Calculation Needed for 50% Time Dialation

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Offline litespeed

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Calculation Needed for 50% Time Dialation
« on: 05/11/2009 19:21:20 »
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%..

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Offline LeeE

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Calculation Needed for 50% Time Dialation
« Reply #1 on: 06/11/2009 16:17:30 »
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.
...And its claws are as big as cups, and for some reason it's got a tremendous fear of stamps! And Mrs Doyle was telling me it's got magnets on its tail, so if you're made out of metal it can attach itself to you! And instead of a mouth it's got four arses!

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Offline litespeed

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Calculation Needed for 50% Time Dialation
« Reply #2 on: 06/11/2009 16:56:54 »
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.


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Offline LeeE

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Calculation Needed for 50% Time Dialation
« Reply #3 on: 07/11/2009 16:31:43 »
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.
...And its claws are as big as cups, and for some reason it's got a tremendous fear of stamps! And Mrs Doyle was telling me it's got magnets on its tail, so if you're made out of metal it can attach itself to you! And instead of a mouth it's got four arses!

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Offline ukmicky

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Calculation Needed for 50% Time Dialation
« Reply #4 on: 08/11/2009 15:33:20 »
http://www.cthreepo.com/lab/math1.shtml

Scrool down for time dialation