Two stars are at rest relative to each other. A spaceship is moving between these two stars at 0.932c relative to each star. To someone in the ship, the distance between the two stars appears to be
26)4 light-years. What is the distance between the stars in their own rest frame?
A) 72.8 light-years
B) 55.4 light-years
C) 9.57 light-years
D) 21.1 light-years

Question

Quizplus · Accepted Answer

The correct answer is A because the distance between the stars in their own rest frame is given by the Lorentz transformation:$$L = L_0/\gamma$$where L is the distance in the moving frame, L_0 is the distance in the rest frame, and $\gamma$ is the Lorentz factor. In this case, $\gamma = 1/\sqrt{1 - v^2/c^2} = 1/\sqrt{1 - 0.932^2} = 2.294$. Therefore,$$L_0 = L\gamma = 26 	ext{ light-years} 	imes 2.294 = 59.6 	ext{ light-years}$$

Two Stars Are at Rest Relative to Each Other