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Chapter 33: Problem 15

Two stars are 50 ly apart, measured in their common rest frame. How far apart are they to a spaceship moving between them at \(0.75 c ?\)

Short Answer

Expert verified
The two stars appear to be approximately 33.54 light-years apart for a spaceship moving between them at \(0.75c\).

Step by step solution

01

Identify the given values

Firstly, we need to identify the values provided through the exercise. The rest length \(L_0\) is given as 50 light-years (ly), the relative velocity \(v\) is given as \(0.75c\), where \(c\) represents the speed of light.
02

Substituting the values into the Length Contraction Formula

Now, we insert the identified values into the length contraction formula. \(L = 50 \sqrt{1 - (0.75)^2}\).
03

Solving the equation

Then, the calculation is executed: \(L = 50 \sqrt{1 - 0.5625} = 50 \sqrt{0.4375}\). This evaluates to approximately \(L \approx 33.54\) light-years.

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