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
Bussard ramjet to accelerate into the solar wind. However, in their calculations they assumed that: In the Zubrin/Andrews interplanetary ramjet design, they calculated that the drag force d/dt("mv") equals the mass of the scooped ions collected per second multiplied by the velocity of the scooped ions within the solar system relative to the ramscoop. The velocity of the (scooped) collected ions from the solar wind was assumed to be 500,000 m/s. The exhaust velocity of the ions when expelled by the ramjet was assumed not to exceed 100,000 m/s. The thrust of the ramjet d/dt("mv") was equal to the mass of ions