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KENNEDY SPACE CENTER, Fla. — From the same pad where NASA launched rockets that carried astronauts to the moon, a big, new American rocket arced into space on Tuesday. But this time, NASA was not involved. The rocket, the Falcon Heavy, was built by SpaceX, the company founded and run by the billionaire entrepreneur Elon Musk.

“It seems surreal to me,” Mr. Musk said during a news conference after the launch.

The launch of this turbocharged version of the workhorse Falcon 9 rocket, which has been carrying cargo to space for years, marks an important milestone in spaceflight, the first time a rocket this powerful has been sent into space by a private company rather than a government space agency.

The rocket carried a playful payload: Mr. Musk’s red Roadster, an electric sports car built by his other company, Tesla. Strapped inside the car is a mannequin wearing one of SpaceX’s spacesuits. They are expected to orbit the sun for hundreds of millions of years.