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
Variable-mass system on a body (F = 0) the variable-mass system motion equation reduces to If the velocity of the ejected propellant, v, is assumed have the opposite direction as the rocket's acceleration, dv/d"t", the scalar equivalent of this equation can be written as from which d"t" can be canceled out to give Integration by separation of variables gives By rearranging and letting Δ"v" = "v" - "v", one arrives at the standard form of the ideal rocket equation: where "m" is the initial total mass, including propellant, "m" is the final total mass, "v" is the effective exhaust velocity (often denoted