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
True mass True mass The term true mass is synonymous with the term mass, but is used in astronomy to differentiate the measured mass of a planet from the lower limit of mass usually obtained from radial velocity techniques. Methods used to determine the true mass of a planet include measuring the distance and period of one of its satellites, advanced astrometry techniques that use the motions of other planets in the same star system, combining radial velocity techniques with transit observations (which indicate very low orbital inclinations), and combining radial velocity techniques with stellar parallax measurements (which also determine orbital inclinations).