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
Minimum mass bodies in extrasolar stellar and planetary systems, an inclination of 0° or 180° corresponds to a face-on orbit (which cannot be observed by radial velocity), whereas an inclination of 90° corresponds to an edge-on orbit (for which the true mass equals the minimum mass). Minimum mass In astronomy, minimum mass is the lower-bound calculated mass of observed objects such as planets, stars and binary systems, nebulae, and black holes. Minimum mass is a widely cited statistic for extrasolar planets detected by the radial velocity method, and is determined using the binary mass function. This method reveals planets by measuring changes