A star system is 100 light-years away.If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?
A)4.1
B)17
C)1.0
D)1.3
E)2.4

Question

Quizplus · Accepted Answer

4.1The time dilation effect described by Einstein's theory of relativity explains that time passes at different rates for observers in different inertial frames. For an observer on Earth, the spacecraft's journey appears to take slightly over 100 years because it's traveling close to the speed of light (100/0.97 ≈ 103.1 years). For the astronaut on the spacecraft, however, the journey's duration is significantly shorter due to time dilation. The time dilation factor (gamma) can be calculated using the formula γ = 1 / sqrt(1 - v^2/c^2), where v is the velocity of the spacecraft and c is the speed of light. Plugging in 0.97c for v gives γ ≈ 4.1, meaning the astronaut experiences time at a rate 4.1 times slower than the observer on Earth. Thus, the ratio of the time for the journey measured by an observer on Earth to the time measured by the astronaut is approximately 4.1.

A Star System Is 100 Light-Years Away