Consider a spacecraft that travels round-trip to the zeta reticuli star system (distance 39.5 light-years) at 99% of the speed of light. If the round-trip travel time as measured from Earth is 79.8 years, how much time would pass for passengers on the spacecraft?
A) 39.9 years
B) 79.8 years
C) 22.6 years
D) 11.3 years

Question

Quizplus · Accepted Answer

The time dilation effect, as described by Einstein's theory of relativity, means that time passes more slowly for objects moving at a significant fraction of the speed of light compared to stationary observers. The formula for time dilation is $ t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} $, where $ t' $ is the time experienced by the moving object, $ t $ is the time measured by the stationary observer, $ v $ is the velocity of the moving object, and $ c $ is the speed of light. Plugging in the values ($ t = 79.8 $ years, $ v = 0.99c $), we find that the time experienced by the passengers is significantly less than the time measured on Earth, which calculates to approximately 11.3 years.

Consider a Spacecraft That Travels Round-Trip to the Zeta Reticuli