## Physics: Principles with Applications (7th Edition)

The value of $\gamma$ is $\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=1.15$. The space-dock personnel measure the dilated time interval of 1.0 s. This is always longer than the proper time. The proper time interval is shorter by a factor of $\gamma$, making it 0.87 s.