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
Numerical model of the Solar System "a", "a") can be calculated from Newton's Law of Gravitation. Each body attracts each other body, the total acceleration being the sum of all these attractions. Next one chooses a small time-step Δ"t" and applies Newton's Second Law of Motion. The acceleration multiplied with Δ"t" gives a correction to the velocity. The velocity multiplied with Δ"t" gives a correction to the position. This procedure is repeated for all other bodies. The result is a new value for position and velocity for all bodies. Then, using these new values one starts over the whole calculation for the next time-step Δ"t". Repeating