A day after Group Captain Shubhanshu Shukla became only the second Indian to travel to space, the Axiom-4 (Ax-4) mission he’s piloting is due to dock with the International Space Station (ISS).

Ax-4’s multi-country crew, led by former Nasa veteran Peggy Whitson and including Slawosz Uznanski-Wisniewski from Poland and Tibor Kapu from Hungary, will spend two weeks on the ISS.

The crew were seen floating in the spacecraft earlier on Thursday in a video shared by private firm Axiom Space on their way to the ISS.

The mission has generated a huge interest in India as it comes 41 years after cosmonaut Rakesh Sharma became the first Indian to fly to space aboard a Russian Soyuz in 1984.

Ax-4 – a commercial flight operated by Houston-based Axiom Space – lifted off from Nasa’s Kennedy Space Center in Florida at 02:31 EDT (06:31 GMT; 12:01 India time) on Wednesday. The docking on Thursday is due at 07:00EDT (11:00 GMT; 1630 India time).

The mission is a collaboration between Nasa, India’s space agency Isro, European Space Agency (Esa) and SpaceX. The two European astronauts will also be taking their countries back to space after more than four decades.

During their two-week mission, the crew would spend most of their time conducting 60 scientific experiments, including seven designed by Indian Space Research Organisation (Isro).

Isro, which has paid 5bn rupees ($59m; £43m) to secure a seat for Group Captain Shukla on Ax-4 and his training, says the hands-on experience he will gain during his trip to the ISS will help India in its human space flights.

Isro has said it wants to launch the country’s first-ever human space flight in 2027 and has announced ambitious plans to set up a space station by 2035 and send an astronaut to the Moon by 2040.

Earlier on Thursday, Axiom Space had a live uplink with the astronauts on board where Group Captain Shukla spoke about his first 24 hours in space.

“What a ride!,” he said, adding that it has been “an amazing feeling to be just floating in space” and that “it’s been fun time”.

“I was not feeling great when we got shot into vacuum, but I’m told I’ve been sleeping a lot, which is a great sign,” he said laughing.

“I’m enjoying the view, the experience and learning anew, like a baby, how to walk, to control yourself and to eat and read,” he added.

As Group Captain Shukla and other crew members spoke, Joy – a small, white toy swan described as Ax-4’s “fifth crew member” – floated in and out of vision.

Axiom has said Joy is “more than a cute companion for the Ax-4 crew” and is travelling to space as their “zero-G [zero-gravity] indicator”.

During Thursday’s broadcast, Group Captain Shukla said the baby swan “symbolises wisdom and ability to discern what is important and what is not” which made it “so important in this age of distractions”.

Soon after Wednesday’s launch, Commander Peggy Whitson revealed the name of their vehicle: Grace.

“Grace is more than a name,” she said. “It reflects the elegance with which we move through space against the backdrop of Earth. It speaks to the refinement of our mission, the harmony of science and spirit, and the unmerited favour we carry with humility.”

The name, she added, was a reminder “that spaceflight is not just a feat of engineering, but an act of goodwill – for the benefit of every human, everywhere”.