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# An astronaut travels to a star system 4.5 ly away at a speed of 0.9c. Assume that the time needed to accelerate and decelerate is negligible.a . How long does the journey take according to Mission Control on earth?b. How long does the journey take according to the astronaut?c. How much time elapses between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?

## a.) $\Delta t=5.0 y$b.) $\Delta \tau=2.2 y$c.) $T_{\text {elapsed }}=9.5 y$

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Let's do part gay. The starting event is the the Astronauts Living Earth. The finishing event is the astronaut arriving in the star system. The time between these events on Earth is Delta T is equal to 4.5 light ear, divided by 0.9 times the speed of light, which is equal to five on zero years. Now let's to part B, but not too events awkward the same position and can be measured with just one clock. Hence, of we have the time dilation relation, which is Delta Towel is adult times. The dialectic time equals Route one minus. We squared, divided by C squared times Delta T. Now let's substitute Values or Delta Tau equals route one minus 0.9 square multiply by 5.0 years. Therefore, Delta Tau is equal to 2.2 years. Now let's do part C. Well, the total elapsed time is so the total elapsed. So the total elapsed time is equal to Delta Deep Lis for find five years and right, so, uh, total elapsed time becomes 9.5 years

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