Question

You take a trip to a star located 1,000 light-years away and return. you travel at an average speed of 0.99c. hint: the time dilation formula is: t′=t1−(vc)2−−−−−−−−√. about how many years will pass on earth while you are gone?

Answer 1

Answer: 70712.44 ly

Using the following time dilation formula:

$t = \frac {t_o} {\sqrt{1- \frac {v^2}{c^2}}}$

where $t_o$ is the time measured in the moving frame, $v$ is the speed of the moving frame,  $c$ is the speed of light and $t$ is time measured in other frame.

Inserting the values:

$t = \frac {1000 ly} {\sqrt{1- \frac {(0.99c)^2}{c^2}}}\\ \Rightarrow t=\frac {1000 ly} {\sqrt{1-(0.99)^2}} \\ \Rightarrow t=\frac{1000ly}{0.0141}=70712.44 ly$

Therefore, when a trip to a star 1000 ly years away is made with speed 0.99 c, 70712.44 ly would have passed on Earth.