Unlimited Space Travel: Solving the Relativity Problem

[goldilocks]

Hello, I would very much appreciate some help getting started with the following problem. As I don't really know where to begin:

Show that for a space-ship to travel a distance, D, from Earth so that its “on-board” proper time elapses by, at most, T, the ship’s speed (relative to Earth) must be such that:

v > c/((1+((c^2*T^2)/D^2))^0.5)

Hence argue, in principle, that relativity imposes no limit to the distance that an astronaut can aspire to travel during his (finite) lifetime, provided his spaceship can reach speeds sufficiently close to c


Thank you very much! xxx :-)

 

[phyzguy]

Can you answer the following two questions:

(1) If the ship is traveling at velocity v in the Earth frame, how far will it travel in time T in the Earth frame?

(2) If the ship is traveling at velocity v in the Earth frame, how much slower does time pass in the ship's frame than the Earth frame?

If you can write down these two expressions, it should be simple to put them together to come up with the answer.