Question

Imagine an astronaut on a trip to Sirius, which lies 8 light-years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8-light-year distance be reconciled with the 6-year duration?

Answer 1

Answer on question #52482, Physics, Relativity

Question Imagine an astronaut on a trip to Sirius, which lies 8 light-years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8-light-year distance be reconciled with the 6-year duration?

Solution Time of trip measured from Earth is

$\frac{8}{0.8}=10\,yr$

Due to time dilation

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

(where $\delta t$ is time measured on Earth) time of trip, measure inside traveling ship is

$10\sqrt{1-0.8^{2}}=6\,yr$