Relativistic Projectile Now if spacecraft A fires a projectile at velocity Vp as measured in A's frame of reference, then the two relevant questions are: 1. How fast will an external observer see the projectile traveling? 2. How fast will B see the projectile approaching? This is an example of Einstein velocity addition.

Taking question #1 first, then in the standard form:



If v A = c and v P = c then u = c .

Note that for low velocities, this is the simple sum of the velocities of the firing spacecraft and the projectile as seen by that spacecraft.



Now to calculate the approach velocity as seen by the targeted spacecraft B:

If u(above) = c and v B = c then u' = c .

For low speeds, this expression yields a value equal to the sum of the magnitudes of the three velocities as indicated in the diagram. The Einstein velocity addition gaurantees that the resultant velocity does not exceed c, even if all three of the indicated velocities approach c!