escape velocity
The minimum speed needed to escape a gravitational field: v_esc = √(2GM/r). For Earth's surface, ~11.2 km/s.
Definition
Escape velocity is the speed at which a body's kinetic energy exactly equals the magnitude of its gravitational potential energy, giving zero total energy. At this speed, the body follows a parabolic trajectory and reaches infinity with zero residual speed. Any faster and it escapes on a hyperbola; any slower and it falls back.
Crucially, escape velocity depends only on the mass of the central body and the distance from its centre — not on the direction of launch or the mass of the escaping object. A bullet fired horizontally at 11.2 km/s from Earth's surface (ignoring air resistance) escapes just as surely as one fired straight up. For the Moon the escape velocity is 2.4 km/s; for Jupiter, 60 km/s; for the Sun's surface, 618 km/s. The concept extends to escaping the entire solar system: at Earth's orbit, the escape velocity from the Sun is about 42 km/s.