Slingshot effect

The Slingshot effect, also know as light-speed breakaway factor, is a method of time travel which involves flying around a gravity well at extreme velocities, the break away speed sending the ship backwards of forwards in time. A successful slingshot effects requires extremely precise calculations.

The first known example of this method was an accident when the USS Enterprise (NCC-1701) trying to break free from the gravity of the planet Psi 2000 was sent three days back in time. Later the same ship was sent much further back in time when it was dragged into the gravity well of a black star. After that the Enterprise purposefully used the technique to conduct historical research in the 1960s. (TOS episodes: The Naked Time, Tomorrow is Yesterday & Assignment: Earth)

The technique was used again 2286 to travel back in time to obtain a pair of humpback whales to satisfy a probe which was devastating 23rd century Earth looking for the then extinct species. (TOS movie: The Voyage Home)

The slingshot effect was used in 2364 when the Enterprise-D was caught in a gravimetric wave. The effect allowed the Enterprise to escape the wave and travel back in time to the source of the wave and destroy it. (TNG comic: History Lesson)