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
Peculiar velocity example, in surveys of type Ia supernovae, peculiar velocities have a significant influence on measurements out to redshifts around 0.5, leading to errors of several percent when calculating cosmological parameters. Peculiar velocities can also contain useful information about the universe. The connection between correlated peculiar velocities and mass distribution has been suggested as a tool for determining constraints for cosmological parameters using peculiar velocity surveys. Peculiar velocity Peculiar motion or peculiar velocity refers to the velocity of an object relative to a rest frame — usually a frame in which the average velocity of some objects is zero. In galactic