Mass driver constrained by a limited amount of onboard spacecraft power. Thrust and momentum from exhaust, per unit mass expelled, scales up linearly with its velocity (momentum = mv), yet kinetic energy and energy input requirements scale up faster with velocity squared (kinetic energy = mv). Too low exhaust velocity would excessively increase propellant mass needed under the rocket equation, with too high a fraction of energy going into accelerating propellant not used yet. Higher exhaust velocity has both benefit and tradeoff, increasing propellant usage efficiency (more momentum per unit mass of propellant expelled) but decreasing thrust and the current rate of
Four-velocity are multiplied by the four-velocity, one then gets new physical four-vectors that have 4 independent components. For example: Effectively, the formula_27 factor combines with the Lorentz scalar term to make the 4th independent component Using the differential of the four-position, the magnitude of the four-velocity can be obtained: in short, the magnitude of the four-velocity for any object is always a fixed constant: The norm is also: so that: which reduces to the definition the Lorentz factor. Four-velocity In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic