The craft blasted off to cheers from onlookers at 2:30 a.m. (0630 GMT) after a three-hour delay from the original launch time late Monday.
The boosters separated safely as the craft began its six-hour mission to deploy the satellites.
The two-side booster rockets returned safely to Earth, landing on adjacent Air Force landing pads, but the rocket’s center booster missed its mark, crashing in the Atlantic ocean.
Musk, who predicted trouble with landing the center booster on SpaceX’s drone ship in the Atlantic, said on Twitter early Tuesday, “It was a long shot.”
The mission, dubbed Space Test Program 2 (STP-2), is the third for the Falcon Heavy rocket, which SpaceX describes as the most powerful launch system in the world.
It was commissioned by the U.S. Department of Defense, the key contractor for commercial space companies such as SpaceX.
The company is putting satellites into orbit for agencies including NASA and the National Oceanic and Atmospheric Administration (NOAA), defense department laboratories, universities and a non-profit organization, SpaceX said.
The mission is one of the most challenging in SpaceX history, with four separate upper-stage engine burns and three separate orbits to deploy satellites, the company said on its website.
The payloads on the satellites Falcon Heavy is putting into orbit include an atomic clock NASA is testing for space navigation, another testing new telescope technologies, and a solar sail project part-funded by the Planetary Society, a non-profit organization headed by Bill Nye, “The Science Guy” on television presentations.
The LightSail is a crowdfunded project that aims to become the first spacecraft in earth orbit propelled solely by sunlight, the society, which has championed solar propulsion for decades, says on its website.
Falcon Heavy is the most powerful operational rocket in the world “by a factor of two,” SpaceX says on its website. It has the ability to lift into orbit nearly 64 metric tons (141,000 pounds) – more than a 737 jetliner loaded with passengers, crew, luggage and fuel.
Only the Saturn V moon rocket, last flown in 1973 from the same launch pad, delivered more payload to orbit, it says.