## College Physics (4th Edition)

Let $\Delta t_0$ be the time measured on the Rolex. Let $T$ be the time measured at mission control. We can find the time measured on the Rolex: $T = \frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2}}}$ $\Delta t_0 = T~\sqrt{1-\frac{v^2}{c^2}}$ $\Delta t_0 = T~\sqrt{1-\frac{(2.0\times 10^8~m/s)^2}{(3.0\times 10^8~m/s)^2}}$ $\Delta t_0 = (12.0~h)~\sqrt{\frac{5}{9}}$ $\Delta t_0 = 8.9~hours$ The trip takes a time of 8.9 hours according to the Rolex.