Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
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