Escape velocity
Also called Escape speed
The speed at which the mechanical energy of a satellite and central-object system equals zero, so the satellite moves away until its speed reaches zero at an infinite distance. It equals the square root of 2GM/r and does not depend on the satellite's mass.
Both AP courses that cover it define this by energy, not by breaking free. AP Physics 1 EK 6.6.A.3 and AP Physics C: Mechanics EK 6.6.A.4 carry the same sentence: the escape velocity of a satellite is the satellite's velocity such that the mechanical energy of the satellite and central-object system is equal to zero.
Set with and the derived equation falls out:
Both CEDs label that a derived equation, and neither course prints it on its table of information. You are expected to reach it from conservation of energy rather than recall it.
Zero energy is the whole idea. The next essential knowledge statement (6.6.A.3.i in AP Physics 1, 6.6.A.4.i in C: Mechanics) says that when the only force exerted on a satellite is gravity from a central object, a satellite that reaches escape velocity will move away from the central body until its speed reaches zero at an infinite distance. It does not leave with speed to spare. It arrives at infinity with nothing left.
The satellite's mass never appears. It cancels on the way through, so a bolt and a probe need the same launch speed from the same radius.
Compare it with a circular orbit at the same radius. Orbital velocity is , so escape takes exactly times that speed, about 41 percent more.
Direction does not enter the calculation, because energy is a scalar. Any launch direction that clears the surface escapes at the same speed, which is why the quantity behaves like a speed even though the CED calls it a velocity.