Speed of Light - Time it take to...

[Jimmy Ray]

If for example a star that you want to travel to is 28 million light years away. From the perspective of the people travelling on the ship, travelling at 99.99% the speed of light. Would it take 28 million light years to get there or a much shorted time. It would be 28 million years for those of us on earth not travelling though right? Thanks

[Janus]

For those in the ship the trip would take 395,967 years, compared to the 28 million years the trip would take fro those on the Earth.

[Klaynos]

But that's ignoreing acceleration completely...

[Neil9327]

For those in the ship the trip would take 395,967 years, compared to the 28 million years the trip would take fro those on the Earth.

 

That can't be right. Can it?

Surely the idea is that even from the perspective of those travelling you can't get to your destination in less time than the distance to the destination divided by c?

[Klaynos]

That can't be right. Can it?

Surely the idea is that even from the perspective of those travelling you can't get to your destination in less time than the distance to the destination divided by c?

 

It's because of time dilation, it's ignoreing the acceleration, I havn't done the maths so can't tell you whether that number is actually correct though...

[swansont]

And from the other perspective, length contraction. Those in the spaceship don't see the length as being 28 million light-years.

[Jimmy Ray]

Maybe I should have asked:

 

From the perspective of the people on the ship travelling at 99.99% the speed of light, in one year for them how many light years would they travel, also how many years would it have been for the people left on the earth.

 

I would really like to know the answer to this or even how you can figure this out for yourself.

[Klaynos]

Well in the simplest sence you can consider special relativity.

 

http://en.wikipedia.org/wiki/Special_relativity#Lorentz_contraction_and_time_dilation

 

But this does not take into account the acceleration the space craft would have to preform to get to that speed, which makes a very big difference according to general relativity.

[timo]

But this does not take into account the acceleration the space craft would have to preform to get to that speed, which makes a very big difference according to general relativity.

I cannot really understand what good it is to start talking about acceleration and GR here. It is not asked for and also does not really seem to add much interesting effects here (except for the nessecary breaking of the "either one could be the inertial reference system"-symmetry). Taking into account acceleration does not lead to any qualitative changes (the time experienced for the travellers will always be smaller than the time experienced for the people left behind) and in the limit of an arbitrarily strong acceleration you´ll also get the same quantitative result. This can be understood if you calculate the time tau experienced for the people in the rocket as [math] \tau = \int_{t_0}^{t_1} \gamma(t)^{-1} dt [/math] where t is the time coordinate in the system of the people left behind and gamma is the Gamov factor due to current velocity which always is >=1.

 

As a sidenote: I am not sure if there´s really an official definition saying that dealing with accelerating frames is GR. I´ve seen both: Statements saying that GR begins at the point at which you consider arbitrary coordinate systems (this includes dealing with acceleration and stands in contrast to the "normal" use of inertial coordiante systems only) and statements saying GR begins at the point where gravitity comes into play (the arbitrary coordinate trafos are a nessecary condition for dealing with it but both things are not completely equivalent).

[The Peon]

28 million light years would take you to a galaxy far far away, but more likely empty space....