The time elapsed in the earth will be 14.625 years.
To comprehend this, we first determine how long it took her to travel 6.5 light years, and then how long it took for the signal to arrive on Earth.
Time she takes to travel 6.5 light years:
0.8t = 6.5 ( because 1 light year = distance traveled by light in a year)
t = 6.5/0.8
t = 8.125 years
So, she travelled for 8.125 years.
The time it takes for the signal:
1.0 t = 6.5 ( because radio signals travel at the same speed of light)
t = 6.5/1.0
t = 6.5 years
Sum of these two gives us how much time elapsed on earth between the two mentioned events.
So,
8.125 + 6.5 = 14.625 years
So, the time elapsed on earth between the launch and the arrival of the first radio signal is 14.625 years.
Complete question:
An astronaut travels to a star system 6.5 ly away at a speed of 0.80c. Assume that the time needed to accelerate and decelerate is negligible. How much time elapses in earth between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?
Learn more about the time elapsed here:
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