It was a giant leap for the men on board too – like cosmonaut Valery Kubasov, the second pilot in the Soyuz crew.

“When we docked with Apollo, it was one of the most significant moments in history for Russia and the US,” Kubasov says. “Before, everything was secret, all the details of our space programs – every detail. With the Soyuz-Apollo project, we could finally pass that barrier.”

Valery still remembers all the details of that flight, from the technical side to the happy banter between Russian and American astronauts.

“We were showing the guys different cities and places in Russia, and when we were flying over the US, Vance D. Brand was showing us Florida. I remember, he said 'this is where all the pensioners go to live',” Kubasov recalls.

Thirty-five years on, most of those men will once again get the chance to meet and share memories of their historic link-up.

Aleksey Leonov, the Soyuz commander, is in the United States for the big day.

“The launch was during the height of the Cold War. So this project wasn't just of technical and scientific importance, it was also a great step towards cooperation between Russia and the US. There were no losers,” Leonov says.

There are plans for Aleksey and his Apollo counterpart, Thomas Stafford, to meet President Obama – but not until the friends have had a chance to catch up with each other.

“It was a very meaningful symbol to the people of the world – when we opened the hatch and Aleksey and I shook hands. That showed the world that the space race has ended in a way,” Thomas Stafford says.

The joint space project had a huge impact on both sides of the Atlantic – as it was a time when rocket launches captured millions of imaginations worldwide.

Dmitry Akinfeev was a teenager when he watched the Soyuz launch into the sky – and vividly remembers every emotion it stirred.

“I remember the day perfectly. I was in the 4th grade, and it was a huge celebration, not just for the school, but the entire city,” he recalls. “We got handed balloons, flags – and went to meet the cosmonauts. We were quite little, so of course, we couldn’t understand all the implications of this flight – but we felt the excitement. And then later on, we were all outside again to watch the actual launch. I remember my dad, who worked at the launch pad; he told me this was the most important event of the century.”

Thirty-five years later, the Apollo-Soyuz project still fires people's feelings, and some are even banking on it.

Both crews were equipped with special watches designed by Omega. Now the company has released a limited anniversary edition of the timepiece.