Apollo 1 was the scene of a tragic fire which killed all three astronauts and destroyed the command module. It would not be until a year had passed before the next manned mission was launched. For further information, see Apollo 1.
Apollo 9 successfully launched both the command/service module and the lunar module into Earth orbit, and marked for the first time that both modules were docked in space. For further information, see Apollo 9.
Apollo 13 was the next mission in the Apollo program. The motto for this mission, "Ex Luna, Scientia" ("From the Moon, knowledge"), was the inspiration for that of Starfleet Academy — "Ex Astris, Scientia" ("From the stars, knowledge"). (TNG: "The First Duty"; Star Trek Encyclopedia)
Apollo 13 was crewed by Jim Lovell, Jack Swigert, and Fred Haise. The spacecraft suffered a catastrophic explosion en route to Luna, forcing cancellation of the planned lunar landing and a perilous return journey to Earth. The lunar module served as a makeshift shelter until the astronauts landed safely on Earth. The motto itself was a modification of a motto first used by the United States Navy: "Ex scientia tridens" ("From knowledge, sea power"). For further information, see Apollo 13.
Apollo 14 landed in the Fra Mauro, the intended landing site of Apollo 13. Footage of Alan Shepard before the launch of Apollo 14 was in the opening credits of Star Trek: Enterprise. For further information, see Apollo 14.
Apollo 17 landed in the Taurus-Littrow. This was the last Apollo mission. For further information, see Apollo 17. The mission patch for the Apollo 17 mission was modified and used for the Charybdis mission patch in TNG: "The Royale".