CAPE CANAVERAL, FLA.—Elon Musk’s SpaceX has launched a top-secret spy satellite for the U.S. government.

The unmanned Falcon 9 rocket lifted off Monday morning from its NASA-leased pad at Kennedy Space Center in Florida. It hoisted a classified satellite for the National Reconnaissance Office.

Several minutes into the flight, the first stage booster — its job done — aimed for a touchdown at Cape Canaveral Air Force Station. SpaceX strives to return most of its first-stage boosters for reuse.

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This was the fourth SpaceX booster landing at Cape Canaveral; even more have landed on an ocean platform. Sonic booms, as usual, rattled the area around the launch site.

“Launch and landing of the NRO spy satellite was good,” CEO Musk said on Twitter. “Tough call, as high altitude wind shear was at 98.6% of the theoretical load limit.”

Minutes before the launch, Musk had warned that “winds aloft are unusually high,” calling the conditions “worrying, but not a showstopper.”

The company’s first recycled rocket flew last month.

Sunday’s launch attempt was foiled at the last minute by a bad sensor.

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SpaceX’s Falcon 9 rocket won U.S. air force certification for national security space missions in May 2015, breaking a lock long-held by United Launch Alliance, a joint venture between Boeing Co. and Lockheed Martin Corp. Contracts for military launches include satellites that let troops communicate on battlefields and are estimated to be valued at about $70 billion through 2030.

SpaceX plans to fly 20 to 24 missions in 2017 for customers that include the National Aeronautics and Space Administration and commercial satellite operators. The Hawthorne, California-based company has contracts with NASA valued at $4.2 billion to resupply the International Space Station using an unmanned Dragon spacecraft and to ferry astronauts there with a version of Dragon that is capable of carrying crews.

— With files from Bloomberg

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