# Light hours special relativity time dilation

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1. Sep 21, 2016

1. The problem statement, all variables and given/known data
http://phy240.ahepl.org/Chp1-Relativity-Serway.pdf#page=39
#32
Planet R is 25 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. The clocks are synchronized at the beginning. What is the spacecraft's time (from their frame of reference)?

2. Relevant equations
Time dilation
{{math|Δ''t''}}:
:$\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$

3. The attempt at a solution

25/√[ 1 - ((20/c)/c)2] = 25

I think this is wrong because I don't know how to convert to speed without light. Also do I need to have everything in m/s?

Last edited: Sep 21, 2016
2. Sep 22, 2016

### Jonathan Scott

Firstly, you have a typo copying the question: the planet is 20 light hours away, not 25.
You need to express the speed only as a fraction of the speed of light, to get v/c and hence determine the time dilation factor. This question selects a very simple case.
You then need to think about which way round to use the time dilation formula. As a sanity check, the time shown by a clock on board the spacecraft will be running more slowly than the earth observer's time.