Escape velocity

In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically stated as an ideal speed, ignoring atmospheric friction. Although the term "escape velocity" is common, it is more accurately described as a speed than a velocity because it is independent of direction. The escape speed is independent of the mass of the escaping object, but increases with the mass of the primary body; it decreases with the distance from the primary body, thus taking into account how far the object has already traveled. Its calculation at a given distance means that no acceleration is further needed for the object to escape: it will slow down as it travels—due to the massive body's gravity—but it will never quite slow to a stop. On the other hand, an object already at escape speed needs slowing (negative acceleration) for it to be captured by the gravitational influence of the body. "Non-propelled" is important. As evidenced by Voyager program, an object starting even at zero speed from the ground can escape, if sufficiently accelerated. A rocket can escape without ever reaching escape speed, since its engines counteract gravity, continue to add kinetic energy, and thus reduce the needed speed. It can achieve escape at any speed, given sufficient propellant to provide new acceleration to the rocket to counter gravity's deceleration and thus maintain its speed. Any means to provide acceleration will do (gravity assist, solar sail, etc.). Likewise, hindrances like air drag are also considered propulsion (only, negative), so they are not part of the escape speed calculation, but are to be taken into account later in further calculation of trajectories. More generally, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero; an object which has achieved escape velocity is neither on the surface, nor in a closed orbit (of any radius).