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 $\text { 26.4 light-years. }$ What is the distance between the stars in their own rest frame?

Question

Quizplus · Accepted Answer

The phenomenon described is known as length contraction, which is a principle of special relativity. The formula for length contraction is $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the contracted length (the length observed by an observer moving relative to the object), $L_0$ is the proper length (the length of the object in its rest frame), $v$ is the velocity of the observer relative to the object, and $c$ is the speed of light. We are given $L = 26.4$ light-years and $v = 0.932c$, and we need to solve for $L_0$.Rearranging the formula to solve for $L_0$, we get $L_0 = L / \sqrt{1 - v^2/c^2}$.Plugging in the given values, $L_0 = 26.4 / \sqrt{1 - (0.932)^2}$.This calculation gives $L_0 \approx 72.8$ light-years, which means the distance between the stars in their own rest frame is approximately 72.8 light-years.

Two Stars Are at Rest Relative to Each Other 26.4 light-years. \text { 26.4 light-years. } 26.4 light-years.

Two Stars Are at Rest Relative to Each Other $\text { 26.4 light-years. }$