Respuesta :
Answer:
14.357 years
Explanation:
Total distance travelled is 10+10 ly = 20 ly
Time they stayed on the planet is 3 years
Total time from leaving to returning is 26 years
So, time they travelled is 26-3 = 23 years
Speed of light = c
Average speed
[tex]v=\frac{20}{23}c[/tex]
[tex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\\\Rightarrow \gamma=\frac{1}{\sqrt{1-\frac{\left (\frac{20}{23} \right)^2c^2}{c^2}}}\\\Rightarrow \gamma=\frac{1}{\sqrt{1-0.83^2}}\\\Rightarrow \gamma=2.025\ years[/tex]
So, elapsed time
[tex]\frac{23}{2.025}=11.357\ years[/tex]
Including 3 years stationary time we get
14.357 years
∴ Time elapsed on the astronauts' chronometers is 14.357 years
