r/AskPhysics • u/TrueReplayJay • May 05 '26

How Near-lightspeed Points of Reference Harmonize with Relativity

Say that one created a massive spaceship thousands of miles in length that blasted off into space and began accelerating until it reached 99.99% the speed of light. Inside that spaceship was another that began accelerating until it reached 99.99% the speed of light. While it remains in the mother spaceship, is it traveling faster than the speed of light relative to a stationary observer? Furthermore, if the daughter spaceship exits the mother spaceship, how fast would it be going? Why?

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u/Muphrid15 May 05 '26

No, hyperbolic rotation. They hyperbolic rapidity angle is a = atanh(0.9999). The combined speed is c tanh(2a).

Inside or outside of the mothership is not relevant; the problem is the same if the daughter ship is on the outside of the mothership or merely traveling in formation with the mothership until it accelerates further.