[litespeed (OP)]

THOUGHT EXPERIMENT

FIRST: We specify three places in space all in a straight line: 1) A destination exactly one light year from 2)The observation point of the experiment, and 3) A place sufficiently distant behind us that we can accelerate a vessel to a relativistic speed where we observe the travelers cesium clock exactly 1/2 the one we have as he passes us towards the destination.

We ask him to use celestial navigation to report his position from time to time. He will report he arrived at the destination in half the time predicted by the speed we observed as he passed.

From our point of view at possition B, how fast would the vessel need to go in order to achieve this time dialation of 50%..

[LeeE]

The Lorentz equation for working out time dilatation is actually very simple and is basically just pythagorus's right-angle triangle solution.  Because of this, you can actually solve it by trigonometry, and as you've chosen a value for the degree of time dilation of 50%, which corresponds to sin(30°), the solution is simply cos(30°) = 0.866 * 'c' = 86.6% of the speed of light.

[litespeed (OP)]

LeeE

Very helpful post. Now let me think. We see the astronaut travel the specified distance of one light year in about forteen months. However, the astronaut will report back to us he got he got there in about seven. During the flight he uses clestial navigation to report his progress. He notices he is exceeding the speed of light.

[LeeE]

When he tries out his celestial navigation skills by taking fixes on various stars he finds that their positions in relation to each other now suggest that that the universe has contracted and that he hasn't had to travel as far as he thought he would to get from where he started to where he ended up.

[ukmicky]

http://www.cthreepo.com/lab/math1.shtml

Scrool down for time dialation