Escape velocity was the minimum velocity needed for a celestial body or other object to escape the gravitional attraction of another body.
This was one of the physical characteristics listed in a celestial body's file. It was measured in kilometer per seconds. (DIS: "The Sound of Thunder")
After an encounter with a black star in 2267 that sent the USS Enterprise back in time to 1969, warp engines became non-operational so Montgomery Scott overrode the automatic helm setting to hold the ship in orbit of Earth on impulse power. However, they were too low in the atmosphere to retain orbit but they did have sufficient impulse power to achieve escape velocity, though obtaining altitude was sluggish. (TOS: "Tomorrow is Yesterday")
Ockmenic 9 was stated in its file from the planetary catalog database to have an escape velocity of 11.18 kilometers per second. (LD: "The Stars At Night")