Proper velocity the traveling object. It equals the object's momentum p divided by its rest mass "m", and is made up of the space-like components of the object's four-vector velocity. William Shurcliff's monograph mentioned its early use in the Sears and Brehme text. Fraundorf has explored its pedagogical value while Ungar, Baylis and Hestenes have examined its relevance from group theory and geometric algebra perspectives. Proper velocity is sometimes referred to as celerity. Unlike the more familiar coordinate velocity v, proper velocity is synchrony-free (does not require synchronized clocks) and is useful for describing both super-relativistic and sub-relativistic motion. Like coordinate velocity
Chirp mass terms of other common mass parameters: where formula_7 is the total mass of the system, formula_8 is the reduced mass of the system, formula_9 is the mass ratio, and formula_10 is the symmetric mass ratio. In general relativity, the phase evolution of a binary orbit can be computed using a post-Newtonian expansion, a perturbative expansion in powers of the orbital velocity formula_11. The first order gravitational wave frequency, formula_12, evolution is described by the differential equation where formula_14 and formula_15 are the speed of light and Newton's gravitational constant, respectively. Integrating equation () with respect to time gives: where C