Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
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