Definition:Escape Velocity

Definition
Let a body be propelled vertically upwards from the surface of a planet

Let the body keep travelling away from the planet indefinitely.

Let resistance from the atmosphere of the planet be considered as negligible.

The smallest initial speed at which this is possible is known as the escape velocity of the planet.

Also see

 * Escape Velocity of Projectile fired Upwards: this value is shown to be $\sqrt {2 g R}$.