Relativistic Velocity Addition

A ship races away from a station at a large fraction of the speed of light and fires a probe forward at another large fraction of light speed, measured in the ship's own frame. Simple Newtonian addition says just add the two speeds — but this simulator renders the real, relativistically correct trajectory alongside a "Newtonian ghost" computed the naive way, so you can watch the ghost visibly threaten to outrun an expanding pulse of light while the true probe never can. Two sliders control the ship's speed and the probe's launch speed, live readouts compare the Newtonian sum against Einstein's u = (v+u′)/(1+vu′/c²), and a station-time clock and light-front gap track how the discrepancy grows as both speeds climb toward c.