Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
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