When does an astronaut travel from Earth to the Moon?

The trip isn't a straight line at constant speed. After reaching Earth orbit, the Saturn V's third stage performed trans-lunar injection, a burn that sent the spacecraft onto an elongated trajectory toward the Moon. From there the stack kept slowing under Earth's gravity, sped up again as it approached the Moon, and fired the service module's engine to be captured into lunar orbit. That profile took around 76 hours, just over three days, to cover an average distance of 384,400 km. Apollo 11 launched on July 16, 1969, and the lunar module touched down in the Sea of Tranquility on July 20.

The duration depends on how much energy you're willing to spend. The Soviet probe Luna 1 passed near the Moon in 1959 after about 34 hours of flight, on a fast trajectory with no braking. At the opposite extreme, missions that save propellant use gravity-assisted transfer orbits: the European probe SMART-1 used electric propulsion and took more than a year to spiral from Earth orbit to lunar orbit. Crewed flights can't afford that kind of slowness, because every added day means more oxygen, water, food, and radiation exposure.

Orion follows a logic similar to Apollo's, with transit times of several days each way. The difference is in the destination: instead of a low lunar orbit, the plan calls for a highly elliptical halo orbit, cheaper to reach and leave, where the Gateway station will be assembled. The return window and reentry geometry still shape, as they did then, the mission's entire schedule.