A spaceship travels at 0.80c from Earth to a star 10 light years distant, as measured in the Earth–star reference frame. Let event A be the ship’s departure from Earth and event B its arrival at the star.
(a) Find the distance and time between the two events in the Earth–star frame.
(b) Repeat for the ship’s frame. (The distance in the ship frame is the distance an observer has to move with respect to that frame to be at both events not the same as the Lorentz-contracted distance between Earth and star.)
(c) Compute the square of the spacetime interval in both frames to show explicitly that it’s invariant.