A helicopter from a Chinese ship set down nearby, bringing in a crew to assess the landing situation.
The aircraft left but then returned to begin ferrying the first passengers out to an Australian ice-breaker.
Akademik Shokalskiy has been trapped since Christmas Eve. Its 22 crew are expected to remain on board once the 52 scientists and tourists have left.
The scientific mission ship was trapped by thick sheets of ice driven by strong winds, about 1,500 nautical miles south of Hobart – the capital of the Australian state of Tasmania.
The vessel is being used by the Australasian Antarctic Expedition to follow the route explorer Douglas Mawson travelled a century ago.
“The Chinese helicopter has arrived at the Shokalskiy. It’s 100% we’re off! A huge thanks to all,” expedition leader Chris Turney tweeted.
Chris Turney’s post showed a video of a red helicopter touching down on a site that had been marked out by the Akademik’s crew.
Members of the helicopter crew checked the site and the aircraft took off again.
Three hours later, Chris Turney tweeted: “The first of the helicopters to take us home. Thanks everyone!”
The Australian Maritime Safety Authority’s (AMSA) Rescue Co-ordination Centre, which is overseeing the operation, had earlier said it was unlikely the rescue would go ahead on Thursday as hoped because of the sea-ice conditions.
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