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We're leaving our live coverage there - here's a recap of today's historic events:

Two astronauts from a SpaceX capsule in Earth's orbit carried out the world's first private spacewalk, tethered to the Crew Dragon spacecraft in the vacuum of space while two others watched from inside - more than 400 miles above Earth.

Billionaire Jared Isaacman then SpaceX engineer Sarah Gillis became the first two civilians to conduct such an excursion in space. All their manoeuvres were broadcast live on the company's website.

The mission appeared to successfully test equipment, including slim spacesuits and a process to fully depressurise the Crew Dragon cabin - technology that could be used in future private space missions.

It was one of the riskiest treks yet for Elon Musk's space company, the only private firm capable of routinely sending humans to and from Earth's orbit.

"Back at home we all have a lot of work to do, but from here, Earth sure looks like a perfect world," Mr Isaacman said after emerging from the spacecraft, silhouetted with the half-lit planet glittering 434.9 miles below him.

Before the spacewalk began, the capsule was completely depressurised, with all four crew members relying on their slim, SpaceX-developed spacesuits for oxygen, provided via an umbilical connection to Crew Dragon.

The spacewalk was scheduled to last only about 30 minutes, but the procedures to prepare for it and to finish it safely lasted an hour and 46 minutes. It marked a riAG百家乐在线官网 test of the new spacesuit designs and procedures for the capsule, among other things, in a mission meant to push the boundaries of what private companies can do in Earth's orbit.

By Thomas Moore, science correspondent

The first privately funded spacewalk was box-office from start to finish.

With the air sucked out of the Dragon capsule, and the hatch open to the void of space, we watched as the billionaire bankrolling the Polaris Dawn mission hauled himself outside to reveal planet Earth below.

This was never going to be a zero-gravity ballet on the outside of the capsule.

Jared Isaacman only stood by the door with the safety of handrails never far away and attached by an umbilical cable to his life support systems.

But this was still a significant moment. Up to now, only government-funded space agency astronauts have exited a space capsule. Now a commercial operator can do it too.

The whole purpose was to test new SpaceX suits that are being developed for private missions to the Moon and Mars.

So we saw Commander Isaacman twist, turn and move his arms, confirming that he had the mobility that will be needed to work in space.

And in these more enlightened times he was followed by SpaceX employee Sarah Gillis who performed the same checks, confirming that the suit was a good fit for women too.

It's a much slimmer suit than the puffed-up protective layers worn by astronauts when they venture outside the International Space Station.

And significantly, the SpaceX suit can be manufactured at scale. Elon Musk wants thousands made for all the privately funded astronauts he believes will be heading to Mars in the next few years.

The tests seemed to go well. But a spacewalk is riAG百家乐在线官网 and never more so when it's being done from a space capsule that wasn't designed to host one.

The Dragon was only ever meant to be depressurised to a vacuum in an emergency.

So we saw the crew make-do without the normal airlock, the double-doored chamber that seals the ISS from space when astronauts venture outside.

It added even more drama. Even the crew remaining inside, in their seats, had to wear the new suit to stay alive.

You can be sure SpaceX will want to do this again on a future mission.

Elon Musk has said the next generation of suit will be even better, with its own jetpack.

Now that really will be something to watch.

As we digest the events from the capsule more than 400 miles about the surface of the Earth, watch the dramatic moments Jared Isaacman stepped out into open space for the first of two historic spacewalks. 

With the repressurisation and leak tests now finished, the spacewalk - or extravehicular activity (EVA), as it is less catchily known - is now declared officially complete.

The crew will now carry out their various post-operation processes before getting out of their space suits and being able to move around the craft more freely.

The cabin atmosphere is "looking pretty good, very stable", mission control tells the crew, adding that their seats can now be rotated back to their previous positions.

While the mission has been completed successfully, there was at least one minor hitch along the way, science correspondent Thomas Moore points out.

"There was a moment when it was clear that the automatic door mechanism wasn't working properly, so they had to go for a manual opening," he said.

"And then Sarah Gillis was actually pointing at the seal of the door hatch itself.

"That would have been really dangerous and they would have had to change the whole course of the mission if there had been a problem."

In images that will be of some relief to everyone involved, the astronauts are seen back inside the capsule and safely in front of their screens.

Their visors are still up as they carry out a final leak check of the cabin.

The presenters on the SpaceX live feed are unsurprisingly impressed by the spectacle.

"That was really cool," says one.

On board the Dragon capsule, the cabin is being repressurised and crew members being checked. It will need to rise to around 9 PSI.

And just like that, they're both back inside the capsule and the hatch is closed!

"Pressure indicates good seal," mission control tells the astronauts, reassuringly.

In a reminder of the perils inherent in the mission, Ms Ellis is told to begin her return into the capsule - or "ingress" - and told she has what sounded like 5.9 minutes of oxygen supply remaining.

"Copy," she replies.

There is clearly no panic here though, it should be said, as mission control then asks her to check something else on her return into the capsule.

The second member of the crew, mission specialist Sarah Ellis, has exited the Dragon capsule - also accompanied by the customary whoops and cheers of celebration from the nerds back at mission control.

She has yet to offer any awed remarks on the dramatic nature of her surroundings, but did just say something was "pretty good" - although perhaps that was a reference to an element of the mobility tests she is carrying out.