Musk boasts the second generation satellites are an 'order of magnitude better' than the first generation of Starlink satellites.
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Starliner's arrival comes eight years after Boeing was first contracted by NASA to deliver a commercial spacecraft.
While the rocket capture was brief, Rocket Lab has claimed it was a 'monumental step forward' in helping the company make Electron a reusable launch vehicle.
US Vice President Kamala Harris has described the initiative as a step towards establishing "new international norm for responsible behavior in space".
The pair will share data to enhance Earth observation and help Australia build its sovereign space capability.