USS Enterprise slingshots around Sol
The slingshot effect, also known as the light-speed breakaway factor, is a method of time travel that requires a starship to travel at warp speed towards a star. As the ship approaches the star, it begins to travel back in time, using the gravitational field of the star, then breaking free the starship is sent forward or backward in time. It requires very precise calculations - variables include availability of fuel components, acceleration, and vessel mass through a time continuum.
This method was used by Captain Kirk and his crew of the USS Enterprise at least twice to return to the 23rd century after being hurtled back in time to 20th century Earth. (TOS: "Tomorrow is Yesterday", "Assignment: Earth")
Kirk and his crew applied the slingshot effect again in 2286, using a hijacked Klingon Bird-of-Prey to travel back to Earth in the latter half of the 20th century, although this subsequently drained the Bird-of-Prey of most of its power. There, they retrieved two humpback whales and brought them back to their own time so they could respond to an alien probe that was threatening Earth in the 23rd century. (Star Trek IV: The Voyage Home)
Further references
- TNG: "Time Squared"
Apocrypha
In the novel Engines of Destiny, Scotty acquires another Bird-of-Prey and attempts to use the slingshot effect to travel back in time and prevent Kirk's death on the USS Enterprise-B. The maneuver itself is successful, but as a result, a timeline is created where the Borg have assimilated Earth (without Kirk in the Nexus, Jean-Luc Picard either failed to stop Tolian Soran's attempt to return to the Nexus or died in the process, and thus, without Picard's unique insight into the hive mind, the Borg assimilated Earth when they went back in time in Star Trek: First Contact), and it requires the intervention of the USS Enterprise-D to undo Scotty's mistake and return Kirk to the Nexus.