in a time exposure at Cape Canaveral Air Force Station, on the launcher's first mission since a June failure
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