CAPE CANAVERAL — SpaceX launched its first recycled rocket Thursday, the biggest leap yet in its bid to drive down costs and speed up flights. The Falcon 9 blasted off from Florida’s Kennedy Space Center, hoisting a broadcasting satellite into the early evening clear sky on the historic rocket reflight. SpaceX granted SES insight into the entire process of getting the booster ready to fly again, Halliwell said, providing confidence everything would go well. SpaceX began flying back the Falcon’s first-stage, kerosene-fueled boosters in 2015; it has landed eight, three at Cape Canaveral and five on ocean platforms. Blue Origin, an aerospace company started by another tech billionaire, Jeff Bezos, already has reflown a rocket. During the space shuttle program, the twin booster rockets dropped away two minutes into flight and parachuted into the Atlantic for recovery. SpaceX — which aims to launch up to six reused boosters this year — is familiar with uncharted territory. Besides becoming the first commercial cargo hauler to the International Space Station, SpaceX is building a capsule to launch NASA astronauts as soon as next year.