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I always had a question about relativity. Suppose an astronaut in orbit Saturn just must reach earth fast as possible.

Your ship can travel at any speed between 0 and the speed of light. the distance is 60 minutes in lightspeed. But if he travels near the 0.99c there will be an expansion of 8x time, which will make the travel last 8 hours.

If he travels at light speed, it will take all eternity to reach earth, so, he will "never" reach.. If he travels at 0c he will never reach either...

So, what is the best speed to get to the earth fast as possible?

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    $\begingroup$ You have got time-dilation the wrong way round. A journey of 60 minutes, as seen by an observer on Earth ( or Saturn ) will take 60 / 8 or 7.5 minutes for a traveller travelling at .99 c. $\endgroup$ – Arif Burhan Mar 27 '16 at 0:12
  • $\begingroup$ And how long (for the traveler point of view) will take at lightspeed (1c). will it be zero? $\endgroup$ – Daniel Santos Mar 27 '16 at 0:16
  • $\begingroup$ You can't reach $c$. $\endgroup$ – pfnuesel Mar 27 '16 at 0:39
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    $\begingroup$ Do you really believe that light from Saturn has never reached earth? $\endgroup$ – WillO Mar 27 '16 at 0:52
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    $\begingroup$ "What is the fas", can somebody please edit the title. $\endgroup$ – Conifold Mar 27 '16 at 3:13
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From an Earth-bound observer, it really doesn't differ much the time it takes to travel this distance with a velocity of C or 0.99C. If propagating with C takes him/her 60 minutes, (assuming you have calculated it correctly,) it is easy to see that 0.99C will take him/her 60 minutes and 36 seconds. (unlike what you have claimed.) However, from his/her own stand of point, lengths will be contracted (or internal clocks will be slowed compared to Earth clocks) and he/she will reach Earth in a shorter period of time. In particular, he/she will be there instantaneously (again unlike what you have claimed) if "sitting on a photon" (which is impossible) and about 7 times shorter than what it took him/her from the standpoint of an Earth-bound observer if travelling with 0.99C. (So instead of 60 minutes and 36 seconds, it will take him/her only 8 minutes and 33 seconds.)

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