Formula: Relativistic Velocity Addition Velocity in system S    Relative velocity    Velocity in system S'    Speed of light

Formula: Relativistic Velocity Addition
Two Inertial Systems Move Relative to Each Other

Velocity in system S

We consider two intertial systems S and S'. Here \(u\) is the velocity of a body in the reference frame S at rest.

If, for example, two spaceships seen from the resting earth (system S'), each fly with 0.6-fold speed of light in opposite direction, then one spaceship (body) moves away with 0.88x speed of light from the view of the other spaceship (system S) and not, as one would expect classically with 1.2x speed of light: \begin{align} u &~=~ \frac{0.6\,c ~+~ 0.6\,c}{1 ~+~ \frac{ 0.6\,c ~\cdot~ 0.6\,c}{c^2}} \\\\ &~=~ \frac{1.2}{1 ~+~ 0.6 \cdot 0.6} \, c \\\\ &~=~ 0.88 \, c \end{align}

Relative velocity

Relative velocity of the systems S and S'.

Velocity in system S'

Velocity of a body in the reference frame S'.

Speed of light

Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum: $$ c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} } $$

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