I remember an exercise I had given to my students long time ago, where they computed that reaching a speed of 0.999999998 times the speed of light would allow to get to the center of our galaxy in less than 40 years. On Earth, this would have meant more than 60000 years ;)
The tricky part of the calculation is that the spacecraft cannot accelerate too quickly, without killing the people on board because of too many g's in their face. Therefore, you need to account for this. In principle, it takes a year to reach speeds close to the speed of light if the acceleration equals 1 g.
From there, the only problem can be the energy necessary to maintain an acceleration equal to 1g during a year.
oh yes, I remember Stephen hawking talk about this as well. Forgot to mention that part in the post. Thanks for pointing this out :)
I didn't know about Stephen Hawking mentioning this. But the exercise is very common in special relativity books. I have by far not invented it ;)
hehe sounds interesting. I would like to learn it too :D
The only reference I have is a book in French. I cannot find anything on the web. I may write a post on it next week, if you want. That is a funny topic :)