Well you almost have it right but not quite Its like going over a hill To quote Chaiken It was as if the moonship were coasting up a hill one that became less and less steep as it went along About two days from now on the afternoon of December 23 Apollo 8 would reach the gentle crest of that hill the place where the earth s gravitational influence gave way to the moon s From then on it would begin falling toward its destination Chaiken p 95 All bodies in space have a gravitational field even an astronaut on an EVA has a gravitational field around them In this case the moon s gravitational influence becomes stronger and the earth s disappears even though the moon orbits the earth it s the moon s gravity that is having an effect on the spacecraft when it reaches a certain point in space Therefore it is correct to say that Apollo 8 was the first manned mission to leave the earth s influence