The crew of four started on Wednesday.
Four people, including the first Native American woman to travel to space and a Russian cosmonaut, were launched by SpaceX on a NASA mission to the International Space Station.
The arrival of the multinational crew is scheduled for Thursday.
There will be a six-month stay on the space station. A member of one of the Indian tribes, two NASA astronauts, a Japanese astronaut, a Russian cosmonaut, and a Japanese astronaut make up the crew.
At 4:57 p.m. ET on Thursday, the Dragon spacecraft is due to dock with the International Space Station, where it will be welcomed by astronauts already residing there.
Later this month, the previous crew of astronauts will return to Earth in their Dragon spacecraft, which has been attached to the space station ever since their arrival.