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 a single-lined spectroscopic binary if the radial motion of only one of the two binary components can be measured. In this case, a lower limit on the mass of the "other" (unseen) component can be determined. The true mass and true orbital velocity cannot be determined from the radial velocity because the orbital inclination is generally unknown. (The inclination is the orientation of the orbit from the point of view of the observer, and relates true and radial velocity.) This causes a degeneracy between mass and inclination. For example, if the measured radial velocity is low, this can mean that