Escape velocity (Ve) is the velocity necessary to escape from the gravity of a body such as a planet or star, or group of bodies such as a galaxy. Something moving as fast or faster than escape velocity will escape. The escape velocity varies with position: if something is set on a trajectory away from a planet at escape velocity, it will slow, but after some slowing it will be at the escape velocity for its new current position. For a spherically-symmetric body distant from any other mass, the magnitude of the escape velocity (i.e., speed) depends only on the distance from the its center. Also, in such a case, the necessary speed does not depend upon the direction: the same speed will escape in any direction as long as its path does not intersect with the body itself, i.e., it must not "hit the ground" while on its way.
The defining characteristic of a black hole is that its gravity is so high that the escape velocity within a certain surrounding region exceeds the speed of light in a vacuum, and nothing can escape, not excepting EMR.
An object's escape velocity is that at which the kinetic energy of the object equals (or more precisely, counterbalances) its potential energy due to gravity of the body it is escaping. The velocity is easily calculated by equating the two, given the law of gravity.
Example escape velocities:
|escaping Earth from its surface||11.186 km/s|
|escaping the Moon from its surface||2.38 km/s|
|escaping Jupiter from its surface||60.2 km/s|
|escaping the Sun from its surface||617.5 km/s|
|escaping the solar system from 1 astronomical unit distance from the Sun||42.1 km/s|