Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took $5.78 y$ What is the speed of the spaceship,assuming the planets are at essentially at rest?

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Quizplus · Accepted Answer

The time dilation formula is $\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}$, where $\Delta t'$ is the time interval measured by the moving observer (5.78 years), $\Delta t$ is the time interval measured by the stationary observer (10.0 years), $v$ is the velocity of the moving observer, and $c$ is the speed of light. Rearranging for $v$, we get $v = c \sqrt{1 - (\Delta t'/\Delta t)^2}$. Substituting $\Delta t' = 5.78$ years and $\Delta t = 10.0$ years, we find $v \approx 0.816 c$.

Someone in Earth's Rest Frame Says That a Spaceship's Trip 5.78y5.78 y5.78y

Someone in Earth's Rest Frame Says That a Spaceship's Trip $5.78 y$