The Falcon Heavy had been scheduled to lift off from the Kennedy Space Center on Wednesday but was delayed because of fierce winds in the upper atmosphere.
Minutes after launch, the two side cores dropped away and descended to make separate touchdowns at two landing zones on the Florida coast, not far from the launch pad.
Then, at around nine minutes after takeoff, the core booster landed on the "Of Course I Still Love You" droneship, which is stationed in the Atlantic Ocean. It was the first time the company had landed all three boosters for Falcon Heavy.
SpaceX's Crew Dragon capsule, atop a Falcon 9 rocket, cleared its first unmanned test flight in March ahead of its crewed mission planned for July, while the first unmanned test for Boeing's Starliner capsule is slated for August on ULA's Atlas 5 rocket.More news: Israeli Spacecraft Fails To Land On The Moon
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Because this was an upgraded version of the rocket with unproven changes, SpaceX chief executive Elon Musk cautioned in advance that things might go wrong. A standard Falcon Heavy launch costs $90 million, according to the company's website, compared to $62 million for the Falcon 9.
SpaceX has two operational rockets: the Falcon 9, which with 21 launches in 2018 dominates the USA market, and the Falcon Heavy, which as its name suggests is created to lift much heavier payloads into more distant orbits.
Until SpaceX came along, boosters were discarded in the ocean after satellite launches. The vehicle, which was carrying a space-suited mannequin nicknamed Starman, was vaulted into outer space and is expected to orbit the sun for the foreseeable future. It will include coverage of the landing attempts and satellite deploy.
The Falcon Heavy rocket exerts 5.1 million pounds of thrust - that of more than a dozen jetliners, SpaceX said.
Falcon Heavy carried a communications satellite forSaudi-based telecom firm Arabsat, which will beam internet and television services over Africa, Europe and the Middle East. The U.S. Air Force also chose Falcon Heavy for STP-2, its Space Test Program 2 mission.