Two stars are at rest relative to each other.In their common rest frame,these stars are 90.0 light-years apart.If they are measured to be $68.7 \text { light-years }$ apart by the navigator of a spaceship traveling between them,how fast is the spaceship moving relative to these stars?

Question

Quizplus · Accepted Answer

The length contraction formula is given by $L = L_0\sqrt{1 - \frac{v^2}{c^2}}$, where $L$ is the contracted length (68.7 light-years), $L_0$ is the proper length (90.0 light-years), and $v$ is the velocity of the spaceship. Rearranging the formula to solve for $v$, we get $v = c\sqrt{1 - \frac{L^2}{L_0^2}}$. Substituting the given values, we find $v = c\sqrt{1 - \frac{(68.7)^2}{(90.0)^2}}$, which calculates to approximately $0.646c$.

Two Stars Are at Rest Relative to Each Other 68.7 light-years 68.7 \text { light-years }68.7 light-years

Two Stars Are at Rest Relative to Each Other $68.7 \text { light-years }$