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
Binary mass function hole), the mass function becomes formula_33 and since formula_34 for formula_35, the mass function gives a lower limit on the mass of the unseen object 2. In general, for any formula_20 or formula_3, formula_38 In an orbit with eccentricity formula_39, the mass function is given by formula_40 If the accretor in an X-ray binary has a minimum mass that significantly exceeds the Tolman–Oppenheimer–Volkoff limit (the maximum possible mass for a neutron star), it is expected to be a black hole. This is the case in Cygnus X-1, for example, where the radial velocity of the companion star has been measured.