Velocity quantity, momentum, is a vector and defined by In special relativity, the dimensionless Lorentz factor appears frequently, and is given by where γ is the Lorentz factor and "c" is the speed of light. Escape velocity is the minimum speed a ballistic object needs to escape from a massive body such as Earth. It represents the kinetic energy that, when added to the object's gravitational potential energy, (which is always negative) is equal to zero. The general formula for the escape velocity of an object at a distance "r" from the center of a planet with mass "M" is where
Velocity-addition formula for the perpendicular and parallel components can be cast in vector form as follows, a trick which also works for Lorentz transformations of other 3d physical quantities originally in set up standard configuration. Introduce the velocity vector in the unprimed frame and in the primed frame, and split them into components parallel ( ∥ ) and perpendicular (⊥) to the relative velocity vector (see hide box below) thus then with the usual Cartesian unit basis vectors , set the velocity in the unprimed frame to be which gives, using the results for the standard configuration, where · is the dot