Total time elapsed is =8.2y
The starting event is the astronaut leaving Earth. The finishing event is the astronaut arriving at the star system. The time between these events on Earth is:
Δt=3.9ly/0.9c
Δt=4.3y
For the astronaut, two events occur at the same position and can be measured with just one clock. Hence,
Δτ
Δτ
Δτ=1.8ly
The total elapsed time is:
T elapsed=Δt+3.9
T elapsed=4.3+3.9
T elapsed=8.2y
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