During a stop on Jupiter's satellite Europa to investigate a possible liquid ocean under the ice, you spot a spaceship passing Europa at 97% of the speed of light. While you see 2 s tick past on the spaceship's clock, how much time ticks by on your own clock?

Question

Quizplus · Accepted Answer

The time dilation effect, as described by the theory of relativity, indicates that time moves slower for objects moving at a significant fraction of the speed of light relative to an observer at rest. The formula to calculate the time observed in the stationary frame (Δt) when the time in the moving frame (Δt') and the velocity (v) are known is Δt = Δt' / sqrt(1 - v^2/c^2), where c is the speed of light. Given v = 0.97c and Δt' = 2 s, substituting these values into the formula yields a time dilation effect where more time passes in the stationary frame (on Europa) compared to the moving spaceship. This results in Δt being significantly greater than Δt', specifically 8.2 seconds, demonstrating the relativistic effect of time dilation at high velocities.

During a Stop on Jupiter's Satellite Europa to Investigate a Possible