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The webcast view was obscured by fog, making it difficult to see the vehicle's landing. Debris from the spacecraft was found scattered five miles away from its landing site.
The Starship was one in a series of prototypes for the heavy-lift rocket being developed by billionaire entrepreneur Elon Musk's private space company to carry humans and 100 tons of cargo on future missions to the moon and Mars.
The complete Starship rocket, which will stand 394 feet (120 metres) tall with its super-heavy first-stage booster included, is SpaceX's next-generation fully reusable launch vehicle - the center of Musk's ambitions to make human space travel more affordable and routine.
A first orbital Starship flight is planned for year's end. Musk, who also heads the electric carmaker Tesla Inc , has said he intends to fly Japanese billionaire Yusaku Maezawa around the moon in the Starship in 2023.
Starships SN8 and SN9 previously exploded upon landing during their test runs. SN10 achieved an upright landing earlier this month, but then went up in flames about eight minutes after touchdown.