1. The problem statement, all variables and given/known data A spaceship is approaching a planet at a speed v. Suddenly, the spaceship explodes and releases a sphere of photons traveling outward as seen in the spaceship frame. The explosion occurs in the planet frame when the spaceship is a distance L away from the planet. In the ship's frame, how far is it from the planet at the time of the explosion? 2. Relevant equations Lorentz transformations: x = [itex]\gamma[/itex](x' - vt) t = [itex]\gamma[/itex](t - vx/c^2) 3. The attempt at a solution I began by directly applying a Lorentz transformation: x = [itex]\gamma[/itex](-L - vt) = -[itex]\gamma[/itex]L This would mean that the planet is a distance [itex]\gamma[/itex]L from the planet in its own frame when it explodes. However, I recalled that to apply a Lorentz transformation, the origins of S' and S must coincide at time t = 0. I'm not quite sure how to apply this requirement to the problem, as the spaceship never reaches the planet. I imagined attaching a long pole to the spaceship such that at the time of explosion in the ship's frame, the end of the pole just reaches the planet (so that something coincides with the planet at time t = 0). Then I got even more confused because the pole reaching the planet and the rocket exploding occurs at different times in the planet frame. Could you guys help me with this problem? Also, is there a way that the Lorentz transformation can be generalized so that it is not necessary for the two coordinate systems to coincide at t = 0? Thanks!