"The Naked Time" and the Enterprise being flung into the past was meant to be the first part of a two-part story. The second part was "Tomorrow Is Yesterday," eventually the 21st episode of the first season. In this story, the USS Enterprise is accidentally flung back to 1969. This episode developed the "slingshot" effect, in which the ship warps around the sun and uses that to break the "time barrier." In this story, the Enterprise is able to successfully erase its presence in the past by undoing the changes they made. In Season 2, Episode 26, "Assignment: Earth," The Enterprise is again in the past on what's supposed to be a "routine" observation mission. Instead, they help Gary Seven -- a mysterious human called a Watcher" -- prevent a nuclear detonation.

However, in the famous episode "City on the Edge of Forever," a crazed Doctor McCoy accidentally goes back in time through the "Guardian of Forever" gate and changes history. The USS Enterprise disappeared, but the away team on the planet did not. This was the first time that changes in the past were immediately reflected in the timeline, which is the de facto way time travel manifests in Star Trek.