rvanveshana.com
t = 0.00s
EarthLight Pulse (c = 1.0c)Classical Missile (u_class = 1.10c)Actual Relativistic Missile (u = 0.846c)S'Ship (v = 0.60c)

Live Telemetry & Summary

Observe the three moving elements. The classical missile position is a simple sum of velocity. Notice that if the classical sum exceeds $1.0c$, it speeds ahead of the light pulse. However, the actual relativistic missile lags behind the light pulse, respecting the speed limit of $c$!

Ship Speed relative to Earth (v):0.60 c
Missile Speed relative to Ship (u'):0.50 c
Galilean Speed Sum (Classical):1.10 c
Einstein Speed Sum (Actual):0.8462 c

Variable Adjuster

Ship Velocity (v)0.6c
00.95
Missile Velocity (u')0.5c
00.95

Relativistic Velocity Addition

VADD

In classical mechanics, velocities are simply additive. If a spaceship moving at 0.6c launches a missile forward at 0.5c, the classical speed of the missile relative to Earth would be 1.1c, exceeding the speed of light. Relativistic velocity addition accounts for spacetime contraction, guaranteeing that no object can exceed c.

u=u′+v1+u′vc2u = \frac{u' + v}{1 + \frac{u'v}{c^2}}

Whiteboard Solver Steps

Step 1

Classical Galilean Velocity Addition

In classical mechanics, velocities are simply added directly. If this exceeded 1.0c, it would violate relativity.

uclassical=u′+v=0.500c+0.600c=1.100cu_{classical} = u' + v = 0.500c + 0.600c = 1.100c
Step 2

Einstein Relativistic Velocity Addition

Relativistic velocity addition guarantees that the combined velocity never exceeds the speed of light c (1.0c).

u=u′+v1+u′vc2=0.500+0.6001+(0.500⋅0.600)=0.8462cu = \frac{u' + v}{1 + \frac{u'v}{c^2}} = \frac{0.500 + 0.600}{1 + (0.500 \cdot 0.600)} = 0.8462c