To calculate the time experienced by the passengers on a spacecraft traveling to Zeta Reticuli at 99% of the speed of light, time dilation formula is applied, resulting in 11.3 years passing for the passengers, demonstrating significant relativistic effects.
Step-by-step explanation:
The question involves calculating time dilation for passengers on a spacecraft traveling to the Zeta Reticuli star system and back. Time dilation is a consequence of Einstein's theory of special relativity, which tells us that time passes differently for observers in different inertial frames, especially when they are moving at speeds close to the speed of light.
To calculate the time experienced by passengers on the spacecraft, we use the time dilation formula:
t' = t / √(1 - v^2/c^2)
where:
t' is the time experienced by passengers on the spacecraft
t is the round-trip travel time as measured from Earth
v is the speed of the spacecraft (0.99c)
c is the speed of light
Plugging in the values:
t' = 79.8 years / √(1 - (0.99c)^2/c^2)
= 79.8 years / √(1 - 0.9801)
= 79.8 years / √0.0199
= 79.8 years / 0.141
=~ 11.3 years
Therefore, the answer is D) 11.3 years. This shows the significant impact of relativistic effects at high velocities near the speed of light.