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
Velocity Moments image formula_14, and similarly for formula_20. formula_21 introduces velocity into the equation as where formula_23 is the formula_18 coordinate of the centre of mass for the previous image, formula_25, and again similarly for formula_20. After the Cartesian velocity moment is calculated, it can be normalised by where formula_28 is the average area of the object, in pixels, and formula_29 is the number of images. Now the value is not affected by the number of images in the sequence or the size of the object. As Cartesian moments are non-orthogonal, so are Cartesian velocity moments, so different moments can be closely