Variable-mass system the momentum of the system varies for Therefore, by Newton's second law Noting that u - v is the velocity of d"m" relative to "m", symbolized as v, this final equation can be arranged as In a system where mass is being ejected or ablated from a main body, the derivation is slightly different. At time "t", let a mass "m" travel at a velocity v, meaning the initial momentum of the system is Since the main body will be losing mass, d"m" will be negative, meaning that at a time "t" + d"t" the momentum of the system becomes
Mass in special relativity and the mass formula_27 perpendicular to the direction of motion (where formula_28 is the Lorentz factor, "v" is the relative velocity between the aether and the object, and "c" is the speed of light). Only when the force is perpendicular to the velocity, Lorentz's mass is equal to what is now called "relativistic mass". Max Abraham (1902) called formula_29 "longitudinal mass" and formula_30 "transverse mass" (although Abraham used more complicated expressions than Lorentz's relativistic ones). So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity. Also Albert Einstein