You are 20 years old and embark on a mission to a star system that is 200 light-years away. Your ship leaves Earth in 2013 and travels at 0.999c. You do not spend much time at the destination, just head back to Earth. What year is it when you arrive back on Earth? How old are you?
Hint: 0.999c = 299,700 km/s =22.4 seconds duration of one “tick” on a moving clock, as measured by an observer past whom the clock is moving
The Attempt at a Solution
I converted 200 light years into km = 1.89216 * 1015 km / 299,700 km/s = 6,313,513,514 seconds
6,313,513,514 seconds / 31,536,000seconds/year = 200.200 years
so it would be 2013 + 200.200 years = the year 2213 but my age would be 200.200/22.4 time dilation = 8.9375 + 20 (original age) = 29 years old.
Would that be correct? If not, can someone be so kind and explain to me how it's done? I find this theory very confusing. Thanks in advance!