A spaceship is moving between two distant stars at 0.932c. To someone in the ship, the distance between the two stars appears to be 26.9 light-years (ly). What is the distance between the stars in the rest frame of the stars?
A) 74.2 ly
B) 9.75 ly
C) 21.5 ly
D) 56.5 ly

Question

Quizplus · Accepted Answer

According to special relativity, distances appear to be shorter when observed from a fast-moving object's frame of reference. This effect is known as length contraction.

Let's denote the distance between the two stars in their rest frame as D. From the spaceship's frame of reference, the distance appears to be 26.9 ly. We can use the formula for length contraction to find the actual distance D:

D = 26.9 ly / sqrt(1 - v^2/c^2)

where v = 0.932c, the speed of the spaceship, and c is the speed of light.

Plugging in the values, we get:

D = 26.9 ly / sqrt(1 - (0.932c)^2/c^2) = 74.2 ly

Therefore, the distance between the stars in their rest frame is 74.2 ly, which corresponds to choice A).

A Spaceship Is Moving Between Two Distant Stars at 0