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
Relaxation (physics) test star has velocity "v". As the star moves along its orbit, its motion will be randomly perturbed by the gravitational field of nearby stars. The relaxation time can be shown to be where "ρ" is the mean density, "m" is the test-star mass, "σ" is the 1d velocity dispersion of the field stars, and ln "Λ" is the Coulomb logarithm. Various events occur on timescales relating to the relaxation time, including core collapse, energy equipartition, and formation of a Bahcall-Wolf cusp around a supermassive black hole. Relaxation (physics) In the physical sciences, relaxation usually means the return of a