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
Binary mass function An exoplanet causes its host star to move in a small orbit around the center of mass of the star-planet system. This 'wobble' can be observed if the radial velocity of the star is sufficiently high. This is the radial velocity method of detecting exoplanets. Using the mass function and the radial velocity of the host star, the minimum mass of an exoplanet can be determined. Applying this method on Proxima Centauri, the closest star to the solar system, led to the discovery of Proxima Centauri b, a terrestrial planet with a minimum mass of . Pulsar planets are planets