Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Mass driver velocity would rather be around 62.75% of total mission delta v if operating at constant specific impulse, except greater optimization could come from varying exhaust velocity during the mission profile (as possible with some thruster types, including mass drivers and variable specific impulse magnetoplasma rockets). Since a mass driver could use any type of mass for reaction mass to move the spacecraft, a mass driver or some variation seems ideal for deep-space vehicles that scavenge reaction mass from found resources. One possible drawback of the mass driver is that it has the potential to send solid reaction mass travelling at