After touching down, an emotional Shatner placed his hands on Bezos’s shoulders and told him “what you have given me is the most profound experience… I’m so filled with emotion about what just happened”.
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“I hope I never recover from this,” he added.
Before the launch, Shatner had admitted he was a “little frightened”.
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The 18-metre New Shepard rocket sent the quartet just above the internationally-recognised boundary of space known as the Karman Line, reaching about 66 miles (106km) above Earth.
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Shatner hugs Bezos as he emerges from space capsule
The reusable rocket detached from the capsule carrying the astronauts and fired its engines to land itself upright back on the launch pad.
Shatner experienced weightlessness on his trip before three parachutes delivered the capsule gently back to Earth, touching down in the desert at about 15mph.
Bezos opened the hatch as Shatner and the others stepped out to cheers and hugs from their families.
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Shatner and crew ring bell as they board capsule
The others on the flight were former NASA engineer Chris Boshuizen, clinical research entrepreneur Glen de Vries and Blue Origin vice president and engineer Audrey Powers.
The company tweeted that the rocked reached 2,235 mph (3,597 km/h) and the mission lasted 10 minutes and 17 seconds.
Blue Origin’s rocket system is called New Shepard, named after the Mercury astronaut Alan Shepard who was the first American to go into space.
The company aims to attract regular paying customers in future and had its maiden space tourism flight on 20 July, when Bezos and three others flew to the edge of space.
Other billionaires are also competing in the space race, notably Elon Musk’s SpaceX and Richard Branson’s Virgin Galactic.
Millions of Americans are voting in an historic election that could put Donald Trump back into the White House or make Kamala Harris the first woman to become US president.
The two candidates are neck and neck in the polls after bitter campaign that saw two assassination attempts against Republican Mr Trump as well as the shock withdrawal of President Joe Biden.
In around 100 days, Ms Harris has found her feet and mounted a fierce challenge to her opponent.
With just hours left before polls close, the election has come down to the wire and could be decided by a handful of crucial battleground states.
The first ballots cast on Tuesday mirrored the national divide. Overnight, the six registered voters in the tiny hamlet of Dixville Notch, New Hampshire, split their votes between the two candidates in voting just past midnight.
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Former President Mr Trump, 78, voted in Palm Beach, Florida, near his Mar-a-Lago club.
Wearing his trademark red “Make America Great Again” baseball cap, he said at the polling station that he was feeling “very confident”.
“I hear we’re doing very well,” he said. “It looks like Republicans have shown up in force.”
Elon Musk, the world’s richest man and Trump donor, said he will watch results unfold with the former president.
In the meantime, Ms Harris, the 60-year-old Democratic vice president, did radio interviews in the battleground states of Pennsylvania, Georgia and North Carolina.
What do the polls say?
Many polls are too tight to call and, with a large margin of error, most experts are refusing to predict the outcome.
Georgia could be among the first battleground to declare, with polls there closing at 7pm local time (midnight UK time). State election officials told Sky News they could have a result as early as 10pm (3am UK time).
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North Carolina could also give an early indication of how the vote is going.
Even so, it could be several days before the US has a definitive result.
An exit poll by conducted today by Sky News’ sister outlet NBC News and other US outlets suggests that democracy is the top issue on the minds of voters as they cast their ballots.
Some 35% of people said it was their most important issue, closely followed by the economy on 31% and with abortion ranked third at 14%.
Voters are not just selecting a president. A number of seats in the House of Representatives and the Senate are up for grabs. In addition, 10 states will hold abortion-related ballots, half of which would overturn existing restrictions.
Voters across 50 states are preparing to cast their ballots after a bitterly contested US election campaign, which will see Donald Trump or Kamala Harris become president.
In the last few hours, both candidates have been giving their final pitches. “The momentum is on our side,” Ms Harris told a crowd in Philadelphia that chanted back, “We will win”.
“Tonight, then, we finish as we started: with optimism, with energy, with joy,” she said, while enjoying the support of celebrity endorsements on the day from Katy Perry, Lady Gaga and Jon Bon Jovi.
In contrast, Mr Trump ended his campaign in Michigan, repeating key messages about the economy and immigration.
A handful of states will play a crucial role in determining the outcome of the election. Arizona, Georgia, Michigan, Nevada, North Carolina, Pennsylvania and Wisconsin hold the keys to the White House.
To become president, the winning candidate needs 270 electoral votes or more, with each state carrying a different number of votes.
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But the focus has been on Pennsylvania which carries 19 electoral votes, the most of all the swing states.
It has been a remarkable journey for both candidates – with Mr Trump surviving two assassination attempts and Ms Harris not even originally in the running.
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For more than a year, the 2024 presidential race seemed destined for a rematch between Joe Biden and Mr Trump – but a disastrous TV debate by Mr Biden eventually forced him to withdraw from the ticket.
The Democratic party’s decision to replace Mr Biden with his vice president transformed the race and shifted polls in Ms Harris’s favour. But only just.
Many polls are too tight to call and, with a large margin of error, most experts are refusing to predict the outcome.
Later, attention will turn to those battleground states including Georgia, which is among the first polls to close at 7pm local time (midnight UK time).
State election officials told Sky News they could have a result as early as 10pm (3am UK time).
Even so, it could be several days before the US has a definitive result.
Voters are not just selecting a president. In addition, 10 states will hold abortion-related ballots, half of which would overturn existing restrictions.
Predict who you think will win in each swing state and we’ll tell you who the president will be if you’re right.
Tonight, Sky News will have access to the most comprehensive exit poll and vote-counting results from every state, county and demographic across America through its US-partner network NBC.
You can find out more about Sky News’ coverage here.