In order to attempt to understand relativity, I thought of the following 'paradox', which I hope to resolve mathematically. An astronomer makes a terrifying observation. An asteroid is on a crash course towards Earth at almost the speed of light. An ultra advanced nuclear rocket is launched to intercept and break up the asteroid before it is able to reach Earth. The rocket accelerates to almost the speed of light relative to Earth in the direction of the asteroid. Observers on Earth see the rocket destroy the asteroid at somewhere close to where the midpoint between where the rocket and the asteroid were when the rocket reached it's max velocity. The Earth is saved. To an observer on the Asteroid, the rocket, like the Earth, is already heading towards it at nearly the speed of light. The rocket is only able to gain an indiscernible amount of velocity relative to the Asteroid after it has been launched. The observer is unable to notice any difference in speed between the rocket and the Earth. Both the Earth and the rocket crash into it at nearly the same moment. The Earth is destroyed. Of course this cannot be what actually happens. How can you solve this problem mathematically? Say you use the following set of initial conditions: The Earth and the Rocket were converging at a speed S = C - 10^-(10^10) m/s. At the moment the Rocket was fired, they were 1 light year apart. For the sake of this problem say the Rocket were able to reach the same speed S (relative to Earth) in 1 second. Feel free to change the values to make the problem easier to solve.